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A comprehensive review on molecular dynamics simulations of forced convective heat transfer in nanochannels.

1. Introduction

2. fundamentals of the md simulation method in fcht-nc, 2.1. step 1: initial preparation, 2.1.1. selection of nanochannel wall and fluid materials, 2.1.2. construction of the initial simulation box, 2.1.3. determination of suitable potential energy functions, 2.2. step 2: geometry optimization, 2.3. step 3: equilibrium md (emd) simulation, 2.3.1. definition of ensembles, 2.3.2. definition of initial velocities, 2.4. step 4: non-equilibrium md (nemd) simulation, 2.4.1. flow creation, 2.4.2. heat generation.

• All-wall thermostat model (or cold-wall model): in this model, all nanochannel wall layers are selected as the region where the thermostat is applied to induce heat flux (see Figure 8 a).
• Partial-wall thermostat model (or thermal wall model): in this model, a small number of wall layers, called “temperature control layers,” which are sufficiently distant from the solid–fluid interface, are chosen as the region where a thermostat is applied. The next inner layers, called “thermal conductive layers,” interact freely with the neighboring atoms under an NVE ensemble (see Figure 8 b).

3. Analysis of the MD Simulation of FCHT-NC

3.1. basic governing equations, 3.2. overall heat transfer performance, 3.3. influencing parameters on fcht-nc, 3.3.1. effect of surface wettability, 3.3.2. effect of nanochannel wall material, 3.3.3. effect of surface coating, 3.3.4. effect of surface roughness, 3.3.5. effect of adding nanoparticles, 3.3.6. effect of channel height, 3.3.7. effect of fluid velocity, 3.3.8. effect of nanochannel wall temperature, 4. conclusions: challenges and future directions.

• While various water models such as SPC/E, TIP4P, and TIP4P/2005 are typically utilized to simulate the fluid domain, five-site water models like TIP5P-Ew are anticipated to provide more accurate representations for future research.
• Although Cu and Pt are frequently used as nanochannel wall materials mainly due to being practically applicable and simple, silicon, as a more commonly used material in practical applications, should receive greater attention.
• Generally, researchers apply the LJ 12–6 and EAM potentials to represent the interactions between solid-solid nanochannel wall atoms. On one hand, the common length and energy parameters in the LJ 12–6 potential for metallic solid wall materials cannot account for the strong bonding and thermal motion of metallic solid atoms. On the other hand, using the EAM potentials may require significant computational resources. Meanwhile, Heinz et al. [ 65 ] introduced parameters for the LJ 12–6 potentials, which would be effectively employable and an excellent alternative.
• In MD simulations of FCHT-NC using the Poiseuille flow model, two distinct arrangements for the forcing zone and temperature reset zone order, referred to as the “thermal pump method”, have been implemented: the Markvoort method and the Ge method. Although the Ge method has become the most common and demonstrates effective control of the inlet fluid temperature, it results in unrealistic axial heat conduction. Consequently, improvements to the Ge thermal pump method are essential for future studies.
• More studies are required to gain a comprehensive understanding of the complex relationship between the flowing fluid velocity and FCHT, particularly on nanostructured surfaces.
• Using more complex morphologies (such as random surface roughness [ 116 , 117 , 118 ]) instead of these simple morphologies would be more realistic. Furthermore, since researchers have recently focused on using nanoporous materials to improve microchannel performance (refer to Refs. [ 119 , 120 ], for example), it would be intriguing to investigate their impact on the FCHT-NC system’s performance.
• Recent studies indicate that adding nanoparticles into base fluids significantly improves the heat transfer efficiency. Future research should be carried out to explore commonly used nanoparticles like SiO 2 , CuO, TiO 2 , and Al 2 O 3 for an optimal heat transfer performance.
• Some research shows that raising the channel height can improve FCHT performance by lowering the Kapitza resistance. Others, however, show no significant effect or even negative impact. Therefore, conducting more research is necessary to comprehend the connection between the channel height and the FCHT efficiency.
• The fluid velocity in nanochannels can be regulated by external forces, with MD simulations showing speeds of ~3 to ~300 m/s. While some studies suggest that higher velocities do not enhance the FCHT-NC performance and may even hinder it, experimental evidence does not support these claims. Therefore, the relationship between fluid velocity and the FCHT efficiency in nanochannels remains uncertain and requires more study.

Author Contributions

Conflicts of interest.

• Zhang, X.; Ji, Z.; Wang, J.; Lv, X. Research progress on structural optimization design of microchannel heat sinks applied to electronic devices. Appl. Therm. Eng. 2023 , 235 , 121294. [ Google Scholar ] [ CrossRef ]
• Jana, K.K.; Srivastava, A.; Parkash, O.; Avasthi, D.K.; Rana, D.; Shahi, V.K.; Maiti, P. Nanoclay and swift heavy ions induced piezoelectric and conducting nanochannel based polymeric membrane for fuel cell. J. Power Sources 2016 , 301 , 338–347. [ Google Scholar ] [ CrossRef ]
• Bigham, A.; Hassanzadeh-Tabrizi, S.A.; Rafienia, M.; Salehi, H. Ordered mesoporous magnesium silicate with uniform nanochannels as a drug delivery system: The effect of calcination temperature on drug delivery rate. Ceram. Int. 2016 , 42 , 17185–17191. [ Google Scholar ] [ CrossRef ]
• Akbari, O.A.; Saghafian, M.; Shirani, E. Investigating the effect of obstacle presence on argon fluid flow characteristics in rough nanochannels using molecular dynamics method. J. Mol. Liq. 2023 , 386 , 122462. [ Google Scholar ] [ CrossRef ]
• Atofarati, E.O.; Sharifpur, M.; Meyer, J.P. Pulsating nanofluid-jet impingement cooling and its hydrodynamic effects on heat transfer. Int. J. Therm. Sci. 2024 , 198 , 108874. [ Google Scholar ] [ CrossRef ]
• Selimefendigil, F.; Ghachem, K.; Albalawi, H.; Alshammari, B.M.; Labidi, T.; Kolsi, L. Effects of using magnetic field and double jet impingement for cooling of a hot oscillating object. Case Stud. Therm. Eng. 2024 , 60 , 104791. [ Google Scholar ] [ CrossRef ]
• Forster, M.; Ligrani, P.; Weigand, B.; Poser, R. Experimental and numerical investigation of jet impingement cooling onto a rib roughened concave internal passage for leading edge cooling of a gas turbine blade. Int. J. Heat Mass Transf. 2024 , 227 , 125572. [ Google Scholar ] [ CrossRef ]
• Selimefendigil, F.; Benabdallah, F.; Ghachem, K.; Albalawi, H.; Alshammari, B.M.; Kolsi, L. Effects of using sinusoidal porous object (SPO) and perforated porous object (PPO) on the cooling performance of nano-enhanced multiple slot jet impingement for a conductive panel system. Propuls. Power Res. 2024 , 13 , 166–177. [ Google Scholar ] [ CrossRef ]
• Tian, J.; Li, B.; Wang, J.; Chen, B.; Zhou, Z.; Wang, H. Transient analysis of cryogenic cooling performance for high-power semiconductor lasers using flash-evaporation spray. Int. J. Heat Mass Transf. 2022 , 195 , 123216. [ Google Scholar ] [ CrossRef ]
• Tian, J.; He, C.; Chen, Y.; Wang, Z.; Zuo, Z.; Wang, J.; Chen, B.; Xiong, J. Experimental study on combined heat transfer enhancement due to macro-structured surface and electric field during electrospray cooling. Int. J. Heat Mass Transf. 2024 , 220 , 125015. [ Google Scholar ] [ CrossRef ]
• Qenawy, M.; Wang, J.; Tian, J.; Li, B.; Chen, B. Investigation of unsteady flow behavior of cryogen-spray coupled with cold air jet. Appl. Therm. Eng. 2023 , 235 , 121406. [ Google Scholar ] [ CrossRef ]
• Karimipour, A.; D’Orazio, A.; Shadloo, M.S. The effects of different nano particles of Al 2 O 3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Phys. Rev. E 2017 , 86 , 146–153. [ Google Scholar ] [ CrossRef ]
• Okechi, N.F. Stokes slip flow in a rough curved microchannel with transversely corrugated walls. Chin. J. Phys. 2022 , 78 , 495–510. [ Google Scholar ] [ CrossRef ]
• Nagayama, G.; Matsumoto, T.; Fukushima, K.; Tsuruta, T. Scale effect of slip boundary condition at solid-liquid interface. Sci. Rep. 2017 , 7 , 43125. [ Google Scholar ] [ CrossRef ]
• Dey, R.; Das, T.; Chakraborty, S. Frictional and heat transfer characteristics of single-phase microchannel liquid flows. Heat Transf. Eng. 2011 , 33 , 425–446. [ Google Scholar ] [ CrossRef ]
• Roy, P.; Anand, N.K.; Banerjee, D. Liquid slip and heat transfer in rotating rectangular microchannels. Int. J. Heat Mass Transf. 2013 , 62 , 184–199. [ Google Scholar ] [ CrossRef ]
• Liu, Y.; Liu, L.; Zhou, W.; Wei, J.A. Study of convective heat transfer by using the hybrid MD-FVM method. J. Mol. Liq. 2021 , 340 , 117178. [ Google Scholar ] [ CrossRef ]
• Kandlikar, S.G. Boiling and evaporation in microchannels. In Encyclopedia of Microfluidics and Nanofluidics , 1st ed.; Li, D., Ed.; Springer Science & Business Media: New York, NY, USA, 2008; pp. 158–159. [ Google Scholar ]
• Yao, S.; Wang, J.; Jin, S.; Tan, F.; Chen, S. Atomistic insights into the microscope mechanism of solid–liquid interaction influencing convective heat transfer of nanochannel. J. Mol. Liq. 2023 , 371 , 121105. [ Google Scholar ] [ CrossRef ]
• Thekkethala, J.F.; Sathian, S.P. The effect of graphene layers on interfacial thermal resistance in composite nanochannels with flow. Microfluid. Nanofluid. 2015 , 18 , 637–648. [ Google Scholar ] [ CrossRef ]
• Markvoort, A.J.; Hilbers, P.A.J. Molecular dynamics study of the influence of wall-gas interactions on heat flow in nanochannels. Phys. Rev. 2005 , 71 , 066702. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Yao, S.; Wang, J. Effect of rough morphology on the flow and heat transfer in nanochannel. In Proceedings of the International Conference on Applied Energy, Bangkok, Thailand, 1–10 December 2020. [ Google Scholar ]
• Yao, S.; Wang, J.; Liu, X. The influence of wall properties on convective heat transfer in isothermal nanochannel. J. Mol. Liq. 2021 , 324 , 115100. [ Google Scholar ] [ CrossRef ]
• Yao, S.; Wang, J.; Liu, X. Role of wall-fluid interaction and rough morphology in heat and momentum exchange in nanochannel. Appl. Energy 2021 , 298 , 117183. [ Google Scholar ] [ CrossRef ]
• Yao, S.; Wang, J.; Liu, X. Influence of nanostructure morphology on the heat transfer and flow characteristics in nanochannel. Int. J. Therm. Sci. 2021 , 165 , 106927. [ Google Scholar ] [ CrossRef ]
• Yao, S.; Wang, J.; Liu, X. The impacting mechanism of surface properties on flow and heat transfer features in nanochannel. Int. J. Heat Mass Transf. 2021 , 176 , 121441. [ Google Scholar ] [ CrossRef ]
• Yao, S.; Wang, J.; Jin, S.; Tan, F.; Chen, S. Effect of surface coupling characteristics on the flow and heat transfer of nanochannel based on the orthogonal test. Int. J. Therm. Sci. 2024 , 203 , 109161. [ Google Scholar ] [ CrossRef ]
• Yao, S.; Wang, J.; Liu, X. The Influencing mechanism of surface wettability on convective heat transfer in copper nanochannel. In Proceedings of the International Conference on Applied Energy, Bangkok, Thailand, 29 November–5 December 2021. [ Google Scholar ]
• Song, Z.; Cui, Z.; Cao, Q.; Lio, Y.; Li, J. Molecular dynamics study of convective heat transfer in ordered rough nanochannels. J. Mol. Liq. 2021 , 337 , 116052. [ Google Scholar ] [ CrossRef ]
• Song, Z.; Cui, Z.; Lio, Y.; Cao, Q. Heat transfer and flow characteristics in nanochannels with complex surface topological morphology. Appl. Therm. Eng. 2022 , 201 , 117755. [ Google Scholar ] [ CrossRef ]
• Song, Z.; Shang, X.; Cui, Z.; Lio, Y.; Cao, Q. Investigation of surface structure-wettability coupling on heat transfer and flow characteristics in nanochannels. Appl. Therm. Eng. 2023 , 218 , 119362. [ Google Scholar ] [ CrossRef ]
• Motlagh, M.B.; Kalteh, M. Molecular dynamics simulation of nanofluid convective heat transfer in a nanochannel: Effect of nanoparticles shape, aggregation and wall roughness. J. Mol. Liq. 2020 , 318 , 114028. [ Google Scholar ] [ CrossRef ]
• Motlagh, M.B.; Kalteh, M. Simulating the convective heat transfer of nanofluid Poiseuille flow in a nanochannel by molecular dynamics method. Int. Commun. Heat Mass Transf. 2020 , 111 , 104478. [ Google Scholar ] [ CrossRef ]
• Motlagh, M.B.; Kalteh, M. Investigating the wall effect on convective heat transfer in a nanochannel by molecular dynamics simulation. Int. J. Therm. Sci. 2020 , 156 , 106472. [ Google Scholar ] [ CrossRef ]
• Assadi, S.; Kalteh, M.; Motlagh, M.B. Investigating convective heat transfer coefficient of nanofluid Couette flow in a nanochannel by molecular dynamics simulation. Mol. Simul. 2022 , 48 , 702–711. [ Google Scholar ] [ CrossRef ]
• Chatterjee, S.; Paras, H.H.; Chakraborty, M.A. Review of nano and microscale heat transfer: An experimental and molecular dynamics perspective. Processes 2023 , 11 , 2769. [ Google Scholar ] [ CrossRef ]
• Ran, Y.; Bertola, V. Achievements and prospects of molecular dynamics simulations in thermofluid sciences. Energies 2024 , 17 , 888. [ Google Scholar ] [ CrossRef ]
• Kim, B.H.; Beskok, A.; Cagin, T. Viscous heating in nanoscale shear driven liquid flows. Microfluid. Nanofluid. 2010 , 9 , 31–40. [ Google Scholar ] [ CrossRef ]
• Bao, L.; Priezjev, N.V.; Hu, H.; Luo, K. Effects of viscous heating and wall-fluid interaction energy on rate-dependent slip behavior of simple fluids. Phys. Rev. E 2017 , 96 , 033110. [ Google Scholar ] [ CrossRef ]
• Dinh, Q.V.; Vo, T.Q.; Kim, B. Viscous heating and temperature profiles of liquid water flows in copper nanochannel. J. Mech. Sci. Technol. 2019 , 33 , 3257–3263. [ Google Scholar ] [ CrossRef ]
• AbdulHussein, W.A.; Abed, A.M.; Mohammad, D.B.; Smaisim, G.F.; Baghaei, S. Investigation of boiling process of different fluids in microchannels and nanochannels in the presence of external electric field and external magnetic field using molecular dynamics simulation. Case Stud. Therm. Eng. 2022 , 35 , 102105. [ Google Scholar ] [ CrossRef ]
• Wang, M.; Sun, H.; Cheng, L. Flow condensation heat transfer characteristics of nanochannels with nanopillars: A molecular dynamics study. Langmuir 2021 , 37 , 14744–14752. [ Google Scholar ] [ CrossRef ]
• Wang, M.; Sun, Q.; Yang, C.; Cheng, L. Molecular dynamics simulation of thermal de-icing on a nanochannel with hot fluids. J. Mol. Liq. 2022 , 354 , 118859. [ Google Scholar ] [ CrossRef ]
• Wang, M.; Sun, H.; Cheng, L. Enhanced heat transfer characteristics of nano heat exchanger with periodic fins: A molecular dynamics study. J. Mol. Liq. 2021 , 341 , 116908. [ Google Scholar ] [ CrossRef ]
• Sun, H.; Li, F.; Wang, M.; Xin, G.; Wang, X. Molecular dynamics study of convective heat transfer mechanism in a nano heat exchanger. RSC Adv. 2020 , 10 , 23097. [ Google Scholar ] [ CrossRef ]
• Rapaport, D.C. The Art of Molecular Dynamics Simulation , 1st ed.; Cambridge University Press: Cambridge, UK, 2004. [ Google Scholar ]
• Pal, S.; Ray, B.C. Molecular Dynamics Simulation of Nanostructured Materials: An Understanding of Mechanical Behavior , 1st ed.; Taylor & Francis Group: Abingdon, UK, 2020. [ Google Scholar ]
• Sadus, R.J. Molecular Simulation of Fluids: Theory, Algorithms, Object-Orientation , 1st ed.; Elsevier Science: Amsterdam, The Netherlands, 2023. [ Google Scholar ]
• Gonzalez, I.; Law, D. Effect of single nanoparticle diameter on a nanochannel fluid flow and heat transfer. In Proceedings of the ASME 2022 Fluids Engineering Division Summer Meeting, Toronto, ON, Canada, 3–5 August 2022. [ Google Scholar ]
• Tang, Y.; Fu, T.; Mao, Y.; Zhang, Y.; Yuan, W. Molecule dynamics simulation of heat transfer between argon flow and parallel copper plates. J. Nanotechnol. Eng. Med. 2014 , 5 , 034501. [ Google Scholar ] [ CrossRef ]
• Guillot, B.A. Reappraisal of what we have learnt during three decades of computer simulations on water. J. Mol. Liq. 2002 , 101 , 219–260. [ Google Scholar ] [ CrossRef ]
• Kargar, S.; Baniamerian, Z.; Moran, J.L. Molecular dynamics calculations of the enthalpy of vaporization for different water models. J. Mol. Liq. 2024 , 393 , 123455. [ Google Scholar ] [ CrossRef ]
• Berendsen, H.J.C.; Grigera, J.R.; Straatsma, T.P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987 , 91 , 6269–6271. [ Google Scholar ] [ CrossRef ]
• Jorgensen, W.L.; Chandrasekhar, J.; Madura, J.D.; Impey, R.W.; Klein, M.L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983 , 79 , 926–935. [ Google Scholar ] [ CrossRef ]
• Abascal, J.L.F.; Vega, C.A. General purpose model for the condensed phases of water: TIP4P/2005. J. Chem. Phys. 2005 , 123 , 234505. [ Google Scholar ] [ CrossRef ]
• Cui, W.; Shen, Z.; Yang, J.; Wu, S. Flow and heat transfer behaviors of water-based nanofluids confined in nanochannel by molecular dynamics simulation. Dig. J. Nanomater. Biostructures 2015 , 10 , 401–413. [ Google Scholar ]
• Asgari, A.; Nguyen, Q.; Karimipour, A.; Bach, Q.; Hekmatifar, M.; Sabetvand, R. Develop molecular dynamics method to simulate the flow and thermal domains of H 2 O/Cu nanofluid in a nanochannel affected by an external electric field. Int. J. Thermophys. 2020 , 41 , 126. [ Google Scholar ] [ CrossRef ]
• Dehkordi, R.B.; Toghraiea, D.; Hashemian, M.; Aghadavoudi, F.; Akbari, M. Molecular dynamics simulation of ferro-nanofluid flow in a microchannel in the presence of external electric field: Effects of Fe 3 Oe nanoparticles. Int. Commun. Heat Mass Transf. 2020 , 116 , 104653. [ Google Scholar ] [ CrossRef ]
• Qin, Y.; Zhao, J.; Liu, Z.; Wang, C.; Zhang, H. Study on effect of different surface roughness on nanofluid flow in nanochannel by using molecular dynamics simulation. J. Mol. Liq. 2022 , 346 , 117148. [ Google Scholar ] [ CrossRef ]
• Yu, H.; Tao, Y.; Zhao, Y.; Sha, J. The effect of flow velocity on the convection in nanochannel. In Proceedings of the International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale, Xi’an, China, 2–6 August 2021. [ Google Scholar ]
• Marable, D.C.; Shin, S.; Nobakht, A.Y. Investigation into the microscopic mechanisms influencing convective heat transfer of water flow in graphene nanochannels. Int. J. Heat Mass Transf. 2017 , 109 , 28–39. [ Google Scholar ] [ CrossRef ]
• Kusalik, P.G.; Svishchev, I.M. The spatial structure in liquid water. Science 1994 , 265 , 1219–1221. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Mahoney, M.W.; Jorgensen, W.L. A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J. Chem. Phys. 2000 , 112 , 8910–8922. [ Google Scholar ] [ CrossRef ]
• González, M.A.; Abascal, J.L.F. The shear viscosity of rigid water models. J. Chem. Phys. 2010 , 132 , 096101. [ Google Scholar ] [ CrossRef ]
• Vega, C.; Abascal, J.L.F. Simulating water with rigid non-polarizable models: A general perspective. Phys. Chem. Chem. Phys. 2011 , 13 , 19663–19688. [ Google Scholar ] [ CrossRef ]
• Lee, S.H.; Kim, J. Transport properties of bulk water at 243–550 K: A comparative molecular dynamics simulation study using SPC/E, TIP4P, and TIP4P/2005 water models. Mol. Phys. 2018 , 117 , 1926–1933. [ Google Scholar ] [ CrossRef ]
• Mao, Y.; Zhang, Y. Thermal conductivity, shear viscosity and specific heat of rigid water models. Chem. Phys. Lett. 2012 , 542 , 37–41. [ Google Scholar ] [ CrossRef ]
• Rick, S.W. A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums. J. Chem. Phys. 2004 , 120 , 6085–6093. [ Google Scholar ] [ CrossRef ]
• Luo, K.; Li, W.; Ma, J.; Chang, W.; Huang, G.; Li, C. Silicon microchannels flow boiling enhanced via microporous decorated sidewalls. Int. J. Heat Mass Transf. 2022 , 191 , 122817. [ Google Scholar ] [ CrossRef ]
• Chakraborty, P.; Ma, T.; Cao, L.; Wang, Y. Significantly enhanced convective heat transfer through surface modification in nanochannels. Int. J. Heat Mass Transf. 2019 , 136 , 702–708. [ Google Scholar ] [ CrossRef ]
• Zhou, K.; Liu, B. Molecular Dynamic Simulation: Fundamentals and Applications , 1st ed.; Elsevier Science: Amsterdam, The Netherlands, 2022. [ Google Scholar ]
• Rosa, P.; Karayiannis, T.G.; Collins, M.W. Single-phase heat transfer in microchannels: The importance of scaling effects. Appl. Therm. Eng. 2009 , 29 , 3447–3468. [ Google Scholar ] [ CrossRef ]
• Alavi, S. Molecular Simulations: Fundamentals and Practice , 1st ed.; Wiley-VCH: Weinheim, Germany, 2020; pp. 79–81. [ Google Scholar ]
• Ge, S.; Gu, Y.; Chen, M. A molecular dynamics simulation on the convective heat transfer in nanochannels. Mol. Phys. 2014 , 113 , 703–710. [ Google Scholar ] [ CrossRef ]
• Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications , 1st ed.; Elsevier Science: Amsterdam, The Netherlands, 2001; pp. 34–35. [ Google Scholar ]
• Li, L.; Liu, Z.; Qi, R. Molecular dynamics simulations in hydrogel research and its applications in energy utilization: A review. Energy Rev. 2024 , 3 , 100072. [ Google Scholar ] [ CrossRef ]
• Gennes, P.G. Wetting: Statics and dynamics. Rev. Mod. Phys. 1985 , 57 , 827. [ Google Scholar ] [ CrossRef ]
• Wang, M.; Sun, H.; Cheng, L. Investigation of convective heat transfer performance in nanochannels with fractal Cantor structures. Int. J. Heat Mass Transf. 2021 , 171 , 121086. [ Google Scholar ] [ CrossRef ]
• Tucker, Q.J.; Ivanov, D.S.; Zhigilei, L.V.; Johnson, R.E.; Bringa, E.M. Molecular dynamics simulation of sputtering from a cylindrical track: EAM versus pair potentials. NIM-B 2005 , 228 , 163–169. [ Google Scholar ] [ CrossRef ]
• Sekerka, R.F. Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers , 1st ed.; Elsevier Science: Amsterdam, The Netherlands, 2015; pp. 273–274. [ Google Scholar ]
• Sun, H.; Liu, Z.; Xin, G.; Xin, Q.; Zhang, J.; Cao, B.Y.; Wang, X. Thermal and flow characterization in nanochannels with tunable surface wettability: A comprehensive molecular dynamics study. Numer. Heat Transf. Part A Appl. 2020 , 78 , 231–251. [ Google Scholar ] [ CrossRef ]
• Fallahzadeh, R.; Bozzoli, F.; Cattani, L.; Azam, M.W. Effect of cross nanowall surface on the onset time of explosive boiling: A molecular dynamics study. Energies 2024 , 17 , 1107. [ Google Scholar ] [ CrossRef ]
• Daw, M.S.; Foiles, S.M.; Baskes, M.I. The embedded-atom method: A review of theory and applications. Mater. Sci. Rep. 1993 , 9 , 251–310. [ Google Scholar ] [ CrossRef ]
• Wang, W.; Zhang, H.; Tian, C.; Meng, X. Numerical experiments on evaporation and explosive boiling of ultra-thin liquid argon film on aluminum nanostructure substrate. Nanoscale Res. Lett. 2015 , 10 , 158. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Daw, M.S.; Chandross, M. Simple parameterization of embedded atom method potentials for FCC metals. Acta Mater. 2023 , 248 , 118771. [ Google Scholar ] [ CrossRef ]
• Heinz, H.; Vaia, R.A.; Farmer, B.L.; Naik, R.R. Accurate simulation of surfaces and interfaces of face-centered cubic metals using 12-6 and 9-6 Lennard-Jones potentials. J. Phys. Chem. C 2008 , 112 , 17281–17290. [ Google Scholar ] [ CrossRef ]
• Din, X.D.; Michaelides, E.E. Kinetic theory and molecular dynamics simulations of microscopic flows. Phys. Fluids. 1997 , 9 , 3915–3925. [ Google Scholar ] [ CrossRef ]
• Barrat, J.L.; Bocquet, L. Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett. 1999 , 82 , 4671. [ Google Scholar ] [ CrossRef ]
• Hagler, A.T.; Lifson, S.; Dauber, P. Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 2. a benchmark for the objective comparison of alternative force fields. J. Am. Chem. Soc. 1979 , 101 , 5122–5130. [ Google Scholar ] [ CrossRef ]
• Hagler, A.T.; Huler, E.; Lifson, S. Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. J. Am. Chem. Soc. 1974 , 96 , 5319–5327. [ Google Scholar ] [ CrossRef ]
• Waldman, M.; Hagler, A.T. New combining rules for rare gas van der Waals parameters. J. Comput. Chem. 1993 , 14 , 1077–1084. [ Google Scholar ] [ CrossRef ]
• Delhommelle, J.; Millie, P. Inadequacy of the Lorentz-Berthelot combining rules for accurate predictions of equilibrium properties by molecular simulation. Mol. Phys. 2001 , 99 , 619–625. [ Google Scholar ] [ CrossRef ]
• Weeks, J.D.; Chandler, D.; Andersen, H.C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971 , 54 , 5237–5247. [ Google Scholar ] [ CrossRef ]
• Jiang, H.; Patel, A.J. Recent advances in estimating contact angles using molecular simulations and enhanced sampling methods. Curr. Opin. Chem. Eng. 2019 , 23 , 130–137. [ Google Scholar ] [ CrossRef ]
• Debye, P.; Erich, H. The theory of electrolytes. I. Freezing point depression and related phenomena. Phys. Z. 1923 , 24 , 185–206. [ Google Scholar ]
• Nichita, D.V.; Petitfrere, M. Phase equilibrium calculations with quasi-Newton methods. Fluid Phase Equilib. 2015 , 406 , 194–208. [ Google Scholar ] [ CrossRef ]
• Hestenes, M.R.; Stiefel, E. Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 1952 , 49 , 2379. [ Google Scholar ] [ CrossRef ]
• Hoover, W.G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985 , 31 , 1695. [ Google Scholar ] [ CrossRef ]
• Chen, W.-H.; Wu, C.-H.; Cheng, H.-C. Modified Nosé-Hoover thermostat for solid state for constant temperature molecular dynamics simulation. J. Comput. Phys. 2011 , 230 , 6354–6366. [ Google Scholar ] [ CrossRef ]
• Rowlinson, J.S. The maxwell–Boltzmann distribution. Mol. Phys. 2005 , 103 , 2821–2828. [ Google Scholar ] [ CrossRef ]
• Hu, C.; Bai, M.; Lv, J.; Li, X. An investigation on the flow and heat transfer characteristics of nanofluid by nonequilibrium molecular dynamics simulations. Numer. Heat Transf. Part B 2016 , 70 , 152–163. [ Google Scholar ] [ CrossRef ]
• Ashurst, W.T.; Hoover, W.G. Dense-fluid shear viscosity via nonequilibrium molecular dynamics. Phys. Rev. A 1975 , 11 , 658. [ Google Scholar ] [ CrossRef ]
• Khare, R.; de Pablo, J.; Yethiraj, A. Molecular simulation and continuum mechanics study of simple fluids in non-isothermal planar couette flows. J. Chem. Phys. 1997 , 107 , 2589–2596. [ Google Scholar ] [ CrossRef ]
• Zheng, B.; Huang, Z.; Zheng, Z.; Chen, Y.; Yan, J.; Cen, K.; Yang, H.; Ostrikov, K. Accelerated ion transport and charging dynamics in more ionophobic sub-nanometer channels. Energy Storage Mater. 2023 , 59 , 102797. [ Google Scholar ] [ CrossRef ]
• Fallahzadeh, R.; Bozzoli, F.; Cattani, L. Effect of closed-loop nanochannels on the onset of explosive boiling: A molecular dynamics simulation study. J. Phys. Conf. Ser. 2024 , 2685 , 012013. [ Google Scholar ] [ CrossRef ]
• Hu, H.; Lu, Y.; Guo, L.; Chen, X.; Wang, Q.; Wang, J.; Li, Q. Effects of system pressure on nucleate boiling: Insights from molecular dynamics. J. Mol. Liq. 2024 , 402 , 124745. [ Google Scholar ] [ CrossRef ]
• Barisik, M.; Beskok, A. Boundary treatment effects on molecular dynamics simulations of interface thermal resistance. J. Comput. Phys. 2012 , 231 , 7881–7892. [ Google Scholar ] [ CrossRef ]
• Qin, S.; Chen, Z.; Wang, Q.; Li, W.; Xing, H. Effect of surface structure on fluid flow and heat transfer in cold and hot wall nanochannels. Int. J. Heat Mass Transf. 2024 , 151 , 107257. [ Google Scholar ] [ CrossRef ]
• Schneider, T.; Stoll, E. Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions. Phys. Rev. B 1978 , 17 , 1302. [ Google Scholar ] [ CrossRef ]
• Berendsen, H.J.; Postma, J.V.; Van Gunsteren, W.F.; DiNola, A.R.H.J.; Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984 , 81 , 3684–3690. [ Google Scholar ] [ CrossRef ]
• Thomas, T.M.; Vinod, N. Convective heat transfer between liquid argon flows and heated carbon nanotube arrays using molecular dynamics. J. Appl. Fluid Mech. 2019 , 12 , 971–980. [ Google Scholar ] [ CrossRef ]
• Gu, Y.W.; Ge, S.; Chen, M. A molecular dynamics simulation of nanoscale convective heat transfer with the effect of axial heat conduction. Mol. Phys. 2016 , 114 , 1922–1930. [ Google Scholar ] [ CrossRef ]
• Yu, F.; Wang, T.; Zhang, C. Effect of axial conduction on heat transfer in a rectangular microchannel with local heat flux. J. Therm. Sci. Technol. 2018 , 13 , JTST0013. [ Google Scholar ] [ CrossRef ]
• Cole, K.D.; Çetin, B. The effect of axial conduction on heat transfer in a liquid microchannel flow. Int. J. Heat Mass Transf. 2011 , 54 , 2542–2549. [ Google Scholar ] [ CrossRef ]
• Chen, C.; Li, Y. Studying the influence of surface roughness with different shapes and quantities on convective heat transfer of fluid within nanochannels using molecular dynamics simulations. J. Mol. Model. 2024 , 30 , 42. [ Google Scholar ] [ CrossRef ]
• Stojanovic, N.; Maithripala, D.H.S.; Berg, J.M.; Holtz, M.J.P.R. Thermal conductivity in metallic nanostructures at high temperature: Electrons, phonons, and the Wiedemann-Franz law. Phys. Rev. B 2010 , 82 , 075418. [ Google Scholar ] [ CrossRef ]
• Heino, P.; Ristolainen, E. Thermal conduction at the nanoscale in some metals by MD. Microelectron. J. 2003 , 34 , 773–777. [ Google Scholar ] [ CrossRef ]
• Stamper, C.; Cortie, D.; Yue, Z.; Wang, X.; Yu, D. Experimental confirmation of the universal law for the vibrational density of states of liquids. J. Phys. Chem. Lett. 2022 , 13 , 3105–3111. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Peethan, A.; Unnikrishnan, V.K.; Chidangil, S.; George, S.D. Laser-Assisted tailoring of surface wettability-fundamentals and applications: A critical review. Prog. Adhes. Adhesives. 2020 , 5 , 331–365. [ Google Scholar ] [ CrossRef ]
• Zhang, C.B.; Xu, Z.L.; Chen, Y.P. Molecular dynamics simulation on fluid flow and heat transfer in rough nanochannels. Acta Phys. Sin. 2014 , 63 , 214706. [ Google Scholar ] [ CrossRef ]
• Zhang, T.; Cui, T. Enhanced wetting properties of silicon mesh microchannels coated with SiO 2 /SnO 2 nanoparticles through layer-by-layer self-assembly. Sens. Actuators B Chem. 2011 , 157 , 697–702. [ Google Scholar ] [ CrossRef ]
• Wu, H.Y.; Cheng, P. An experimental study of convective heat transfer in silicon microchannels with different surface conditions. Int. J. Heat Mass Transf. 2003 , 46 , 2547–2556. [ Google Scholar ] [ CrossRef ]
• Toghraie, D.; Mokhtari, M.; Afrand, M. Molecular dynamic simulation of Copper and Platinum nanoparticles Poiseuille flow in a nanochannels. Physica. E 2016 , 84 , 152–161. [ Google Scholar ] [ CrossRef ]
• Fu, T.; Wang, Q. Effect of nanostructure on heat transfer between fluid and copper plate: A molecular dynamics simulation study. Mol. Simul. 2018 , 44 , 697–702. [ Google Scholar ] [ CrossRef ]
• Liu, H.; Deng, W.; Ding, P.; Zhao, J. Investigation of the effects of surface wettability and surface roughness on nanoscale boiling process using molecular dynamics simulation. Nucl. Eng. Des. 2021 , 382 , 111400. [ Google Scholar ] [ CrossRef ]
• Liu, H.; Qin, X.; Ahmad, S.; Tong, Q.; Zhao, J. Molecular dynamics study about the effects of random surface roughness on nanoscale boiling process. Int. J. Heat Mass Transf. 2019 , 145 , 118799. [ Google Scholar ] [ CrossRef ]
• Fallahzadeh, R.; Bozzoli, F.; Cattani, L.; Pagliarini, L.; Naeimabadi, N.; Azam, M.W. A molecular dynamics perspective on the impacts of random rough surface, film thickness, and substrate temperature on the adsorbed film’s liquid-vapor phase transition regime. Sci 2024 , 6 , 33. [ Google Scholar ] [ CrossRef ]
• Piekiel, N.W.; Morris, C.J.; Currano, L.J.; Lunking, D.M.; Isaacson, B.; Churaman, W.A. Enhancement of on-chip combustion via nanoporous silicon microchannels. Combust. Flame 2014 , 161 , 1417–1424. [ Google Scholar ] [ CrossRef ]
• Morshed, A.M.; Rezwan, A.A.; Khan, J.A. Two-phase convective flow in microchannel with nanoporous coating. Procedia Eng. 2014 , 90 , 588–598. [ Google Scholar ] [ CrossRef ]
• Ahmad, S.; Deng, W.; Liu, H.; Khan, S.A.; Chen, J.; Zhao, J. Molecular dynamics simulations of nanoscale boiling on mesh-covered surfaces. Appl. Therm. Eng. 2021 , 195 , 117183. [ Google Scholar ] [ CrossRef ]
• Ahmad, S.; Khan, S.A.; Ali, H.M.; Huang, X.; Zhao, J. Molecular dynamics study of nanoscale boiling on double layered porous meshed surfaces with gradient porosity. Appl. Nanosci. 2022 , 12 , 2997–3006. [ Google Scholar ] [ CrossRef ]
• Guan, S.Y.; Zhang, Z.H.; Wu, R.; Gu, X.K.; Zhao, C.Y. Boiling on nano-porous structures: Theoretical analysis and molecular dynamics simulations. Int. J. Heat Mass Transf. 2022 , 191 , 122848. [ Google Scholar ] [ CrossRef ]
• Islam, M.A.; Rony, M.D.; Hasan, M.N. Thin film liquid-vapor phase change phenomena over nano-porous substrates: A molecular dynamics perspective. Heliyon 2023 , 9 , e15714. [ Google Scholar ] [ CrossRef ]
• Gürdal, M.; Arslan, K.; Gedik, E.; Minea, A.A. Effects of using nanofluid, applying a magnetic field, and placing turbulators in channels on the convective heat transfer: A comprehensive review. Renew. Sustain. Energy Rev. 2022 , 162 , 112453. [ Google Scholar ] [ CrossRef ]
• Wen, D.; Ding, Y. Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. Int. J. Heat Mass Transf. 2004 , 47 , 5181–5188. [ Google Scholar ] [ CrossRef ]
• Yang, Y.; Zhang, Z.G.; Grulke, E.A.; Anderson, W.B.; Wu, G. Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow. Int. J. Heat Mass Transf. 2005 , 48 , 1107–1116. [ Google Scholar ] [ CrossRef ]
• Sun, H.; Wang, M. Atomistic insights into heat transfer and flow behaviors of nanofluids in nanochannels. J. Mol. Liq. 2022 , 345 , 117872. [ Google Scholar ] [ CrossRef ]
• Hashemi, S.M.H.; Fazeli, S.A.; Zirakzadeh, H.; Ashjaee, M. Study of heat transfer enhancement in a nanofluid-cooled miniature heat sink. Int. Commun. Heat Mass Transf. 2012 , 39 , 877–884. [ Google Scholar ] [ CrossRef ]
• Sakanova, A.; Keian, C.C.; Zhao, J. Performance improvements of microchannel heat sink using wavy channel and nanofluids. Int. J. Heat Mass Transf. 2015 , 89 , 59–74. [ Google Scholar ] [ CrossRef ]
• Rahimi-Gorji, M.; Pourmehran, O.; Hatami, M.; Ganji, D.D. Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis. Eur. Phys. J. Plus. 2015 , 130 , 22. [ Google Scholar ] [ CrossRef ]
• Shahrestani, M.I.; Maleki, A.; Shadloo, M.S.; Tlili, I. Numerical investigation of forced convective heat transfer and performance evaluation criterion of Al 2 O 3 /water nanofluid flow inside an axisymmetric microchannel. Symmetry 2020 , 12 , 120. [ Google Scholar ] [ CrossRef ]
• Lin, X.; Mo, S.; Jia, L.; Yang, Z.; Chen, Y.; Cheng, Z. Experimental study and Taguchi analysis on LED cooling by thermoelectric cooler integrated with microchannel heat sink. Appl. Energy 2019 , 242 , 232–238. [ Google Scholar ] [ CrossRef ]

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Fallahzadeh, R.; Bozzoli, F.; Cattani, L.; Naeimabadi, N. A Comprehensive Review on Molecular Dynamics Simulations of Forced Convective Heat Transfer in Nanochannels. Energies 2024 , 17 , 4352. https://doi.org/10.3390/en17174352

Fallahzadeh R, Bozzoli F, Cattani L, Naeimabadi N. A Comprehensive Review on Molecular Dynamics Simulations of Forced Convective Heat Transfer in Nanochannels. Energies . 2024; 17(17):4352. https://doi.org/10.3390/en17174352

Fallahzadeh, Rasoul, Fabio Bozzoli, Luca Cattani, and Niloofar Naeimabadi. 2024. "A Comprehensive Review on Molecular Dynamics Simulations of Forced Convective Heat Transfer in Nanochannels" Energies 17, no. 17: 4352. https://doi.org/10.3390/en17174352

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• Published: 05 September 2024

Experimental investigation of zinc ferrite/insulation oil nanofluid natural convection heat transfer, AC dielectric breakdown voltage, and thermophysical properties

• Hadi Pourpasha 1 ,
• Saeed Zeinali Heris 1 , 2 ,
• Reza Javadpour 2 ,
• Mousa Mohammadpourfard 3 &
• Yaqing Li 1  

Scientific Reports volume  14 , Article number:  20721 ( 2024 ) Cite this article

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• Engineering
• Materials science
• Nanoscience and technology

Improving the thermal and dielectric properties of insulation oil (INO) with nanoadditives is an important challenge, and achieving dispersion stability in these nanofluids is quite challenging, necessitating further investigation. The main goal of this study is the synthesis and use of the hydrophobicity of zinc ferrite (ZnFe 2 O 4 ) nanoparticles, which can improve both the thermal and dielectric properties of the INO. This oil is made from distillate (petroleum), including severely hydrotreated light naphthenic oil (75–85%) and severely hydrotreated light paraffinic oil (15–25%). A comprehensive investigation was carried out, involving the creation of nanofluids with ZnFe 2 O 4 nanoparticles at various concentrations, and employing various characterization methods such as X-ray diffraction (XRD), Fourier-transform infrared (FTIR), scanning electron microscopy, energy dispersive X-ray (EDX), zeta potential analysis, and dynamic light scattering (DLS). The KD2 Pro thermal analyzer was used to investigate the thermal characteristics, including the thermal conductivity coefficient (TCC) and volumetric heat capacity (VHC). Under free convection conditions, the free convection heat transfer coefficient (FCHTC) and Nusselt numbers (Nu) were evaluated, revealing enhancements ranging from 14.15 to 11.7%. Furthermore, the most significant improvement observed in the AC Breakdown voltage (BDV) for nanofluids containing 0.1 wt% of ZnFe 2 O 4 amounted to 17.3%. The most significant finding of this study is the improvement in the heat transfer performance, AC BDV, and stability of the nanofluids.

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Introduction.

Insulation oil (INO), also referred to as dielectric oil, is a specialized type of oil intended for insulating electrical equipment. This type of oil finds common application in electrical systems and other high-voltage equipment, serving the purpose of electrical insulation and heat dissipation. Its primary role is to safeguard the integrity and efficiency of electrical systems by averting electrical breakdowns and offering protection against arcing. To avoid damage to the parts of high-voltage equipment and prevent performance degradation, it is crucial to cool this system. When the temperature of the INO exceeds a certain limit, the electrical system and other high-voltage equipment stop operating 1 . The dielectric coefficient, heat transfer coefficient, and AC BDV are critical parameters of INO that have a significant impact on its performance. For INO to be effective, it must possess both electrical insulating and heat transfer characteristics 2 . It is imperative to use additives that will not negatively affect the properties of INO to enhance its performance. While many additives studied thus far have been found to positively impact INO’s heat transfer, their usage often leads to a decrease in AC BDV 3 . Nanoadditives such as carbon nanotubes (CNTs), tungsten oxide (WO 3 ), aluminum oxide (Al 2 O 3 ), and graphene have been observed to have adverse effects on AC BDV 4 . To improve these properties, researchers have used the combination of this additive with metal oxide nanoparticles such as silicon dioxide (SiO 2 ) + CNTs, Al 2 O 3  + CNTs, and titanium dioxide (TiO 2 ) + CNTs, which relatively improved the dielectric properties, but it was less than the pure dielectric oil of nanofluid 5 . However, some metal oxide nanoparticles with a high AC BDV, such as zinc oxide (ZnO) and TiO 2 , can be used to enhance AC BDV 6 .

Many nanoparticles are created using bottom-up processes from chemical precursors 7 , 8 . Co-precipitation 9 , 10 , sol–gel procedures 11 , microemulsion 12 , 13 , and solvothermal techniques 14 , 15 are all included in this group. INOs are characterized primarily by their base oils, which are the key component. Oils contain far fewer additives, but additives are necessary for improving the qualities and compensating for the shortcomings of pure oils 16 , 17 , 18 . Therefore, in the present study, the co-precipitation process was used to synthesize ZnFe 2 O 4 nanoparticles, and they were used for the first time in INO to enhance AC BDV and heat transfer properties.

Nanoparticles, on the other hand, have a high surface-to-volume ratio, which increases the surface energy of the particles and leads to the tendency for nanoparticles to aggregate 19 . Surface treatment of nanoparticles is employed to reduce surface energy and mitigate the potential for nanoparticle aggregation 20 , 21 , 22 . In the pursuit of enhancing stability and dispersion within nanofluids, a combination of techniques may be implemented 23 . Among these strategies, those incorporating surfactants such as gum arabic, oleic acid, sodium dodecyl sulfate, and Triton X100 have been widely employed 24 . Moreover, ultrasonics 25 , 26 , and alterations in pH levels 27 have also shown efficacy toward the same end. With the goal of optimizing both stability and dispersion of nanoparticles in mind, this study aimed to improve their surface properties by treating them with oleic acid. This approach is known to be associated with enhanced nanofluid stability. Furthermore, ultrasonic waves were employed to further enhance the dispersion of the nanoparticles.

Several investigations have been carried out on the influence of nanoadditives on the thermal performance, thermophysical features, and AC BDV of INO, as described below. Siddique et al. 6 explored how the presence of nanoparticles, specifically TiO 2 and ZnO, influenced AC BDV in INO. According to the research, TiO 2 /INO and ZnO/INO nanofluids have a higher AC BDV than base oils, and with increasing TiO 2 and ZnO additives, the maximum enhancements of AC BDV are 30% and 28%, respectively. Rajňák et al. 28 conducted a study to examine how magnetic nano-additives influenced AC BDV in INO. Their findings from experiments indicate that AC BDV of the magnetic nanofluids studied did not improve over that of the basic INO. The effects of three nanoadditives, CNTs + TiO 2 , CNTs + SiO 2 , and CNTs + Al 2 O 3 , on the thermal properties and AC BDV of INO were investigated by Ghaffarkhah et al. 5 . By adding these nano additives, the INO’s thermal characteristics were enhanced. Nevertheless, AC BDV of all nanofluids was reduced with increasing nanoparticle concentration. Aberoumand et al. 29 conducted a study on the influence of WO 3 and silver nanoparticles on the thermal characteristics and AC BDV of INO. Their findings showed that the TCC improved by 41% when 4 wt% of the nanocomposite was added to INO. However, AC BDV of the nanofluids declined by 33.96%. Alizadeh et al. 30 investigated how CNTs-OH nanoparticles affect heat transfer and AC BDV. Their conclusion showed that the addition of 0.01 wt% of the additive to INO increased the FCHT by 30.08%. However, AC BDV of the nanofluid decreased by 23.44% with the same amount of additive. Pourpasha et al. 31 assessed the impact of TiO 2 -doped CNTs nanomaterials on the features of INO. In their study, it was discovered that the incorporation of 0.2 wt% of these additives into INO resulted in an 8.6% boost in the TCC and a substantial 23.08% increase in FCHT. Amiri et al. 32 examined how hexylamine functionalized CNTs affected heat transfer and AC BDV of INO. With the addition of nanoparticles in the INO, the FCHTC increased by approximately 23%, and the TCC of the INO was boosted by about 10%. Nevertheless, AC BDV decreased by about 11% at 0.005 wt%. Marulasiddeshi et al. 33 investigated the thermohydraulic behavior and the rate of thermodynamic irreversibility of a water-based Al 2 O 3 and Al 2 O 3  + CuO hybrid nanofluid flowing through a circular copper tube under a constant heat flux of 8625 W/m 2 . Their findings showed that the maximum increase in Nu was 51%, 59%, and 79.7% for 1 vol% nanofluid compared to water at temperatures of 30 °C, 45 °C, and 60 °C, respectively.

Wanatasanappan et al. 34 investigated the effect of the Al 2 O 3  + Fe 2 O 3 nanocomposite on the viscosity of water-ethylene glycol. Their experimental data illustrated that the Al 2 O 3  + Fe 2 O 3 composition of 40/60 resulted in the highest viscosity value at all temperatures investigated, while the 60/40 composition recorded the lowest viscosity value. Besides, the increase in temperature of nanofluid shows a maximum viscosity reduction of 87.2% as the temperature is increased from 0 to 100 °C.

Previous studies conducted by researchers showed that most nanoparticles had a positive impact on the thermal properties of INO. However, these nanoparticles 5 , 28 , 29 , 30 , 31 , 32 , 35 , 36 had a negative effect on the AC BDV of INO, except for TiO 2 and ZnO 6 , which were studied in a few cases. Additionally, there were limited comprehensive studies that investigated various properties of INOs, such as viscosity, viscosity index, flash point, fire point, pour point, natural convection heat transfer, TCC, VHC, and AC BDV. It was crucial to select a nanoparticle that did not have a negative effect on the dielectric properties of INO, as it was one of the vital properties of INO. Furthermore, it was important to examine most properties of INO and its stability. To address these limitations, an extensive investigation was conducted to assess the influence of ZnFe 2 O 4 additives on both the thermal properties, AC BDV characteristics, and stability of ZnFe 2 O 4 /INO nanofluids.

The novelty of this study lies in the comprehensive examination of the influence of the hydrophobicity of ZnFe 2 O 4 nanoparticles on a range of crucial properties that are essential for the efficient and reliable functioning of INO in electrical equipment. By elucidating the relationship between the hydrophobicity of ZnFe 2 O 4 nanoparticles and these properties, the study can contribute to the development of improved INO formulations with enhanced performance and tailored characteristics.

To improve AC BDV, thermal properties, and better dispersion of nanoparticles in INO, ZnFe 2 O 4 nanoparticles were first synthesized. The ZnFe 2 O 4 surface was treated with oleic acid to improve the stability. Then, the influence of the additive weight percentages on AC BDV and thermal properties such as TCC, VHC, flash point, pour point, VI, and kinematic viscosity were analyzed. In addition, the influence of the weight percentages of nanoparticles and various INPs of FCHTC was investigated. To the best of our knowledge, in most of the conducted studies, the most important and necessary parameters such as TCC, specific heat capacity, and viscosity were obtained by different theoretical equations. To reduce the error and obtain more accurate results, all parameters were determined by experimental tests, which is one of the new and strong sides of the present work. This study can establish the experimental basis for further research and optimization of the use of nanoparticles in INO to improve AC BDV.

The ZnFe 2 O 4 nanoadditive was synthesized by a chemical technique using Zn(CH 3 CO 2 ) 2 ·2H 2 O (zinc acetate), Fe(NO 3 ) 3 ·9H 2 O (ferric nitrate), and NaOH (sodium hydroxide) purchased from Merck Co. The surface modification of the nanoparticles was carried out with oleic acid produced by Merck Co. INO is a product of APAR Co. whose properties are illustrated in Table 1 . This oil is made from distillate (petroleum), including severely hydrotreated light naphthenic oil (75–85%) and severely hydrotreated light paraffinic oil (15–25%).

Synthesis of nanoparticles and nanofluids

9 g of zinc acetate and 1 g of ferric nitrate were mixed in 150 ml of distilled water and 150 ml of ethanol for 1 h. After the addition of 10 g NaOH, the mixture was stirred for 2 h at room temperature 37 . Particles were separated by a centrifuge, and then washed with ethanol and distilled water several times. The nanoparticles were subsequently subjected to a drying process in an oven at 100 °C for a duration of 5 h, followed by calcination in a laboratory furnace at 400 °C for 3 h 37 . To increase the hydrophobicity of nanoparticles, the following method was used 38 . An ethanol solution containing 100 ml of ZnFe 2 O 4 additives was mixed with 1 g of ZnFe 2 O 4 additives at 40 °C using a magnetic stirrer. An oleic acid solution of 10 g and an ethanol solution of 50 ml were blended and added to the suspension, which was stirred for 24 h. Using centrifugation, the suspension was separated into nanoparticles. Several rinses of acetone and ethanol were conducted on the nanoparticles. Finally, the nanoparticles were dried for 9 h in a 70 °C oven.

The nanofluids were prepared in two steps. To prepare nanofluids, 0.05, 0.1, 0.15 and 0.2 wt% ZnFe 2 O 4 nanoparticles were mixed with INO and dispersed for 15 min using an ultrasonic probe (Misonix Sonicator XL2020 Ultrasonic Liquid Processor, 550 Watts, 20 kHz, 1500 V rms). In the subsequent step, mechanical agitation was conducted at a speed of 1500 rpm for a duration of 2 h.

Characterization techniques

In this study, the composition of the additive was analyzed via X-ray diffraction (XRD). Fourier-transform infrared (FTIR) analysis serves the purpose of identifying a sample’s chemical composition and gaining insights into its molecular structure. Scanning electron microscopy (SEM) was employed to assess the nanoparticles’ shape, size, and morphology. Energy dispersive X-ray (EDX) analysis explores materials’ elemental makeup. Moreover, to analyze particle size distributions and stability of nanofluids, DLS and zeta potential were employed.

Thermophysical properties measurement methods

To evaluate the temperatures at the flash point and pour point, the open cup device PT-1015M and the digital instrument PT-1210 were used. The KD2 Pro thermal property analyzer (manufactured by Decagon) was used to investigate the thermal characteristics, including TCC and VHC. The nanofluid prepared earlier was placed in the testing chamber of the KD2 Pro instrument. The instrument applies a controlled heat pulse to the sample and measures the resulting temperature response over time. As the sample reaches thermal equilibrium, the instrument records the temperature response. The collected data includes the temperature change as a function of time. The collected data was then analyzed using the software provided with the KD2 Pro instrument. The software typically offers options to calculate VHC based on the recorded temperature response. The kinematic viscosity of the nanofluid was evaluated at different concentrations and temperatures of the nanofluid. ASTM D2270 and ASTM D445 test procedures were used to determine the kinematic viscosity and viscosity index (VI) of ZnFe 2 O 4 /INO nanofluids. Kinematic viscosities of both INO and nanofluids were determined using a Cannon Fenske Opaque viscometer. Each test was repeated at least twice to ensure that the findings were correct. The kinematic viscosity of nanofluids at various temperatures was measured using a precision temperature-controlled bath specifically designed to maintain a stable temperature. Additionally, a Cannon–Fenske Opaque viscometer was immersed in the temperature-controlled bath. To measure the kinematic viscosity at different temperatures, each desired temperature was set, and subsequent measurements were performed. Equation ( 1 ) 39 was used to obtain the VI of the INO and nanofluids.

The kinematic viscosity of the oil at 40 °C, denoted as “U”, is an essential factor in determining the oil’s viscosity index. Additionally, “K” represents the kinematic viscosity at 40 °C for oils with a viscosity index of 0, and “H” represents the kinematic viscosity at 40 °C for oils with a viscosity index of 100, which share the same kinematic viscosity as the oil being evaluated at 100 °C. For oils with a basic kinematic viscosity at 100 °C ranging from 2 to 70 cSt, the values of K and H can be obtained from ASTM D2270 tables. However, if the kinematic viscosity exceeds 70 cSt, K and H values are computed using the following equations 39 :

here Y represents the kinematic viscosity at 100 °C for the oil being evaluated for its viscosity index.

The IEC 60,156 test technique for nanofluids was used to determine the AC BDV. Two electrodes are placed in a chamber as part of the AC BDV measuring device. To measure AC BDV, the voltage is slowly increased. To determine the voltage at which the INO loses its dielectric property, the AC BDV experiment was repeated six times.

To study FCHT, a device was constructed that resembles the electrical system and other high-voltage equipment, with the difference that in electrical system and other high-voltage equipment the heat is generated by coils, but in the constructed device it is generated by a heater. Figure  1 shows a schematic representation of the setup used to determine the FCHTC of fluids. The experimental system consists of a liquid container, six thermocouples, six digital temperature displays, glass wool, a variac variable transformer (VVT), and a heating element.

Schematic of the setup.

The system volume is equal to 0.2 × 0.1 × 0.22 = 0.0044 m 3 . Two thermocouples were installed on the central side walls, one thermocouple was installed on the central upper wall, and three thermocouples were placed on the upper wall with a distance of 2.5 cm between each. To prevent heat loss, the upper and lower walls were insulated with glass wool. The heat flux was obtained by heating an electric element with the power supply located in the center of the bottom wall. It should be noted that all measurements were made after the system reached a stable state. Steady state is when there is no noticeable change in wall temperatures.

The FCHT of ZnFe 2 O 4 /INO nanofluids was investigated at 0, 0.05, 0.1, 0.15, and 0.2 wt% of the nanoparticles and at different powers (50.5–124 W). After filling the reservoir, the VVT was utilized to control the electric current (I) and the input voltage (V) of the heater. All temperatures were recorded after they reached stable conditions and the corresponding calculations were performed. To calculate all the data, the hot and cold temperatures were recorded for each run of this test technique, which was carried out using nanofluids with four different mass fractions of additives and four various INPs. The INP to the heater was controlled by VVT. FCHTC was determined using Eq. ( 10 ) by recording the temperatures and INPs. Nu, Gr, and Ra were calculated by computing the FCHTC and Eqs. ( 4 ), ( 8 ), and ( 11 ). Each experiment was carried out three times.

In the FCHT, the Grashof number (Gr), the ratio between buoyancy force and viscous force, is determined through Eq. ( 4 ) 36 .

The temperatures of the hot part (the center of the tank), the temperatures of the cold sides, and the gravitational acceleration are represented by T h , T c , and g, respectively. The volume expansion coefficient (β) is 0.00075 (1/°C), the space between the heater and the wall is denoted by L, and the dynamic viscosity (µ) is determined as follows 36 :

where \({\upnu }\) represents the kinematic viscosity and ρ is density of nanofluids. The calculation of Nu and Pr for FCHT is determined according to the following equations 30 :

h is the FCHTC of fluids, k is the TCC of nanofluids, and C p is the VHC. The Rayleigh number (Ra) is utilized in FCHT as a dimensionless quantity, calculated as follows 40 , 41 :

The value of thermal element INP (Q) is calculated using Eq. ( 9 ) 41 :

The electric current is denoted by I, where V stands for the voltage applied to the thermal element. To determine the mean FCHTC under constant heat flux conditions, the following formula is employed 30 :

The setup has a heat transfer area (A) of 0.129 m 2 . The following equation can be used to calculate the average Nu 39 :

Considering the varied accuracy of each parameter assessed in this study, it is critical to examine the impact of measurement error on the outcomes. If R depends on the parameters x 1 , x 2 , …, x n , the effect of measurement error on the parameter x i can be calculated as illustrated in 42 :

where x i stands for a quantifiable factor, R for a value resulting from measurable quantities, U xi is the error in measurement, and U Ri denotes the maximum possible error in the calculation of a quantity.

Table 2 demonstrates the amount of measurement error.

To calculate standard deviation (SD) for AC breakdown voltage tests, Eq. ( 14 ) is used. x is each individual data point, \(\overline{x}\) is the data mean, and N is the total of data points.

Experimental results

Nanofluid and nanoparticle features.

Figure  2 a–c demonstrate SEM/EDX analyses of ZnFe 2 O 4 nanoparticles. According to Fig.  2 a,b, the nanoparticles’ diameter ranges from 32.09 to 53.50 nm. According to the EDX analysis of ZnFe 2 O 4 (Fig.  2 c), the components of ZnFe 2 O 4 consist of 47.42% oxygen, 48.9 Zn, and 3.68% Fe. Figure  2 d displays distinct crystal structures observed in the ZnFe 2 O 4 nanoparticles during the XRD. The X Pert High Score software (version: 1.0d, produced by: PANalytical B.V Almelo, the Netherlands, license number:50000022) was used to analyze all the peaks. The samples were determined to have a hexagonal wurtzite structure existing in a single phase with the space group P63mc. The dominant peaks observed were at the (100), (002), (101), (102), (110), (103), (200), (112), (201), (004), and (202) positions, and there were no unusual peaks that would be associated with secondary iron oxide phases 37 , 39 . Figure  2 e shows the results of the FTIR analysis performed on the zinc ferrite nanoparticles. A broad peak ranging from 3000 to 3700 cm −1 corresponds to the stretching vibration of hydroxyl groups. Peaks at 2927 cm −1 and 2850 cm −1 , indicating the presence of CH 2 and CH 3 functional groups, respectively 39 . Two peaks, at 1629 cm −1 and 1706 cm −1 correspond to the asymmetric stretching frequencies of C=C and C=O bonds, respectively 39 . A series of peaks ranging from 1226 to 912 cm −1 , which were attributed to the vibration of the ZnO-Fe local bonding environment. Typically, bond frequencies around 1000 cm −1 provide insights into the interactions involving mineral elements. Notably, a prominent peak was observed at 435 cm −1 , which corresponds to the Zn–O stretching band, thereby confirming the formation of the wurtzite crystal structure 39 . The FTIR spectrum confirmed the composite nature of the zinc oxide sample, with an iron-related peak at 563 cm −1 and Fe–O vibration peaks from 700 to 912 cm −1 , indicating good crystallinity in nanocrystalline form 37 , 43 , 44 , 45 .

Analysis of ZnFe 2 O 4 ( a ) and ( b ) SEM, ( c ) EDX, ( d ) XRD, and ( e ) FTIR 39 .

Figure  3 a depicts the DLS analysis results of ZnFe 2 O 4 /INO nanofluids for varying concentrations of ZnFe 2 O 4 . Figure  3 a manifests the size distribution (SD) of ZnFe 2 O 4 nanoparticles at 0.05 wt% with 121.5 nm (67.91%) and 144.5 nm (32.09%). The SD at 0.1 wt% contains particles with the SD of 144.5 nm (14.59%), 171.9 nm (64.5%), and 204.4 nm (20.91%). At 0.15 wt%, the DLS gives 171.9 nm (5.4%), 204.4 nm (65.39%), 243 nm (27.92%), and 289 (1.29%). Finally, at 0.2 wt% of the nanofluid, the statistics from SD indicate 204.4 nm (41.21%), 243 nm (35.12%), 289 nm (17.04%), 344 nm (5.36%), and 409 nm (1.27%). Zeta potential analyses of ZnFe 2 O 4 /INO nanofluids at different concentrations of ZnFe 2 O 4 are demonstrated in Fig.  3 b. The ZnFe 2 O 4 /INO nanofluids exhibited reduced stability with an increase in nanoparticle concentration. The trend of zeta potential with nanoparticle concentration can vary depending on the specific system and factors involved. At low nanoparticle concentrations, individual particles may dominate the system, leading to a higher zeta potential due to the electrostatic repulsion between dispersed particles. As the concentration increases, the likelihood of particle interactions and collisions also increases. This can lead to the formation of particle aggregates or clusters, reducing the overall zeta potential due to decreased electrostatic repulsion between the aggregated particles. However, all the nanofluid samples reflected good stability with a zeta potential of less than − 39.2 mV.

Size distribution and stability of ZnFe 2 O 4 nanofluid in different concentrations: ( a ) DLS and ( b ) Zeta potential.

The images in Fig.  4 depict samples with varying mass fractions of ZnFe 2 O 4 prepared for 1 h (Fig.  4 a–d), 7 days (Fig.  4 e–h), and 14 days (Fig.  4 i–l). These samples proved to be stable for a period of 7 days. After 7 days, precipitation occurred in the nanofluids with 0.15 and 0.2 wt%. The sedimentation process of nanofluids with 0.15 and 0.2 wt% ZnFe 2 O 4 over a period of 14 days is illustrated in Fig.  4 k,l, respectively. It was noted that nanofluids containing lower concentrations of 0.05 wt% and 0.1 wt% displayed satisfactory stability for a duration of up to 14 days, with only minimal precipitation observed (as depicted in Fig.  4 i,j). The findings suggest that treating ZnFe 2 O 4 with oleic acid can enhance its surface area by minimizing the nanoparticles’ surface energy and agglomeration.

Visual images illustrating sedimentation quality.

Breakdown voltage and thermophysical properties

AC BDV of INO is defined as the lowest voltage at which a portion of the dielectric fluid conducts electric current. A crucial feature of INO is the AC BDV, which necessitates the use of nanofluids with higher values in electrical system and other high-voltage equipment. Figure  5 illustrates the variation in mean AC BDV of six test repetitions for ZnFe 2 O 4 /INO nanofluids under identical conditions. As shown in Table 3 and Fig.  5 , adding ZnFe 2 O 4 to INO enhanced the AC BDV of nanofluids. According to the IEC 60,156 standard, the AC BDV should be in the range of 30 to 70 kV. The mean AC BDV values of the nanofluids, which contained 0 to 0.2 wt% were found to vary from 65.15 to 74.02 kV when analyzed. The addition of ZnFe 2 O 4 to INO increased the AC BDV value of the nanofluid due to its low electrical conductivity. This resulted in acceptable AC BDV data that complied with the IEC 60,156 standard. The nanofluid with 0.1 wt% nanoparticles showed the maximum improvement in the mean AC BDV, which was 76.42 kV, an increase of 17.3%. According to Table 3 , the maximum standard deviation was 5.08, which was deemed acceptable. The dielectric properties of nanofluids are determined by the contact surface between nanoparticles and oil. According to the concept of the electrical double-layer (EDL), nanoparticles in the INO carry free charges. These charged nanoparticles attract counter-ions while repelling co-ions 46 . The counter-ions form a stationary layer around the nanoparticles known as the compact layer, which is rigid. Beyond this compact layer, a diffuse layer is formed, extending towards the electrically neutral base INO. The mobile ions in the diffuse layer are easily influenced by electrostatic forces. The EDL reduces the energy of fast electrons in an electrical field and traps them. Due to the uniform distribution of nanoparticles in the oil, interfacial volumes play a significant role in the system, resulting in the creation of numerous traps. Higher concentrations of nanoparticles in the base oil increase the interfacial volume, leading to a greater number of traps. This improvement in the nanofluid’s properties enhances the AC breakdown strength, dissipation factor, and volume resistivity of the oil 46 . According to Fig.  5 , with an increasing concentration of nanoparticles from 0.1 to 0.2 wt%, the mean AC BDV of the nanofluid decreased by 3.14%. This trend may depend on flowability issues, interfacial interactions, reduced nanoparticle dispersion, and agglomeration of nanoparticles. This is because with the addition of nanoparticles exceeding 0.1 wt%, the zeta potential value decreased, and these issues may occur, causing a reduction in AC BDV. Compared to various studies on AC BDV of INO, the results obtained in this study are the best achievement in this field. For instance, according to Table 4 , the use of most nanoparticles, especially carbon-based nanoparticles, leads to a reduction in the AC BDV of INO because these nanoparticles have high electrical conductivity. Among the nanoparticles, TiO 2 and ZnO nanoparticles have a high dielectric coefficient than pure oil, increasing the voltage coefficient of all types of oil. According to Siddique et al. 6 , the suspension of TiO 2 and ZnO nanoparticles in INO, specifically ester oil, has resulted in an enhanced AC BDV for the oil.

Mean AC breakdown voltage of ZnFe 2 O 4 /INO nanofluids.

Figure  6 illustrates thermophysical attributes and viscosity features of the ZnFe 2 O 4 /INO nanofluids, such as TCC, VHC, flash point, fire point, pour point, kinematic viscosity, and viscosity index. The addition of ZnFe 2 O 4 to INO increases TCC and VHC of the nano lubricant because the TCC and VHC of the ZnFe 2 O 4 are greater than those of INO. The highest enhancement in TCC of the nanofluid at a concentration of 0.2 wt% corresponded to 0.358 (W/m K) by a 6.23% increase, as shown in Fig.  6 a. The heat transfer efficiency of nanofluids is strongly influenced by TCC. As a result, nanofluids act as smart fluids that can dissipate more heat at higher temperatures. When heated or cooled, nanofluids demonstrate a faster rate of heat transmission. Based on the observed enhancements in thermal performance, the following controlling mechanisms are proposed: (1) the transportation of phonons through nanoparticles; (2) the random movement of nanoparticles known as Brownian motion; and (3) interactions between particles influenced by the electric double layer 47 . Phonon transport can be understood as the transmission of lattice vibrations. The efficiency of phonons is determined by their mean free path (MFP) relative to the thickness of the nanoparticles. For efficient heat transport through ballistic phonons, the phonon MFP should exceed the thickness of the nanoparticles 47 . This condition ensures improved heat transport 47 . Various factors such as the TCC of the base fluid and solid particles, particle concentration, size, shape, and thickness, as well as temperature play a crucial role in determining the TCC of nanofluids. Moreover, the mechanics of the particles in the base fluid can lead to Brownian motion, thermophoresis and diffusion, which can also influence the TCC of nanofluids 32 , 35 . Figure  6 b demonstrates that the VHC of a nanofluid containing 0.2 wt% nanoadditives improved by 1.874 (MJ/m 3 K), representing a 26.53% increase. This work’s noteworthy finding is the substantial enhancement in VHC of the nanofluid compared to the base fluid, with a slight increase in TCC. Additionally, Fig.  6 c illustrates that increasing the nanoparticle concentration to 0.2 wt% raised the flash point and fire point to 7 °C and 6 °C, respectively. In general, the increased resistance of the oil to burning can be attributed to an increase in TCC due to the existence of nanoparticles that retard the evaporation of ignition vapors. Figure  6 d indicates the pour point of ZnFe 2 O 4 /INO nanofluids with various mass fractions of ZnFe 2 O 4 nanoparticles. The addition of ZnFe 2 O 4 to INO lowers the pour point of the nanofluids because the TCC and VHC of the ZnFe 2 O 4 are larger than the INO. At a concentration of 0.15 wt% nanoparticles, the pour point of the nanofluid was enhanced by 6.25%, resulting in a maximum decrease of − 42.5 °C. The kinematic viscosity of ZnFe 2 O 4 /INO nanofluids with varying mass fractions of ZnFe 2 O 4 nanoparticles at temperatures of 40 °C, 60 °C, 80 °C, and 100 °C is shown in Fig.  6 e. The fluids’ viscosity of the fluids decreased by 76% on average when the temperature increased from 40 to 100 °C. This phenomenon occurs because as the temperature increases, the Brownian motion of nanoparticles in the oil intensifies. Consequently, the intermolecular interactions between the oil and the nanoparticle surfaces decrease due to the heightened random motion of the nanoparticles 30 . As temperature and molecular energy rise, the intermolecular forces within the liquid diminish, resulting in an expansion of the distance between molecules. Raising the temperature decreases the viscosity of the nanofluids. At a temperature of 100 °C, the addition of 0.2 wt% ZnFe 2 O 4 to INO resulted in a 3.47% increase in the kinematic viscosity of the nanofluid. To investigate the VI of fluids with different mass fractions of additives, the kinematic viscosity values at 40 °C and 100 °C were analyzed, and the findings are displayed in Fig.  6 f. The amount of VI is directly proportional to the viscosity at both 40 °C and 100 °C. A higher VI indicates that as temperature increases there’s no much increase in the oil’s viscosity hence maintaining a constant lubrication property. Conversely, low VIs indicate high change in oil viscosity with rise or drop in temperatures thus resulting in performance problems sometimes. The nanofluid with a 0.1 wt% additive had a maximum VI increase of 73.61, which corresponds to an increase of 6.41%. The interactions between particles or molecules in a suspension can significantly impact the VI. With increased concentrations there can be more interactions among them resulting into variations in the flow characteristics of this system which eventually affects its VI.

Thermophysical attributes and viscosity features of the ZnFe 2 O 4 /INO nanofluids, such as ( a ) thermal conductivity coefficient, ( b ) volumetric heat capacity, ( c ) flash point and fire point, ( d ) pour point, ( e ) kinematic viscosity, and ( f ) viscosity index.

Heat transfer evaluation

Figure  7 a depicts the FCHTC of fluids with different concentrations (0.05–0.2 wt%) of ZnFe 2 O 4 at different INPs of 50.5, 75.6, 100, and 124 (W). The FCHTC for INO and nanofluids increased with increasing INP, and so did the heat flux supply. As the FCHTC is directly related to power, and the increase in heat flux was greater than the increase in temperature difference, consequently, the ratio of these two parameters increased. The FCHTC improved with the addition of ZnFe 2 O 4 to oil. The highest FCHTC is related to the mass fraction of 0.1 wt% of ZnFe 2 O 4 and an INP of 124 (W) of ZnFe 2 O 4 , which equals 89.85 (W/m 2  K). The maximum increment in FCHTC occurred with an increase in the mass fraction of ZnFe 2 O 4 to 0.1 wt% at an INP of 50.5 (W), and the FCHTC of the nanofluid improved by 14.15% compared to INO. The value of FCHTC increases as the free heat transfer increases; thus, this parameter is critical in determining the rate of heat transfer. According to the results, FCHTC is a temperature-dependent property. In Fig.  7 b, the impact of ZnFe 2 O 4 on INO’s Nu under various inlet powers is exhibited. The addition of ZnFe 2 O 4 to INO resulted in an improvement of Nu. Nu is determined by the values of h and k, where h is significantly higher than k. The results indicate that the addition of 0.1 wt% ZnFe 2 O 4 to INO at an INP of 50.5 (W) led to an 11.17% increase in Nu. At a mass fraction of 0.1 wt% and an INP of 50.5 W, the h/k ratio was the highest. Figure  7 c shows that Gr varied with input power at different ZnFe 2 O 4 mass fractions. For all ZnFe 2 O 4 mass fractions, Gr improved with increasing INP due to the temperature difference between zones. As the mass fraction of ZnFe 2 O 4 increases due to enhanced heat transfer, the concentration of ZnFe 2 O 4 also increases, leading to a decrease in the temperature difference between hot and cold regions and thus a lower Gr value. At an INP of 50.5 (W), the Gr number of INO is 0.154 × 10 6 , but when 0.15% ZnFe 2 O 4 is added to INO, the Gr value decreases by 56.34% to 0.0985 × 10 6 . Figure  7 d demonstrates the effect of ZnFe 2 O 4 on the Ra value of INO at different input powers. As expected, increasing the INP to the heater resulted in higher Ra. This relationship can be explained by Eq. ( 8 ), which states that Ra is directly proportional to the temperature difference. Addition of 0.05 wt% and 0.1 wt% ZnFe 2 O 4 to INO at various INPs between 75.6 (W) and 124 (W) increased the temperature difference and thus Ra. However, at concentrations of 0.15 wt% and 0.2 wt%, a downward trend in Ra was observed at INPs between 75.6 (W) and 124 (W). At an input power of 50.5 (W), increasing the mass fraction of ZnFe 2 O 4 caused a significant decrease in Ra. In particular, the addition of 0.15 wt% ZnFe 2 O 4 to INO led to a 14.11% decrease in the Ra of the nanofluids compared to INO alone. Table 5 indicates that the suspension of carbon, metal, and metal oxide-based particles in INO leads to an improvement in convective heat transfer. Among the nanoparticles, carbon nanotubes had a greater impact on the thermal performance of the oil, even at low weight percentages, owing to their high TCC.

Variations in ( a ) free convection heat transfer coefficient, ( b ) Nusselt number, ( c ) Grashof number, and ( d ) Rayleigh number of ZnFe 2 O 4 /insulation oil at various input powers.

The study commenced with the synthesis of hydrophobic ZnFe 2 O 4 nano-additives, followed by their characterization through XRD, FTIR, SEM, and EDX analyses. The nanofluid stability was monitored using DLS, zeta potential, and visual observations. Subsequently, the impact of ZnFe 2 O 4 /INO nanofluids with varying mass fractions and different INPs on FCHTC, Nu, Gr, and Ra was investigated. Key findings from the research include:

The diameter of ZnFe 2 O 4 nanoparticles was determined by SEM analysis and varied between 32.09 nm and 53.50 nm.

Nanofluids with low concentrations remained stable for 14 days, with minimal sedimentation.

The nanofluid exhibited fine stability, as reflected by a zeta potential below − 39.2 mV.

The maximum increase in TCC of the nanofluid at 0.2 wt% ZnFe 2 O 4 was 0.358 W/m K, which was equal to 6.23%.

The substantial increase in Nu for fluids is associated with an INP of 50.5 W and 0.1 wt% ZnFe 2 O 4 at an improvement rate of approximately 11.17%.

The maximum increase in FCHTC occurred with increasing the mass fraction of nanoparticles to 0.1 wt% at an INP of 50.5 (W), and the FCHTC the of nanofluid improved by 14.15% compared to INO.

The AC BDV experienced a 17.3% increase, equivalent to 11.27 kV increase in breakdown voltage, upon the addition of 0.1 wt% of nanoparticles.

This research underscores the promising results of ZnFe 2 O 4 nanoparticles in improving the thermal and dielectric properties of INO, particularly through the use of nanofluids. The incorporation of these nanoparticles holds significant implications for the industry by enhancing transformer efficiency and reliability. Notable advancements in TCC and AC BDV offer potential solutions for overheating concerns and bolster the insulation capabilities of transformer systems, leading to increased energy efficiency, higher power transmission capacity, and prolonged equipment lifespan.

Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

Heat transfer area (m 2 )

Aluminum oxide

Breakdown voltage (kV)

Volumetric heat capacity (MJ/m 3  K)

Carbon nanotubes

Dynamic light scattering

Energy dispersive X-ray

Electrical double-layer

Fourier-transform infrared spectroscopy

Free convection heat transfer

Free convection heat transfer coefficient

Grashof number

Gravitational acceleration (m/s 2 )

Convection heat transfer coefficient (W/m 2  K)

Viscosity of fluids with a VI of 100 at 40 °C

Electric current (A)

Insulation oil

Thermal conductivity coefficient (W/m K)

Viscosity of fluids with a VI of zero at 40 °C

Mean free path

Total number of data points

Nusselt number

Prandtl number

Input power (W)

Heat flux (W/m 2 )

Rayleigh number

Standard deviation

Scanning electron microscopy

Silicon dioxide

Temperature

Thermal conductivity coefficient

Titanium dioxide

Viscosity at 40 °C

Maximum possible error

Measurement error

Voltage (V)

Volumetric heat capacity

Viscosity index

Variac variable transformers

Tungsten oxide

The data mean

Measurable parameter

X-ray diffraction

Kinematic viscosity at 100 °C for the oil

Zinc ferrite

Coefficient of volume expansion

Kinematic viscosity

Dynamic viscosity

Wang, P.-Y., Liu, J.-M., Liu, Z.-H. & Chen, Y.-J. Experiment and simulation of natural convection heat transfer of transformer oil under electric field. Int. J. Heat Mass Transf. 115 , 441–452 (2017).

Article   ADS   Google Scholar  

Hussain, M., Mir, F. A. & Ansari, M. Nanofluid transformer oil for cooling and insulating applications: A brief review. Appl. Surf. Sci. Adv. 8 , 100223 (2022).

Article   Google Scholar  

Hessien, M. M., Sabiha, N. A., Ghoneim, S. & Alahmadi, A. A. Enhancement of dielectric characteristics of transformer oils with nanoparticles. Int. J. Appl. Eng. Res. 12 (24), 15668–15673 (2017).

Google Scholar  

Rafiq, M., Shafique, M., Azam, A. & Ateeq, M. The impacts of nanotechnology on the improvement of liquid insulation of transformers: Emerging trends and challenges. J. Mol. Liq. 302 , 112482 (2020).

Article   CAS   Google Scholar  

Ghaffarkhah, A. et al. On evaluation of thermophysical properties of transformer oil-based nanofluids: A comprehensive modeling and experimental study. J. Mol. Liq. 300 , 112249 (2020).

Siddique, Z. B., Basu, S. & Basak, P. Dielectric behavior of natural ester based mineral oil blend dispersed with TiO 2 and ZnO nanoparticles as insulating fluid for transformers. J. Mol. Liq. 339 , 116825 (2021).

Heris, S. Z., Mohammadfam, Y., Javadpour, R. & Pourpasha, H. Nanofluids. In Handbook of Nanomaterials , Vol. 1, 27–56 (Elsevier, 2024).

Mohammadfam, Y. & Heris, S. Z. An experimental study of the influence of Fe 3 O 4 , MWCNT-Fe 3 O 4 , and Fe 3 O 4 @ MWCNT nanoparticles on the thermophysical characteristics and laminar convective heat transfer of nanofluids: A comparative study. Surf. Interfaces 43 , 103506 (2023).

Ovalles, C. et al. In-situ upgrading of heavy crude oils via solvent deasphalting using of nickel oxide nanoparticles as asphaltene co-precipitants. Fuel 313 , 122707 (2022).

Ghanbari, M., Soofivand, F. & Salavati-Niasari, M. Simple synthesis and characterization of Ag 2 CdI 4 /AgI nanocomposite as an effective photocatalyst by co-precipitation method. J. Mol. Liq. 223 , 21–28 (2016).

Soodmand, A. M. et al. A comprehensive review of computational fluid dynamics simulation studies in phase change materials: Applications, materials, and geometries. J. Therm. Anal. Calorim. 148 (20), 10595–10644 (2023).

Mariyate, J. & Bera, A. Recent progresses of microemulsions-based nanofluids as a potential tool for enhanced oil recovery. Fuel 306 , 121640 (2021).

Hu, Z., Nourafkan, E., Gao, H. & Wen, D. Microemulsions stabilized by in-situ synthesized nanoparticles for enhanced oil recovery. Fuel 210 , 272–281 (2017).

Farshchi, M. E. et al. Green valorization of PET waste into functionalized Cu-MOF tailored to catalytic reduction of 4-nitrophenol. J. Environ. Manag. 345 , 118842 (2023).

Ebrahimi Farshchi, M., Aghdasinia, H., Rostamnia, S., Sillanpää, M. Catalytic adsorptive elimination of deleterious contaminant in a pilot fluidised-bed reactor by granulated Fe 3 O 4 /Cu-MOF/cellulose nanocomposites: RSM optimisation and CFD approach. Int. J. Environ. Anal. Chem. 1–22 (2023).

Pourpasha, H., Zeinali Heris, S. & Mohammadfam, Y. Comparison between multi-walled carbon nanotubes and titanium dioxide nanoparticles as additives on performance of turbine meter oil nano lubricant. Sci. Rep. 11 (1), 11064 (2021).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Pourpasha, H., Zeinali Heris, S. & Asadi, A. Experimental investigation of nano-TiO 2 /turbine meter oil nanofluid: Thermophysical and tribological properties. J. Therm. Anal. Calorim. 138 , 57–67 (2019).

Gamal, M., Radwan, M., Elgizawy, I. & Shedid, M. Thermophysical characterization on water and ethylene glycol/water-based MgO and ZnO nanofluids at elevated temperatures: An experimental investigation. J. Mol. Liq. 369 , 120867 (2023).

Kanti, P. K., Sharma, P., Maiya, M. P. & Sharma, K. V. The stability and thermophysical properties of Al 2 O 3 -graphene oxide hybrid nanofluids for solar energy applications: application of robust autoregressive modern machine learning technique. Solar Energy Mater. Solar Cells 253 , 112207 (2023).

Hamzah, M. H., Sidik, N. A. C., Ken, T. L., Mamat, R. & Najafi, G. Factors affecting the performance of hybrid nanofluids: a comprehensive review. Int. J. Heat Mass Transf. 115 , 630–646 (2017).

Article   ADS   CAS   Google Scholar  

Moghadam, A. V. et al. Experimental investigation of multiwall carbon nanotubes/water nanofluid pool boiling on smooth and groove surfaces. Int. J. Energy Res. 46 (14), 19882–19893 (2022).

Pourpasha, H., Farshad, P. & Heris, S. Z. Modeling and optimization the effective parameters of nanofluid heat transfer performance using artificial neural network and genetic algorithm method. Energy Rep. 7 , 8447–8464 (2021).

Kanti, P. K., Sharma, K., Minea, A. A. & Kesti, V. Experimental and computational determination of heat transfer, entropy generation and pressure drop under turbulent flow in a tube with fly ash-Cu hybrid nanofluid. Int. J. Therm. Sci. 167 , 107016 (2021).

Kumar, P., Alruqi, M., Hanafi, H., Sharma, P. & Wanatasanappan, V. V. Effect of particle size on second law of thermodynamics analysis of Al 2 O 3 nanofluid: Application of XGBoost and gradient boosting regression for prognostic analysis. Int. J. Therm. Sci. 197 , 108825 (2024).

Sidik, N. A. C., Samion, S., Ghaderian, J. & Yazid, M. N. A. W. M. Recent progress on the application of nanofluids in minimum quantity lubrication machining: A review. Int. J. Heat Mass Transf. 108 , 79–89 (2017).

Mohammadfam, Y. & Heris, S. Z. Thermophysical characteristics and forced convective heat transfer of ternary doped magnetic nanofluids in a circular tube: An experimental study. Case Stud. Therm. Eng. 52 , 103748 (2023).

Alrowaili, Z., Ezzeldien, M., Shaaalan, N. M., Hussein, E. & Sharafeldin, M. Investigation of the effect of hybrid CuO-Cu/water nanofluid on the solar thermal energy storage system. J. Energy Storage 50 , 104675 (2022).

Rajňák, M. et al. Statistical analysis of AC dielectric breakdown in transformer oil-based magnetic nanofluids. J. Mol. Liq. 309 , 113243 (2020).

Aberoumand, S. & Jafarimoghaddam, A. Tungsten (III) oxide (WO 3 )–Silver/transformer oil hybrid nanofluid: Preparation, stability, thermal conductivity and dielectric strength. Alex. Eng. J. 57 (1), 169–174 (2018).

Alizadeh, H., Pourpasha, H., Heris, S. Z. & Estellé, P. Experimental investigation on thermal performance of covalently functionalized hydroxylated and non-covalently functionalized multi-walled carbon nanotubes/transformer oil nanofluid. Case Stud. Therm. Eng. 31 , 101713 (2022).

Pourpasha, H., Heris, S. Z. & Mohammadpourfard, M. The effect of TiO 2 doped multi-walled carbon nanotubes synthesis on the thermophysical and heat transfer properties of transformer oil: A comprehensive experimental study. Case Stud. Therm. Eng. 41 , 102607 (2023).

Amiri, A. et al. Transformer oil based multi-walled carbon nanotube–hexylamine coolant with optimized electrical, thermal and rheological enhancements. RSC Adv. 5 (130), 107222–107236 (2015).

Marulasiddeshi, H., Kanti, P. K., Prakash, S. & Sridhara, S. Investigation of entropy generation and thermohydraulic characteristics of Al 2 O 3 –CuO hybrid nanofluid flow in a pipe at different inlet fluid temperatures. Int. J. Therm. Sci. 193 , 108541 (2023).

Wanatasanappan, V. V., Kanti, P. K., Sharma, P., Husna, N. & Abdullah, M. Viscosity and rheological behavior of Al 2 O 3 –Fe 2 O 3 /water-EG based hybrid nanofluid: A new correlation based on mixture ratio. J. Mol. Liq. 375 , 121365 (2023).

Beheshti, A., Shanbedi, M. & Heris, S. Z. Heat transfer and rheological properties of transformer oil-oxidized MWCNT nanofluid. J. Therm. Anal. Calorim. 118 , 1451–1460 (2014).

Fontes, D. H., Ribatski, G. & Bandarra Filho, E. P. Experimental evaluation of thermal conductivity, viscosity and breakdown voltage AC of nanofluids of carbon nanotubes and diamond in transformer oil. Diamond Relat. Mater. 58 , 115–121 (2015).

Kanchana, S., Chithra, M. J., Ernest, S. & Pushpanathan, K. Violet emission from Fe doped ZnO nanoparticles synthesized by precipitation method. J. Lumin. 176 , 6–14 (2016).

Agrawal, N., Munjal, S., Ansari, M. Z. & Khare, N. Superhydrophobic palmitic acid modified ZnO nanoparticles. Ceram. Int. 43 (16), 14271–14276 (2017).

Pourpasha, H., Heris, S. Z. & Mousavi, S. B. Thermal performance of novel ZnFe 2 O 4 and TiO 2 -doped MWCNT nanocomposites in transformer oil. J. Mol. Liq. 394 , 123727 (2024).

Karimi Shoar, Z., Pourpasha, H., Zeinali Heris, S., Mousavi, S. B. & Mohammadpourfard, M. The effect of heat transfer characteristics of macromolecule fouling on heat exchanger surface: A dynamic simulation study. Can. J. Chem. Eng. 101 (10), 5802–5817 (2023).

Basiri, M., Goshayeshi, H. R., Chaer, I., Pourpasha, H. & Heris, S. Z. Experimental study on heat transfer from rectangular fins in combined convection. J. Therm. Eng. 9 (6), 1632–1642 (2023).

Pourpasha, H., Heris, S. Z., Mahian, O. & Wongwises, S. The effect of multi-wall carbon nanotubes/turbine meter oil nanofluid concentration on the thermophysical properties of lubricants. Powder Technol. 367 , 133–142 (2020).

Mishra, A. & Das, D. Investigation on Fe-doped ZnO nanostructures prepared by a chemical route. Mater. Sci. Eng. B 171 (1–3), 5–10 (2010).

Feng, X. & Lou, X. The effect of surfactants-bound magnetite (Fe 3 O 4 ) on the photocatalytic properties of the heterogeneous magnetic zinc oxides nanoparticles. Sep. Purif. Technol. 147 , 266–275 (2015).

Hassan, M. M., Khan, W., Azam, A. & Naqvi, A. Effect of size reduction on structural and optical properties of ZnO matrix due to successive doping of Fe ions. J. Lumin. 145 , 160–166 (2014).

Farade, R. A., Wahab, N. I. A. & Mansour, D.-E.A. The effect of nano-additives in natural ester dielectric liquids: A comprehensive review on dielectric properties. IEEE Trans. Dielectr. Electr. Insul. 30 , 1502–1516 (2023).

Farade, R. A., Wahab, N. I. A., Mansour, D.-E.A. & Soudagar, M. E. M. The Effect of nano-additives in natural ester dielectric liquids: A comprehensive review on stability and thermal properties. IEEE Trans. Dielectr. Electr. Insul. 30 , 1478–1492 (2023).

Amiri, A., Shanbedi, M., Ahmadi, G. & Rozali, S. Transformer oils-based graphene quantum dots nanofluid as a new generation of highly conductive and stable coolant. Int. Commun. Heat Mass Transf. 83 , 40–47 (2017).

Yao, W., Huang, Z., Li, J., Wu, L. & Xiang, C. Enhanced electrical insulation and heat transfer performance of vegetable oil based nanofluids. J. Nanomater. 2018 (1), 4504208 (2018).

Mehrvarz, B., Bahadori, F. & Moghaddam, S. Z. Heat transfer enhancement in distribution transformers using TiO 2 nanoparticles. Adv. Powder Technol. 30 (2), 221–226 (2019).

Mansour, D. E. A. et al. Multiple nanoparticles for improvement of thermal and dielectric properties of oil nanofluids. IET Sci. Meas. Technol. 13 (7), 968–974 (2019).

Walvekar, R. et al. Stability, thermo-physical and electrical properties of naphthenic/POME blended transformer oil nanofluids. Therm. Sci. Eng. Prog. 23 , 100878 (2021).

Maharana, M., Bordeori, M. M., Nayak, S. K. & Sahoo, N. Nanofluid-based transformer oil: Effect of ageing on thermal, electrical and physicochemical properties. IET Sci. Meas. Technol. 12 (7), 878–885 (2018).

Abid, M. et al. Dielectric and thermal performance up-gradation of transformer oil using valuable nano-particles. IEEE Access 7 , 153509–153518 (2019).

Rajnak, M. et al. Transformer oil-based magnetic nanofluid with high dielectric losses tested for cooling of a model transformer. IEEE Trans. Dielectr. Electr. Insul. 26 (4), 1343–1349 (2019).

Taghikhani, Z., Taghikhani, M. A. & Gharehpetian, G. Mineral oil based CuO nanofluid-immersed transformers analysis concerning the efficacy of nanocrystalline alloy core in reduction of losses and HST. J. Magn. Magn. Mater. 537 , 168184 (2021).

Farooq, U. et al. Cattaneo-Christov heat flux model in radiative flow of (Fe 3 O 4 –TiO 2 /Transformer oil) and (Cu–TiO 2 /Transformer oil) magnetized hybrid nanofluids past through double rotating disks. Case Stud. Therm. Eng. 45 , 102905 (2023).

Nazari, M., Jafarmadar, S. & Gohari, S. Convective heat transfer behavior and AC dielectric breakdown voltage of electric power transformer oil with magnetic colloidal nano-fluid: An experimental study. Case Stud. Therm. Eng. 45 , 103017 (2023).

Vanitha, K. & Sree Renga Raja, T. Augmenting the insulating and heat transfer properties of silicone oil with filler composite GO-CuO nanoparticles for transformer applications. J. Electron. Mater. 52 (11), 7683–7693 (2023).

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Pourpasha, H., Zeinali Heris, S., Javadpour, R. et al. Experimental investigation of zinc ferrite/insulation oil nanofluid natural convection heat transfer, AC dielectric breakdown voltage, and thermophysical properties. Sci Rep 14 , 20721 (2024). https://doi.org/10.1038/s41598-024-71452-w

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Effect of Forced Convection Heat Transfer on Vapor Quality in Subcooled Flow Boiling

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Kanatani, K. (September 6, 2024). "Effect of Forced Convection Heat Transfer on Vapor Quality in Subcooled Flow Boiling." ASME. J. Heat Mass Transfer . December 2024; 146(12): 121602. https://doi.org/10.1115/1.4066331

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A new theoretical model of vapor quality in subcooled flow boiling is proposed based on energy balance and well-known heat transfer correlations. This model takes into account the enhancement of forced convection heat transfer due to the presence of vapor. It is shown that the vapor quality predicted by our model is much less than that by a previous model for low pressure. This result demonstrates that the convective heat transfer coefficient (HTC) cannot be constant, and the effect of gas phase on forced convection heat transfer cannot be neglected even for subcooled flow boiling, particularly at low pressures. However, the difference between the present and previous models decreases as the pressure increases because (i) the increase of the convective heat transfer coefficient is weakened, and (ii) boiling heat transfer becomes dominant. The difference becomes large if the mass flux is increased or the wall heat flux is decreased, owing to the difference in the form of the convective heat flux. Furthermore, the present model has the capability of locating the point at which bulk boiling commences. In general, this saturation point moves downstream as the wall heat flux and pressure increase, and upstream as the mass flux and tube diameter increase. In addition, the present model can be simplified to a one-variable model, which is a good approximation of the original one especially for low pressures and wall heat flux and high mass flux.

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A comprehensive review of experimental investigations of forced convective heat transfer characteristics for various nanofluids

• Munish Gupta 1 ,
• Neeti Arora 1 ,
• Rajesh Kumar 2 ,
• Sandeep Kumar 2 &
• Neeraj Dilbaghi 2  

International Journal of Mechanical and Materials Engineering volume  9 , Article number:  11 ( 2014 ) Cite this article

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Nanofluids are suspension of nanoparticles (less than 100 nm) in the conventional base fluids. The dispersed solid metallic or non-metallic nanoparticles change the thermal properties like thermal conductivity, viscosity, specific heat, and density of the base fluid. Past studies focused on measuring the thermal properties of nanofluids. These suspended nanoparticles effectively improve the transport properties and heat transfer characteristics of the base fluids. Recently, heat transfer augmentation using suspensions of nanometre-sized solid particles in base liquids have been investigated by various research groups across the world. This paper reviews the state-of-the-art nanofluid studies in the area of forced convection heat transfer enhancement. The results for the heat transfer characteristics in internal flow with constant heat flux and constant wall temperature boundary conditions reported by various researchers have been compiled and reviewed. Further, in heat exchangers, the real boundary conditions are different from the constant heat flux and constant wall temperature boundary conditions. Over a span of 2 decades, the literature in this field is widespread; hence, this review would be useful for researchers to have a precise screening of a wide range of investigations in this area.

Introduction

Energy concerns have come up as the most important problem for the world's scientists and engineers. Thermal loads are increasing day by day and have wide variety of use in electronics, transportation, power plants, food industry, air conditioning, refrigeration, etc. The conventional heat transfer fluids, such as water, oil, ethylene glycol, propylene glycol are mostly used in industries. These fluids contain poor thermal properties. In order to increase heat transfer rates, the use of extended-surface thermal control technologies such as fins and micro channels, vibration of heated surface, injection or suction of fluid and applying electrical or magnetic fields has reached to the bottleneck. Therefore, new technologies with the potential to improve the thermo-physical properties of the conventional cooling fluids have been an area of great potential for researchers. The solids have better thermal properties than fluids. Ahuja ( 1975 ) and Liu et al. ( 2999 ) carried experiments to enhance the thermo-physical properties of fluids by adding micrometre- and millimetre-sized solid particles in the base liquids. However, real-world applications of these fluids are fewer due to the reasons, i.e. large-sized particles tend to quickly settle out of suspension and thereby, in passing through micro channels, cause clogging and a considerable rise in the pressure drop. Furthermore, the abrasive actions of these particles cause erosion of components and pipelines. To overcome these problems, nanosized particles dispersed in the base fluid known as nanofluids, were firstly introduced by Choi ( 1995 ) at the Argonne National Laboratory. These novel fluids indicated improved heat transfer properties such as higher thermal conductivity, long-standing stability and uniformity along with the negligible obstruction in flow channels due to very small sizes and large specific areas of the nanoparticles. The nanoparticles used to prepare the nanofluids are basically metals (e.g. Cu, Ni, Al), oxides (e.g. Al 2 O 3 , TiO 2 , CuO, SiO 2 , Fe 2 O 3 , Fe 3 O 4 , BaTiO 3 ) and some other compounds (e.g. CNT, TNT, AlN, SiC, CaCO 3 , graphene) with a size of 1 to 100 nm. The great quantum of research on heat transfer enhancement shows the appreciable growth and the necessity of heat transfer enhancement technology in the field of nanofluids.

This paper presents the comprehensive review of various experimental investigations in convective heat transfer with the use of nanofluids in laminar and turbulent flow regimes under constant wall temperature and constant heat flux boundary conditions. Further, a detailed review on the use of nanofluids in different types of heat exchangers has been presented. It is vital for reliable applications in engineering thermal systems.

Preparation of nanofluids

This section presents different methods used by researchers for the synthesis of nanoparticles and preparation of nanofluids. For making nanoparticles, the current processes for the synthesis include inert-gas condensation process, chemical precipitation, mechanical milling, chemical vapour deposition, micro-emulsions, spray pyrolysis and thermal spraying. The nanoparticles are mostly used in powdered form for making nanofluids.

In experimental studies, the preparation of nanofluids is the next most essential step. The nanofluids are not simply formed by mixing of solid particles in base liquids. Some special requirements are necessary including uniform, stable and durable suspension, minimal accumulation of particles, no chemical alteration of the fluid, etc. There are mainly two techniques used to produce nanofluids: the single-step and the two-step methods.

One-step method

Akoh et al. ( 1978 ) invented the single-step direct evaporation approach which is called the vacuum evaporation onto a running oil substrate (VEROS) technique. The original requirement behind this method was to produce nanoparticles, but it is not easy to subsequently separate the particles from the fluids to produce dry nanoparticles. Wagener et al. ( 1997 ) proposed a modified VEROS process. They put high-pressure magnetron sputtering for the preparation of suspensions with metal nanoparticles such as Silver (Ag) and Iron (Fe).

Lo et al. ( 2005 ) applied a vacuum-submerged arc nanoparticles synthesis system (SANSS) method to make nanofluid-based copper metal with various dielectric fluids including deionized water, with 30%, 50% and 70% volume ethylene glycol solution and pure ethylene glycol. They investigated that the various morphologies, which are achieved, are mainly affected and determined by the thermal conductivity of the dielectric fluids. Further, CuO, Cu 2 O and Cu-based nanofluids can also be produced by this process efficiently. The advantages of this method are that the nanoparticles agglomeration is minimized and the stability of nanofluids is increased, while the disadvantages are that the high vapour pressure fluids are not suitable with such practices and residual reactants are left in the nanofluids due to incomplete reaction or stabilization. Recently, Lo et al. ( 2006 ) also made a nickel (Ni) nano-magnetic fluid by using the SANSS method.

Two-step method

The two-step method is largely used in the synthesis of nanofluids. In this method, nanoparticles, nanotubes or other non-materials employed are first produced as dry powders by chemical or physical methods. Then the nanosized particles are dispersed in a fluid in the second processing step with the help of ultrasonic agitation, high-shear mixing, homogenizing and ball milling. The two-step method is the most beneficial method to produce nanofluids in large scale, because nanoparticle synthesis processes have already been scaled up to industrial production levels. For example, Wang et al. ( 1999 ) used this method to produce Al 2 O 3 nanofluids. Murshed et al. ( 2005 ) made TiO 2 suspension in water using this method. As compared to the one-step method, the two-step method works better for nanoparticles containing oxides, while it is not effective with metallic particles.

With the exception of the use of ultrasonication methods, certain additional processes are also coming into consideration, including pH control or addition of surface active agents (surfactants) to acquire stability of the nanofluid suspension against sedimentation. These techniques alter the surface properties of the dispersed particles and thus lower the affinity to form particle groups. It should be well-known that the selection of surfactants should rest mainly on the nanoparticles and fluid properties. Xuan and Li ( 2000 ) selected salt and oleic acid as the surfactant to increase the permanency of transformer oil - Cu and water - Cu nanofluids, respectively. Murshed et al. ( 2005 ) used oleic acid and cetyltrimethylammonium bromide (CTAB) surfactants to ensure better stability and proper dispersion of TiO 2 /water nanofluids. Hwang et al. ( 2999 ) cast-off the sodium dodecyl sulphate (SDS) during the preparation of water-based multi-walled carbon nanotube (MWCNT) nanofluids since the fibres are entangled in the aqueous suspension. Xuan et al. ( 2013 ) studied the effect of surfactants on the heat transfer nature of nanofluids. They used Cu-water nanofluids with three volume fractions and two mass fractions of sodium dodecyl benzoic sulphate (SDBS). They showed that the surfactant remarkably affects transport properties and the convective heat transfer performance of nanofluids and suppresses heat transfer enhancement effect of suspended nanoparticles. Rashmi et al. ( 2011 ) reported that stability and thermal conductivity enhancement of carbon nanotube nanofluids using gum arabic surfactants showed considerable increment in same. In general, procedures including altering of pH value, adding surfactants, and ultrasonic vibration goals at changing the surface properties of dispersed particles and reducing the formation of particle groups to obtain uniform and constant suspensions.

Nanofluid properties and non-dimensional numbers

The convective heat transfer coefficient describes the effectiveness of heat transfer. It is a function of a number of thermophysical properties of the nanofluid - the most considerable ones are specific heat, thermal conductivity, viscosity and density. These various properties of the nanofluid are found out by using classical formulas derived from a two-phase mixture under concern as a function of the particle volume concentration and individual properties can be calculated using following respective equations:

Effective density:

Specific heat:

Dynamic viscosity:

However, these properties of nanofluid are not only dependent on the volume concentration of nanoparticles, but also extremely dependent on additional constraints, including particle shape (spherical, disk shape or cylindrical), size, mixture combinations and slip mechanisms, surfactant, etc. Studies demonstrated that the thermal conductivity as well as viscosity both increase by the usage of nanofluid compared to those of base liquid.

The following dimensionless governing parameters are presented for the studies of various properties of nanofluids, namely:

Reynolds number:

Prandtl number:

Grashof number:

Rayleigh number:

Peclet number:

where, the thermal diffusivity of nanofluid is given as

Reviews of nanofluid research

The state-of-the-art reviews have been published by different researchers on nanofluid applications in heat transfer research. The summary along with the various aspects reviewed have been presented in Table  1 .

These evaluations have delivered the discussions of preparation and stability of nanofluid, theoretical and experimental studies on thermophysical properties and forced convective heat transfer characteristics of several nanofluids. Experimental and analytical studies showing various effects of particle size, shape, arrangement, volume concentration, dispersion and migration on convective heat transfer and thermo physical properties, nanofluid heat transfer and pressure drop correlations.

The above summary shows that a number of review articles are published on nanofluids but still there are many issues and matters to be fully investigated. So the present review provides the most recent studies of the convective heat transfer in order to provide database and suggestions for future works for the researchers in order to develop efficient and reliable thermal energy system.

Experimental studies on forced convective heat transfer of nanofluids

Constant heat flux boundary conditions, tungsten oxide (tio 2 ).

He et al. ( 2007 ) studied heat transfer and flow behaviour of aqueous suspensions of given nanoparticles (nanofluids) flowing upward through a vertical pipe. They observed that addition of nanoparticles into the base liquid increases the thermal conduction and the enhancement improves with increasing particle concentration and decreasing particle (agglomerate) size. The viscosity increased with increasing particle concentration and particle (agglomerate) size. For fixed flow Reynolds number and particle size of nanofluid, the convective heat transfer coefficient increased with nanoparticle concentration in both the laminar and turbulent flow regimes and it is also seemed that effect of particle concentration was more considerable in the turbulent flow regime.

Further, a study on convective heat transfer and pressure drop in a turbulent flow of aqueous solution of given nanoparticle (15 nm) through a constantly heated horizontal circular tube containing 0.1, 0.5, 1.0, 1.5 and 2.0% volume concentrations of nanoparticles was performed by Kayhani et al. ( 2012 ). Results indicated that heat transfer coefficients increased with increasing the nanofluid volume fraction but showed no change with changing the Reynolds number. At a Reynolds number of 11800, with 2.0% nanoparticles volume fraction the enhancement in the Nusselt number was observed to be about 8% for nanofluid.

Rayatzadeh et al. ( 2013 ) studied the convective heat transfer and pressure drop with and without continuous induced ultrasonic field in the reservoir tank containing nanofluid. Investigations were performed with volume concentration up to 0.25% for laminar flow regime. They noticed that the Nusselt number increased, by dispersing nanoparticles to the base fluid. It also showed that, when particle concentration increased more improvement in Nusselt number could be seen, except for volume concentration of 0.25%. The Nusselt number also showed dramatically increment with induced ultrasonic field as compared to the results obtained for without sonication. No considerable increment was observed in pressure drop.

Aluminium oxide (Al 2 O 3 )

Wen and Ding ( 2004 ) performed their experiments in the entrance region under laminar flow conditions. It has been observed that the convective heat transfer improved in the laminar flow regime by the using of Al 2 O 3 nanoparticles which is dispersed in water. The convective heat transfer showed enhancement with Reynolds number, as well as particle concentration. In the entrance region, the improvement was particularly significant and decreases with axial distance. The sole reason for the enhancement of the convective heat transfer was the improvement of the effective thermal conductivity. For a non-uniform distribution of thermal conductivity and viscosity field, the particle migration was solely responsible and there was reduction in the thermal boundary layer thickness.

Anoop et al. ( 2009 ) conducted experiments using an aqueous solution of given nanoparticles in the developing region of pipe flow to calculate the convective heat transfer coefficient with the influence of particle size. It was observed that the nanofluid with 45 nm particles showed better heat transfer coefficient than with 150 nm particles. It was concluded that the observed increase in convective heat transfer with nanofluids was not only due to intensification in thermal conductivity but also because of the effects of particle migration and thermal dispersion. Mansour et al. ( 2009 ) investigated the problem of thermally developing laminar mixed convection flow inside an inclined tube. Results showed that with an increase of particle volume concentration from 0 to 4%, the heat transfer coefficient falls marginally.

Hwang et al. ( 2010 ) measured convective heat transfer coefficient and pressure drop of Al 2 O 3 aqueous nanofluids in the fully developed laminar flow regime flowing through a consistently heated circular tube. There was more increment observed in convective heat transfer coefficient as compared to that of thermal conductivity. Based on scale analysis and numerical solutions, they had shown for the first time, the flattening of velocity profiles, induced from large gradients in bulk properties such as nanoparticle concentration, thermal conductivity and viscosity. They proposed that this flattening of the velocity profile is a potential tool for improvement of convective heat transfer coefficient higher than the thermal conductivity augmentation.

The effect of insert wire coil was reported by Chandrasekar et al. ( 2011 ) for heat transfer and friction factor characteristics for given nanoparticles with water as a base fluid. When nanofluid is used with wire coil inserts appreciable enhancement in the Nusselt number was observed. The heat transfer augmentation was credited to the thermal dispersion which flattens the temperature distribution and makes the temperature gradient between the fluid and wall steeper. There was no noteworthy increase in pressure drop for nanofluid.

Yu et al. ( 2012 ) investigated convective heat transfer and the thermophysical properties of specified nanoparticles in solution of polyalphaolefin (PAO) containing both spherical and rod-like nanoparticles. The effective thermal conductivity and effective viscosity of the nanofluids were measured and compared to predictions from various existing theories in the literature. It was noticed that, in addition to the particle volume fraction, other parameters, including the aspect ratio, the dispersion state and the aggregations of nanoparticles as well as the shear field have significant impact on the effective properties of the nanofluids, especially of those containing non-spherical particles. The convection heat transfer coefficient and pressure drop were also measured for the nanofluids in the laminar flow regime. The results indicated that, in order to correctly interpret the experimental data of nanofluids for a convective flow containing non-spherical nanoparticles, the shear-induced alignment and orientation motion of the particles must be considered.

Sahin et al. ( 2013 ) studied the convective heat transfer, the pressure drop characteristics and heat transfer augmentation of water based nanofluid with volume concentration of 0.5%, 1%, 2% and 4% inside a circular tube in the turbulent flow regime. For the events, in which the particle volume fractions were lesser than 2 vol.% addition nanoparticles into pure water heat transfer enhanced. The Nusselt number improved with the rise in the Reynolds number as well as the particle volume fraction up to the particle volume concentration of 1 vol.%. It was concluded that for the concentrations of Al 2 O 3 particles higher than 1 vol.% were not appropriate for heat transfer enhancement. For the particle volume concentrations larger than 1 vol.%, the viscosity growth of the nanofluids was much more dominating than the thermal conductivity of the nanofluids on heat transfer enhancement. The friction factor amplified with rise in the particle volume concentration, due to increase in the viscosity. The highest heat transfer enhancement was achieved at Reynolds number of 8000 and 0.5 vol.%.

Esmaeilzadeh et al. ( 2013 ) considered hydrodynamics and heat transfer characteristics of γ-Al 2 O 3 nanoparticles (15 nm) with distilled water as a base liquid inside a circular tube in laminar flow regime. It was observed that by increasing the particle volume fraction leads to enhancement of convective heat transfer coefficient. Results revealed that the average heat transfer coefficient increased by 6.8% with 0.5% volume concentration and enhanced by 19.1% at 1% volume concentration in comparison with distilled water. The heat transfer coefficient increases with the increase in the heat flux.

Copper (Cu) and copper oxide (CuO)

Suresh et al. ( 2012 ) studied the convective heat transfer and friction factor characteristics of the plain and helically dimpled tube under turbulent flow using CuO/water nanofluid as working fluid. It was revealed that there was an appreciable growth in heat transfer rate with the use of nanofluids in a helically dimpled with negligible increase in friction factor compared to plain tube. The experimental results depicted that the Nusselt number with dimpled tube and nanofluids was about 19%, 27% and 39% (for 0.1%, 0.2% and 0.3% volume concentrations respectively) higher than the Nusselt number obtained with plain tube and water under turbulent flow. The experimental results showed that the dimpled tube friction factors were about 2–10% higher than the plain tube of isothermal pressure drop.

Razi et al. ( 2011 ) studied the pressure drop and heat transfer characteristics of nanofluid flow inside horizontal flattened tubes. When nanofluids flow in flattened tubes, they have superior heat transfer characteristics rather than in the round tube. Highest heat transfer enhancement of 16.8%, 20.5% and 26.4% was achieved for nanofluid flow compared to pure oil flow with 2% weight concentration inside the round tube and flattened tubes with internal heights of 8.3 mm and 6.3 mm, respectively.

Saeedinia et al. ( 2012 ) investigated the heat transfer and pressure drop characteristics of CuO/Base oil nanofluid in a smooth tube with different wire coil inserts in the laminar flow regime. An average, 45% increase in heat transfer coefficient and 63% penalty in pressure drop was observed at the highest Reynolds number inside the wire coil inserted tube with the highest wire diameter (WC3).

Hashemiand Akhavan-Behabadi ( 2012 ) performed an empirical study on heat transfer and pressure drop characteristics of CuO–base oil nanofluid flow in a horizontal helically coiled tube. Nanofluids showed better heat transfer characteristics when flowing in a helical tube rather than in the straight tube. Compared to base oil flow, maximum heat transfer enhancement of 18.7% and 30.4% was obtained for nanofluid flow with 2% weight concentration inside the straight tube and helical tube, respectively.

Selvakumar and Suresh ( 2012 ) showed the performance of convective heat transfer of aqueous nanofluid in an electronic heat sink. As volume flow rate and nanoparticles volume concentration increases, the convective heat transfer coefficient of water block was found to be increased and the maximum rise was 29.63% for the 0.2% volume concentration compared to deionized water. Based on the pressure drop in the water block, pumping power for the deionized water and nanofluids were evaluated and an average increase was 15.11% for the nanofluid volume concentration of 0.2% compared to deionized water.

Yu et al. ( 2013 ) performed the experiments on convective heat transfer with Therminol 59 based nanofluids under turbulent flow regime, containing copper nanoparticles at particle volume concentrations of 0.50% and 0.75%. The heat transfer coefficients calculated from the predicted thermophysical properties of the nanofluids, have enhanced as much as 18% with the introduction of low concentrations (<2.00 vol.%) of nanoparticles for high temperatures conditions. Because therminol-59 is a commonly-used high-temperature heat transfer fluid, that made copper in therminol-59 nanofluids very attractive for many commercial applications.

Ferrous oxide (Fe 3 O 4 )

Sundar et al. ( 2012 ) performed experiments for horizontal circular tube with and without twisted tape inserts for convective heat transfer and friction factor characteristics of magnetic nanofluid under turbulent flow regime. Heat transfer and friction factor enhancement of 0.6% volume concentration of nanofluid in a plain tube with a twisted tape insert of twist ratio H/D = 5 is 51.88% and 1.231 times compared to water flowing in a plain tube under same Reynolds number.

Carbon nanotubes (CNT)

Ding et al. ( 2006 ) showed the heat transfer behaviour of aqueous suspensions flowing through a horizontal tube. The flow condition, CNT concentration and the pH level have significant impact on heat transfer behaviour and the effect of pH was observed to be small. The augmentation was mainly dependent on the axial distance from the inlet of the test section; the augmentation showed rise, reached to the highest, and then fell with growing axial distance.

Chen et al. ( 2008 ) investigated heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids). The results showed a small thermal conductivity enhancement of ~3% at 25°C and ~5% at 40°C for the 2.5 wt. % nanofluid. Despite the small thermal conduction enhancement, an excellent enhancement was observed on the convective heat transfer coefficient, which was much higher than that of the thermal conductivity enhancement.

Garg et al. ( 2009 ) studied with the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids. The maximum percentage enhancement in thermal conductivity was a 20% increased considerably after 24°C. At Reynolds number of 600 ± 100, the largest percentage improvement in heat transfer coefficient was 32%. There was continuous increment in heat transfer coefficient with axial distance. The contribution of significant increase in thermal conductivity with the rise of bulk temperature with axial distance was the reason behind this phenomenon.

Amrollahi et al. ( 2010 ) measured the convective heat transfer coefficients of water-based FWNT nanofluid through a uniformly heated horizontal tube in entrance region under both laminar and turbulent regimes flowing. For the first time, effective parameters such as Reynolds number, mass fraction and temperature, altogether in entrance region has been compared to calculate the convective heat transfer coefficients for functionalized MWNT nanofluid. The experimental results indicated that at a concentration of 0.25 wt. %, the convective heat transfer coefficient of these nanofluids increased up to 33–40% compared with pure water in laminar and turbulent flows respectively at 20°C.

Liu and Liao ( 2010 ) presented the forced convective flow and heat transfer characteristics of aqueous drag-reducing fluid with the carbon nanotubes addition. A new kind of aqueous drag-reducing fluid with carbon nanotubes (CNTs) was developed. The new working fluid was an aqueous CTAC (cetyl trimethyl ammonium chloride) solution with CNTs added and has both special effects of drag-reducing and heat transfer enhancement. Results indicated that there were no obvious differences of the drag-reducing characteristics between conventional drag-reducing fluid and new drag-reducing nanofluid. However, there were obvious differences of the heat transfer characteristics between both fluids. The heat transfer characteristics of new drag-reducing nanofluid have strong dependencies on the liquid temperature, the nanoparticles concentration and the CTAC concentration.

Further, experiments were performed by Behabadi et al. ( 2012 ) on heat transfer improvement of a nanofluid flow inside vertical helically coiled tubes in the thermal entrance region. If nanofluid was used instead of the base fluid, the results showed that the Nusselt number increased up to 45% in the tested straight tube. The heat transfer coefficient enhancement was calculated about 80%. The heat transfer rate increases noticeably on implementation of a helical coil instead of a straight tube. The Nusselt numbers acquired 3 to 7 times higher for the base fluid inside tested helical coils than the values evaluated for the base fluid inside straight tubes with a similar length of the coils. Finally, it was observed that the combination of the two enhancing methods has a noticeably high capability to the heat transfer rate.

Wang et al. ( 2013 ) reported the heat transfer and pressure drop of nanofluids containing carbon nanotubes (CNT) in a horizontal circular tube. A considerable enhancement in the average convective heat transfer was also observed compared with the distilled water. For the nanofluids with volumetric concentration of 0.05% and 0.24%, the heat transfer enhancement are 70% and 190% at Reynolds number of about 120 respectively, while the enhancement of thermal conductivity was less than 10%, therefore, it was concluded that the large heat transfer increase cannot be solely attributed to the enhanced thermal conductivity.

Silicon oxide (SiO 2 )

Azmi et al. ( 2013 ) determined the forced convection heat transfer and friction factor with SiO 2 nanofluid in the turbulent flow regime. The Nusselt number and friction factor at 3.0% nanofluid particle concentration was respectively greater than the values of water by 32.7% and 17.1%. The pressure drop increased with particle concentration up to 3.0% and decreases thereafter. The nanofluid friction factor decreased with increase in Reynolds number at any concentration.

Comparative study among two or more nanoparticles

Kim et al. ( 2009 ) performed a study through a circular straight tube with stable nanofluids, i.e. water-based suspensions of alumina and amorphous carbonic nanoparticles prepared by two and one-step methods in the laminar and turbulent flow regime. The increment in thermal conductivity and convective heat transfer coefficient was 8% and 20%, respectively in alumina nanofluids containing 3 vol. % of suspended particles. For amorphous carbonic nanofluids, the thermal conductivity was similar to that of water, and the convective heat transfer coefficient increased by only 8% in laminar flow. The convective heat transfer enhancement at the entrance region was due to the movements of nanoparticles.

Rea et al. ( 2009 ) examined convective heat transfer and viscous pressure losses for alumina–water and zirconia– water nanofluids with a vertical heated tube in a flow loop laminar flow regime. For alumina–water nanofluid, the heat transfer coefficients obtained to rise by 17% and 27% in the entrance region and in the fully developed region respectively at 6 vol. % with respect to pure water. For zirconia–water nanofluid, at 1.32 vol.%, heat transfer coefficient increased by nearly 2% in the entrance region and 3% in the fully developed region. The calculated pressure loss for the nanofluids was in general much more than that of pure water.

Vajjha et al. ( 2010 ) presented the new correlations for the convective heat transfer and the friction factor developed from the experiments of nanoparticles comprised of aluminium oxide, copper oxide and silicon dioxide dispersed in 60% ethylene glycol and 40% water by mass. Heat transfer coefficient of nanofluids showed an increase with the particle volumetric concentration. For example, at a Reynolds number of 7240, the percentage increase in the heat transfer coefficient over the base fluid for a 10% Al 2 O 3 nanofluid was 81.74%. The pressure loss of nanofluids also increased with an increase in particle volume concentration. The increase of pressure loss for a 10% Al 2 O 3 nanofluid at a Reynolds number of 6700 was about 4.7 times than for the base fluid. This was due to the growth in the viscosity of the nanofluid with concentration.

Hybrid nanofluids

Suresh et al. ( 2011 ) showed the effect of a new type Al 2 O 3 –Cu/water hybrid nanofluid in heat transfer. They showed that Al 2 O 3 –Cu/water hybrid nanofluids have somewhat more friction factor when compared to Al 2 O 3 /water nanofluid at 0.1 vol.%. In a straight circular tube, heat transfer performance improved with Al 2 O 3 –Cu hybrid nanoparticles suspension when compared to that of pure water. The average enhancement in Nusselt number for Al 2 O 3 –Cu/water hybrid nanofluid was 10.94% in comparison with that of pure water. With growing Reynolds number, the convective heat transfer coefficient rises. The experimental results of hybrid nanofluid indicated highest enhancement of 13.56% in Nusselt number at a Reynolds number of 1730 when compared to pure water for laminar flow.

The summary of experimental studies based on forced convection for various nanofluids under constant heat flux boundary conditions and the contrivances suggested by the several researchers is given in Table  2 . A graphical representation of Nusselt versus Reynolds number and heat transfer coefficient versus Reynolds number of various nanofluids at different volume concentrations for turbulent flow regime are depicted in Figures  1 and 2 .

Graphical representation of Nusselt and Reynolds number for various nanoparticles at different volume concentrations for turbulent flow regime.

Graphical representation of heat transfer coefficient and Reynolds number for various nanoparticles at different volume concentrations for turbulent flow regime.

The constant wall temperature boundary conditions

Fotukian and Esfahany ( 2010a ) worked on circular tube with γ-Al 2 O 3 /water nanofluid. They studied the convective heat transfer under turbulent flow regime with nanoparticles having volume fraction, less than 0.2% in the dilute nanofluids. It was observed that, at the Reynold number of 10,000, the heat transfer coefficient increased with 48% compared to pure water with 0.054% volume concentration. It was also noticed that, no further heat transfer enhancement occurred with increasing the nanoparticles concentration. The ratio of the convective heat transfer coefficient of nanofluid to that of pure water reduced with Reynolds number. When the nanofluid streamed in the tube, the wall temperature of test tube decreased considerably compared to the case related to water flowing in the tube. There was 30% intensification in pressure drop of nanofluid at Reynolds number of 20,000 with 0.135% volume concentration as compared to pure water. With increasing the volume fraction of nanoparticles, the pressure drop of nanofluid increased.

Heyat et al. ( 2012 ) explored convective heat transfer characteristics of Al 2 O 3 / water nanofluids in the fully developed turbulent flow regime. The results showed that the heat transfer coefficient of nanofluid was higher than that of the base fluid and increased with increasing the particle concentrations. Moreover, the Reynolds number had a little effect on heat transfer enhancement. The experimental data were compared with traditional convective heat transfer and viscous pressure drop correlations for fully developed turbulent flow.

Copper oxide (CuO)

The CuO/water nanofluid convective heat transfer in turbulent regime inside a tube was investigated by Fotukian and Esfahany ( 2010b ). The nanoparticles volume fractions less than 0.3% were used in the dilute nanofluids. As compared to pure water, the heat transfer coefficient improved by 25%. It was found that there was not so much effect on enhancement of heat transfer by increasing the nanoparticles concentration in the range of studied concentrations. Also the ratio of the convective heat transfer coefficient of nanofluid to that of pure water diminished with enhancing Reynolds number. When the nanofluid streamed in the tube, the wall temperature of test tube decreased considerably compared to the case of water flowing in the tube. With 0.03% volume concentration of nanofluid, the maximum increase in pressure drop was about 20%.

A steady state flow in helically coiled tubes was observed by Akbaridoust et al. ( 2013 ). In this study, heat transfer coefficient and pressure drop of nanofluid were compared to that of base liquid at same flow conditions in different helically coiled tubes. It was observed that, heat transfer and pressure drop was higher for tubes with greater curvature ratio. In various helical coiled tubes, nanofluid with larger values of particle volume concentration exhibited more heat transfer coefficient and pressure drop. Due to the low coil pitch, the coils with equal curvature ratio and different torsion ratio had the same results.

Ferrouillat et al. ( 2011 ) examined the convective heat transfer of specified nanoparticles in base fluid water existing in colloidal suspensions (5–34 wt. %) in a flow loop with a horizontal tube test section whose wall temperature was imposed. Results indicated that the heat transfer coefficient values have increased from 10% to 60% compared to those of pure water. They also showed that the general trend of standard correlations was respected. In order to evaluate the benefits provided by the enhanced properties of the nanofluids studied, an energetic performance evaluation criterion (PEC) is defined. This PEC decreases as the nanoparticles concentration is increased.

The experiment was performed by Anoop et al. ( 2012 ) on forced convective heat transfer of nanofluids in a microchannel. The experimental results indicated that heat transfer increased with a flow rate for both water and nanofluid samples; however, for the nanofluid samples, heat transfer enhancements occurred at lower flow rates and heat transfer degradation occurred at higher flow rates (compared to that of water). Electron microscopy of the heat-exchanging surface revealed that surface modification of the microchannel flow surface occurred due to nanoparticles precipitation from the nanofluid. Hence, the fouling of the microchannels by the nanofluid samples is believed to be responsible for the progressive degradation in the thermal performance, especially at higher flow rates.

Ashtiani et al. ( 2012 ) investigated heat transfer characteristics of MWCNT-heat transfer oil nanofluid flow inside horizontal flattened tubes. Nanoparticles weight fractions used were 0%, 0.1%, 0.2%, and 0.4%. In addition, the heat transfer coefficient increased at a constant volumetric flow rate as the tube profile became more flattened and the hydraulic diameter decreased. Increasing volumetric flow rate results in heat transfer enhancement for a given flattened tube at a constant nanoparticles weight fraction. The heat transfer rate enhanced remarkably on utilizing nanofluids instead of the base fluid. As higher the nanoparticles weight fraction, the more the rate of heat transfer augmentation.

An empirical study performed by Pakdaman et al. ( 2013 ) on pressure drop characteristics of nanofluid flow inside vertical helically coiled tubes for the laminar flow regime. Heat transfer oil was used as the base fluid, and (MWCNTs) were utilized as the additive to provide the nanofluids. Regarding the experimental study, application of helical coiled tubes instead of straight ones increased the pressure drop exponentially. As compared to the base fluid flow, nanofluid flows showed greater rates of pressure drop irrespective of the tube geometry in which the fluid flows. Finally according to the findings, the combination of the two processes used in this investigation causes the pressure of the fluid flow to drop considerably along the test section.

Comparison study among two or more nanoparticles

The experiment was performed by Heris et al. ( 2006 ) on convective heat transfer of oxide nanofluids under laminar flow regime. The results emphasized that the single phase correlation with nanofluids properties (homogeneous model) was not able to forecast heat transfer coefficient improvement of nanofluids. For the comparison between CuO/water and Al 2 O 3 /water nanofluids, the experimental results showed that heat transfer coefficient ratios for nanofluid to the homogeneous model are near to each other in low concentration but by enhancing the volume concentration, more heat transfer augmentation for Al 2 O 3 /water observed.

Hojjat et al. ( 2011 ) studied turbulent flow forced convective heat transfer behaviour of non-Newtonian nanofluids in a circular tube. By adding homogeneously γ- Al 2 O 3 , TiO 2 and CuO nanoparticles into the base fluid, three types of nanofluids were prepared. The rise in the convective heat transfer coefficient of nanofluids was more than the intensification in the effective thermal conductivity of nanofluids.

Meriläinen et al. ( 2013 ) showed the effect of particle size and shape on heat transfer characteristics and pressure losses in water-based nanofluids under turbulent flow regime. They found that on the basis of constant Reynolds number in range of 3000–10,000, average convective heat transfer coefficients of nanofluids improved up to 40% when compared to the base liquid. As compared to the base fluids, the rise in the dynamic viscosity of nanofluids indicated considerable pressure losses impact. To account for this, by matching the improved heat transfer performance to the augmented pumping power requirement, the convective heat transfer efficiency η was determined. Growing the nanoparticles volume concentration above 2% enhanced the heat transfer coefficient but at the similar time sinks heat transfer efficiency ‘η’ due to pressure losses, which outcome from the amplified fluid density and viscosity.

The summary of above experimental forced convection studies under constant wall temperature boundary conditions for various nanofluids is given in Table  3 .

Heat exchangers

Duangthongsuk et al. (Duangthongsuk) showed the heat transfer enhancement and pressure drop characteristics of water based nanofluid in a double-pipe counter-current heat exchanger. The results showed that the convective heat transfer coefficient of nanofluid was 6–11% higher than that of the base liquid. With an increase in the mass flow rate of the hot water and nanofluid, the heat transfer coefficient of the nanofluid increased. Also, heat transfer coefficient of the nanofluid increased with the decrease in the nanofluid temperature, and the temperature of the heating fluid had no significant effect on it. Again, similar work was performed by Duangthongsuk et al. ( 2010 ). This time results showed that the heat transfer coefficient of nanofluid was much more than that of the base fluid and augmented with improving particle concentrations and the Reynolds number. The heat transfer coefficient of nanofluids was nearly 26% more than that of pure liquid. It was also emphasized that the heat transfer coefficient of the nanofluids was approximately 14% lower than that of base fluids at a volume concentration of 2.0 vol.% for given conditions. Increasing the volume concentrations, the pressure drop of nanofluids increased. It was also observed that the pressure drop of nanofluids was somewhat more than the base liquid.

Sajadi et al. ( 2011 ) investigated the convective heat transfer and pressure drop of aqueous suspension of nanofluid in a circular tube in the turbulent flow regime, where the volume fraction of nanoparticles in the base fluid was less than 0.25%. The results showed that heat transfer rate augmented significantly on the addition of small amounts of nanoparticles to the base fluid. There was no much effect on heat transfer enhancement by increasing the volume fraction of nanoparticles. The pressure drop of nanofluid increased with increasing the volume fraction of nanoparticles. The maximum pressure drop was about 25% greater than that of pure water which occurred in the highest volume fraction of nanofluid (0.25%) at Reynolds number of 5000.

Arani et al. ( 2013 ) investigated the convection heat transfer characteristics of water based nanofluid in fully developed turbulent flow. It was observed that all nanofluids, with particles size diameter (10, 20, 30 and 50 nm) showed better Nusselt number than the base liquid. It was further noticed that higher thermal performance was observed by the nanofluid with 20 nm particles size diameter. The average Nusselt number increased with the increase in the Reynolds number and particle volume concentration.

Aluminium Oxide (Al 2 O 3 )

Pandey et al. ( 2012 ) investigated effects of nanofluid (2, 3 and 4 vol. %) and water as coolants on exergy loss, heat transfer and frictional losses, and in a counter flow corrugated plate heat exchanger. It was noticed that the heat transfer characteristics enhance with intensification of Reynolds and Peclet number and with reduction in nanofluid concentration. For a given pumping power more heat could be extracted by the nanofluids relative to water, though with the lowest concentration of nanofluids, the maximum heat transfer rate was found. The non-dimensional exergy loss was observed to remain constant for water. Among the four coolants considered for the experiment, the non-dimensional exergy loss was the lowest with 2 vol. % nanofluid for a coolant flow rate up to 3.7 l lpm beyond which water gave the least value.

Wu et al. ( 2013 ) investigated convective heat transfer characteristics and pressure drop of water and five aqueous suspensions of nanofluids of weight concentrations from 0.78% wt. to 7.04% wt. inside a double-pipe helically coiled heat exchanger for both laminar flow and turbulent flow. Effect of nanoparticles on the critical Reynolds number was negligible. No anomalous heat transfer enhancement was found for both laminar flow and turbulent flow regimes. According to the constant flow velocity basis, the heat transfer enhancement of the nanofluids compared to water is from 0.37% to 3.43%.

Again the work is done on double tube heat exchanger by Darzi et al. ( 2013 ) on heat transfer and flow characteristics of water based nanofluid, and found out the effects of nanofluid with a mean diameter of 20 nm on heat transfer, pressure drop and thermal performance of a double tubes heat exchanger. The effective viscosity of nanofluid was measured in various temperatures ranging from 27°C to 55°C.

Khedkar et al. ( 2013 ) concentrated on the study of the concentric tube heat exchanger for water to nanofluids heat transfer with various concentrations of nanoparticles into base fluids and application of nanofluids as working fluid. It observed that, 3% nanofluids shown optimum performance with overall heat transfer coefficient 16% greater than water.

A study is reported by Tayal et al. ( 2999 ) on the forced convective heat transfer and flow characteristics of a nanofluid consisting of water and different volume concentrations of specified nanoparticles, nanofluid (0.3-2) % flowing in a horizontal shell and tube heat exchanger counter flow under turbulent flow conditions. The results showed that the convective heat transfer coefficient of nanofluid was slightly higher than that of the base liquid at same mass flow rate and at the same inlet temperature. The heat transfer coefficient of the nanofluid increases with an increase in the mass flow rate and with the increase of the volume concentration of the Al 2 O 3 nanofluid. However, increasing the volume concentration caused increase in the viscosity of the nanofluid leading to increase in friction factor.

The convective heat transfer characteristics were determined by Kumaresan et al. ( 2012 ) based CNT nanofluids in a tubular heat exchanger. The results indicated that the maximum enhancement in convective heat transfer coefficient was 160% for the nanofluid containing 0.45 vol. % MWCNT, which could not be attributed uniquely by improved thermal conductivity of the nanofluids. Further, there was a significant decrease in Reynolds number for a known velocity for all the nanofluids. The augmentation in the friction factor is minor at a greater velocity and greater temperature for the MWCNT nanofluids with 0.15 vol. %. Yet again, similar investigation was accomplished by Kumaresan et al. ( 2013 ) with the similar heat exchanger of several lengths for energy efficient cooling/heating system. In contrast to conventional heat transfer concept, the value of the Nusselt number for the nanofluids showed increment with the fall in the Reynolds number as the MWCNT concentration growths. The results revealed that in the entrance region, there was notable improvement in the convective heat transfer coefficient. Migration of the carbon nanotubes was the possible reason for the abnormal augmentation in the heat transfer coefficient for the smaller length of the test section. That migration of carbon nanotubes did not permit the thermal boundary layer to grow at the faster speed.

Copper Oxide (CuO)

Kannadasan et al. ( 2012 ) presented the comparison of heat transfer and pressure drop characteristics of CuO/water nanofluids in a helically coiled heat exchanger held in horizontal and vertical positions. Experiments were conducted using water and CuO/water nanofluids of 0.1% and 0.2% volume concentrations in the turbulent flow regimes. The experimental results showed that in the enhancement of convective heat transfer coefficient and friction factors of nanofluids, there was no much difference between horizontal and vertical arrangements compared to water. The enhancement in internal Nusselt numbers was high for higher concentration nanofluids at turbulent flow irrespective of the positions of the helically coiled heat exchanger.

Godson et al. ( 2011 ) examined the convective heat transfer of nanofluids; experiments were performed using nanofluid made with given nanoparticles with water as base fluid in a horizontal 4.3 mm inner-diameter tube-in-tube counter-current heat transfer test section under laminar, transition and turbulent flow regimes. Experiments showed that convective heat transfer coefficient improved with the suspended nanoparticles by as much as 28.7% and 69.3% for 0.3% and 0.9% of silver content, respectively. Again same investigator Godson et al. [(Godson et al. ᅟ )] performed their work by taking same nanofluid in a shell and tube heat exchanger. The results indicated an increase in convective heat transfer coefficient and effectiveness of nanofluids as the particle volume concentration was increased. A maximum enhancement in convective heat transfer coefficient of 12.4% and effectiveness of 6.14% was recorded.

Further, investigation by taking graphite nanoparticles was performed by Yang et al. ( 2005 ) on heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in a laminar flow. At low weight fraction loadings, the graphite nanoparticles increased the static thermal conductivities of the fluid significantly. However, the experimental results revealed that there was less increase in heat transfer coefficient than predicted by either the conventional heat transfer correlations for homogeneous fluids.

Zamzamian et al. ( 2011 ) examined turbulent flow forced convective heat transfer coefficient in nanofluids of Al 2 O 3 /EG and CuO/EG in a double pipe and plate heat exchangers. They evaluated the effects of operating temperature and particle concentration on the forced convective heat transfer coefficient of the nanofluids. The outcomes showed significant enhancement in convective heat transfer coefficient of the nanofluids as compared to the base fluid, ranging from 2% to 50%. Furthermore, the outcomes showed that the convective heat transfer coefficient of nanofluid growths with increasing nanofluid temperature and nanoparticles concentration.

Further, the heat transfer characteristics of γ-Al 2 O 3 /water and TiO 2 /water nanofluids were measured under turbulent flow condition in a shell and tube heat exchanger by Farajollahi et al. ( 2010 ). There was noteworthy improvement in heat transfer characteristics by adding nanoparticles to the base fluid as observed in results. When compared heat transfer behaviour of two nanofluids indicated that at a certain Peclet number and optimum nanoparticle concentration, heat transfer characteristics of TiO 2 /water nanofluid were higher than those of γ-Al 2 O 3 /water nanofluid while γ-Al 2 O 3 /water nanofluid own superior heat transfer behaviour at larger nanoparticle concentrations.

The comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger was given by Maré et al. ( 2011 ). The first was composed of oxides of alumina (γ-Al 2 O 3 ) dispersed in water and the second one was aqueous suspensions of nanotubes of carbons (CNTs). The viscosity of the nanofluids was measured as a function of the temperature between 2° and 10°C. An experimental device, containing three thermal buckles controlled in temperature and greatly instrumented permitted to study the thermal convective transfers. The evolution of the convective coefficient was presented according to the Reynolds number, at low temperature from 0 to 10°C and for the two aforementioned nanofluids.

Additionally, Tiwari et al. ( 2013 ) investigated the heat transfer performance of the plate heat exchanger employing several nanofluids (CeO 2 , Al 2 O 3 , TiO 2 and SiO 2 ) for various volume concentrations. The study depicted that CeO 2 /water yielded best performance (maximum performance index enhancement of 16%) with comparatively minor optimum concentration (0.75 vol. %) within examined nanofluids.

The summary of above experimental forced convection studies of heat exchangers for various nanofluids is given in Table  4 .

Discussions

The literature review reveal that nanofluids considerably enhance the heat transfer ability of conventional heat transfer liquids including oil or water or ethylene glycol or propylene glycol by dispersing nanoparticles in these fluids. It is understood that following mechanisms are responsible for enhancement of heat transfer coefficient in nanofluids

Increasing particle volume concentration and decreasing particle (agglomerate) size.

Dispersion of dispersed nanoparticles.

Ultrasonication

Non-uniform distribution of thermal conductivity and viscosity field due to influence of particle migration.

Thermal boundary layer thickness reduction.

Particle migration results in flattened velocity profile induced by Brownian diffusion and thermophoresis.

Particle re-arrangement under shear, enhanced wettability and particle shape effect and structuring.

Rise in value of thermal conductivity and Reynolds number of nanofluids.

One of the expected reasons of enhanced heat transfer performance of nanofluids is the reduction in boundary layer thickness by mixing effects of particles near the wall. The application of wire-coil inserts or dimpled tube can be a better option compared to twisted tape, longitudinal strip or spiral rod inserts because the wire-coil inserts or dimpled tube largely interrupts the flow near the wall while the twisted tape or longitudinal tape inserts interrupts the whole flow field. Additionally, wire-coil inserts and dimpled tube have own benefits of lower pressure drop, less cost, easy installation and removal (Chandrasekar et al. 2010 ; Suresh et al. 2012 ; Saeedinia et al. 2012 ; Hashemi & Akhavan-Behabadi 2012 ; SyamSundar et al. 2012 ; Akbaridoust et al. 2013 ; Kannadasan et al. 2012 ). For augmentation of heat transfer rate MWCNT is a promising candidate in specified base fluid because it has shear thinning behaviour at boundary layers so it increases the thermal conductivity which is solely contributes to heat transfer rate (Garg et al. 2009 ; Amrollahi et al. 2010 ; Liu & Liao 2010 ; Akhavan-Behabadi et al. 2012 ; Wang et al. 2013 ; Ashtiani et al. 2012 ; Fakoor-Pakdaman et al. 2013 ; Kumaresan et al. 2012 ; Kumaresan et al. 2013 ). From the above review, the maximum enhancement of 190% in heat transfer as compared to de-ionized water was observed by Wang et al. ( 2013 ) at 0.24 vol.%. For non-spherical nanoparticles, some other parameters including the aspect ratio, the dispersion state and aggregations of nanoparticles as well as shear field have significant impact on effective properties of nanofluid, convection heat transfer coefficient and pressure drop observed by Yu et al. ( 2012 ). It is noticed by Yu et al. ( 2013 ) that therminol 59 shows very attractive features for many commercial applications. Applications of nanofluids have been explored in the literature ( 2013 ) for cooling of micro-devices due to anomalous enhancements in their thermophysical properties as well as due to their lower susceptibility to clogging.

Some of the contradictory behaviours were also observed in this study, Anoop et al. ( 2009 ) performed convective heat transfer experiments employing an aqueous solution of Al 2 O 3 nanoparticles in developing region of pipe flow. They observed heat transfer coefficient falls marginally with rise in particle volume concentration from 0 to 4% range. It was noticed by Sahin et al. ( 2013 ) that concentration of Al 2 O 3 particles higher than 1 vol.% were not suitable for heat transfer enhancement, in their study of convective heat transfer. Fotukian and Esfahany ( 2010a ; 2010b ) observed the other contradictory behaviour in their study that increasing nanoparticle concentration did not show much effect on heat transfer improvement in turbulent flow regime (5000–35000). The maximum value of 48% increase in heat transfer coefficient compared to pure water for 0.054 vol.% at Reynolds number of 10000. Sajadi et al. ( 2011 ) reported that there was no much effect on heat transfer enhancement by increasing the volume fraction of TiO 2 nanoparticles above 0.25%. A similar report was observed by Pandey et al. ( 2012 ), by increasing nanoparticles volume concentration above 2%, there is not so much effect on heat transfer enhancement.

Conclusions

A comprehensive review on forced convection heat transfer characteristics with different nanofluids based on experimental investigations with constant heat flux, constant wall temperature boundary conditions and in heat exchangers is presented in this review paper. Most of the experimental studies showed that nanofluids demonstrate an improved heat transfer coefficient compared to its base fluid. Further it increases significantly with increasing concentration of nanoparticles as well as Reynolds number. The use of nanofluids in a broad range of applications is promising but there is lack of agreement between experimental results from different research groups. Hence, experimental studies are desired to understand the heat transfer characteristics of nanofluids and recognize innovative and unique applications for these fields.

Future directions and challenges

Nanofluids revealed extensive ways in the applications of thermal management systems. Consequently, research efforts are essential to provide attention on the heat transfer applications of nanofluids in engineering, medical and space applications. Some plausible work which can be performed in coming future by researchers listed below:

In future, further efforts are essential to give concentration on outcomes of new models and correlations to forecast accurately convective heat transfer with small deviation with the experimental results and general correlation equations should be developed for use in industrial applications.

The high cost of the nanofluid is one of the major obstacles to employ nanofluids in wide spread range of applications. Efforts should be made to develop new methods for production of nanofluids to make them cost effective and be made use in use for commercial applications.

The concept of hybrid nanofluid is emerging, so further systematic experimental studies should be performed in which a suitable combination of cost and quantity should be performed such that high cost of nanoparticles bearing good properties like thermal conductivity, viscosity, density, specific heat and surface tension etc. is suitably hybridized with nanoparticles bearing low cost and form nanoparticles having better and improved properties and control on an overall cost.

Many researchers have performed work in this field, yet it is emerging and developing and many investigations are still remaining to be performed. Nanofluid is a potential candidate in the field of enhancement of heat transfer rate.

Nomenclature

c p Specific heat (J/Kg K)

D Diameter of copper tube (m)

k Thermal conductivity (W/m K)

h Heat transfer coefficient (W/m 2  K)

Nu Nusselt number

q” Heat flux (W/ m 2 )

Pr Prandtl number

Re Reynolds number

ρ Density (kg/m 3 )

φ Volume fraction

β Ratio of nanolayer thickness

μ Dynamic viscosity (Pa s)

f Base fluid

nf Nanofluids

AbbasianArani, AA, & Amani, J. (2013). Experimental investigation of diameter effect on heat transfer performance and pressure drop of TiO 2 –water nanofluid. Exp Thermal Fluid Sci, 44 , 520–533.

Article   Google Scholar  

Ahuja, AS. (1975). Augmentation of heat transport in laminar flow of polystyrene suspensions. 1. Experiments and results. J Appl Phys, 46 , 3408.

Akbaridoust, F, Rakhsha, M, Abbassi, A, & Saffar-Avval, M. (2013). Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model. Int J Heat Mass Transf, 58 , 480–491.

Akhavan-Behabadi, MA, Fakoor Pakdaman, M, & Ghazvini, M. (2012). Experimental investigation on the convective heat transfer of nanofluid flow inside vertical helically coiled tubes under uniform wall temperature condition. International Communications in Heat and Mass Transfer, 39 , 556–564.

Akoh, H, Tsukasaki, Y, Yatsuya, S, & Tasaki, A. (1978). Magnetic properties of ferromagnetic ultrafine particles prepared by vacuum evaporation on running oil substrate. J Cryst Growth, 45 , 495–500.

Amrollahi, A, Rashidi, AM, Lotfi, R, EmamiMeibodi, M, & Kashefi, K. (2010). Convection heat transfer of functionalized MWNT in aqueous fluids in laminar and turbulent flow at the entrance region. International Communications in Heat and Mass Transfer, 37 , 717–723.

Anoop, KB, Sundararajan, T, & Das, SK. (2009). Effect of particle size on the convective heat transfer in nanofluid in the developing region. International Journal of Heat Mass Transfer , 52 , 2189–95.

Article   MATH   Google Scholar  

Anoop, K, Sadr, R, Yu, J, Kang, S, Jeon, S, & Banerjee, D. (2012). Experimental study of forced convective heat transfer of nanofluids in a microchannel. International Communications in Heat and Mass Transfer, 39 , 1325–1330.

Ashtiani, D, Akhavan-Behabadi, MA, & Fakoor Pakdaman, M. (2012). An experimental investigation on heat transfer characteristics of multi-walled CNT-heat transfer oil nanofluid flow inside flattened tubes under uniform wall temperature condition. International Communications in Heat and Mass Transfer, 39 , 1404–1409.

Azmi, WH, Sharma, KV, Sarma, PK, Mamat, R, Anuar, S, Dharma Rao, V. (2013). Experimental determination of turbulent forced convection heat transfer and friction factor with SiO 2 nanofluid. Experimental Thermal and Fluid Science , 51 , 103–111.

Ben Mansour, R, Galanis, N, & Nguyen, CT. (2011). Experimental study of mixed convection with water-Al 2 O 3 nanofluid in inclined tube with uniform wall heat flux. Int J Therm Sci, 50 , 403–410.

Chandrasekar, M, Suresh, S, & Chandra Bose, A. (2010). Experimental studies on heat transfer and friction factor characteristics of Al 2 O 3 /water nanofluid in a circular pipe under laminar flow with wire coil inserts. Exp Thermal Fluid Sci, 34 , 122–130.

Chandrasekara, M, Sureshb, S, & Senthilkumara, T. (2012). Mechanisms proposed through experimental investigations on thermophysical properties and forced convective heat transfer characteristics of various nanofluids – a review. Renew Sust Energ Rev, 16 , 3917–3938.

Chen, H, Yang, W, He, Y, Ding, Y, Zhang, L, Tan, C, Lapkin, AA, & Bavykin, DV. (2008). Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids). Powder Technol, 183 , 63–72.

Choi, SUS. (1995). Enhancing thermal conductivity of fluids with nanoparticles. Developments and Applications of Non-Newtonian Flows, 66 , 99–105.

Google Scholar  

Corcione, M, Cianfrini, M, & Quintino, A. (2012). Heat transfer of nanofluids in turbulent pipe flow. Int J Therm Sci, 56 , 58–69.

Daungthongsuk, W, & Wongwises, S. (2007). A critical review of convective heat transfer of nanofluids. Renew Sust Energ Rev, 11 , 797–817.

Ding, Y, Alias, H, Wen, D, & Williams, RA. (2006). Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). Int J Heat Mass Transf, 49 , 240–250.

Ding, Y, Chen, H, He, Y, Lapkin, A, Mahboubeh, Y, Šiller, L, & Butenko, YV. (2007). Forced convective heat transfer of nanofluids. Advanced Powder Technol, 18 (6), 813–824.

Duangthongsuk, W, & Wongwises, S. (2010). An experimental study on the heat transfer performance and pressure drop of TiO 2 -water nanofluids flowing under a turbulent flow regime. Int J Heat Mass Transf, 53 , 334–344.

Esmaeilzadeh, E, Almohammadi, H, NasiriVatan, S, & Omrani, AN. (2013). Experimental investigation of hydrodynamics and heat transfer characteristics of γ -Al 2 O 3 /water under laminar flow inside a horizontal tube. Int J Therm Sci, 63 , 31–37.

Fakoor-Pakdaman, M, Akhavan-Behabadi, MA, & Razi, P. (2013). An empirical study on the pressure drop characteristics of nanofluid flow inside helically coiled tubes. Int J Therm Sci, 65 , 206–213.

Farajollahi, B, Etemad, SG, & Hojjat, M. (2010). Heat transfer of nanofluids in a shell and tube heat exchanger. Int J Heat Mass Transf, 53 , 12–17.

Ferrouillat, S, Bontemps, A, Ribeiro, J-P, Gruss, J-A, & Soriano, O. (2011). Hydraulic and heat transfer study of SiO 2 /water nanofluids in horizontal tubes with imposed wall temperature boundary conditions. Int J Heat Fluid Flow, 32 , 424–439.

Fotukian, SM, & Nasr Esfahany, M. (2010a). Experimental investigation of turbulent convective heat transfer of dilute -Al2O3/water nanofluid inside a circular tube. Int J Heat Fluid Flow, 31 , 606–612.

Fotukian, SM, & Nasr Esfahany, M. (2010b). Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube. International Communications in Heat and Mass Transfer, 37 , 214–219.

Ganesh Ranakoti, I, Dewangan, S, Siddhartha, K, & Rohan, N. (2012). Heat transfer enhancement by nano fluids, ME642-Convective Heat and Mass Transfer .

Garg, P, Alvarado, JL, Marsh, C, Carlson, TA, Kessler, DA, & Annamalai a, K. (2009). An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids. Int J Heat Mass Transf, 52 , 5090–5101.

Ghadimi, A, Saidur, R, & Metselaar, HSC. (2011). A review of nanofluid stability properties and characterization in stationary conditions. Int J Heat Mass Transf, 54 , 4051–4068.

Godson, L, Deepak, K, Enocha, C, Jeffersona, B, & Raja, B. (2014). Heat transfer characteristics of silver/water nanofluids in a shell and tube heat exchanger. Archives of Civil and Mechanical Engineering , 14 (3), 489–496.

Hashemi, SM, & Akhavan-Behabadi, MA. (2012). An empirical study on heat transfer and pressure drop characteristics of CuO–base oil nanofluid flow in a horizontal helically c oiled tube under constant heat flux. International Communications in Heat and Mass Transfer, 39 , 144–151.

He, Y, Jin, Y, Chen, H, Ding, Y, Cang, D, & Lu, H. (2007). Heat transfer and flow behaviour of aqueous suspensions of TiO 2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International Journal of Heat Mass Transfer, 50 , 2272–81.

Heyhat, MM, Kowsary, F, Rashidi, AM, Alem Varzane Esfehani, S, & Amrollahi, A. (2012). Experimental investigation of turbulent flow and convective heat transfer characteristics of alumina water nanofluids in fully developed flow regime. International Communications in Heat and Mass Transfer, 39 , 1272–1278.

Hojjat, M. (2011). Seyed Gholamreza Etemad, Rouhollah Bagheri, Jules Thibault. Turbulent forced convection heat transfer of non-Newtonian nanofluids. Experimental Thermal and Fluid Science, 35 , 1351–1356.

Huminic, G, & Huminic, A. (2012a). Application of nanofluids in heat exchangers: a review. Renew Sust Energ Rev, 16 , 5625–5638.

Huminic, G, & Huminic, A. (2012b). Application of nanofluids in heat exchangers: A review. Renew Sust Energ Rev, 16 , 5625–5638.

Hwang, K, Jang, SP, & Choi, SUS. (2009). Flow and convective heat transfer characteristics of water-based Al 2 O 3 nanofluids in fully developed laminar flow regime. Int J Heat Mass Transf, 52 , 193–199.

Hwang, YJ, Ahn, YC, Shin, HS, Lee, CG, Kim, GT, Park, HS, & Lee, JK. (ᅟ). Investigation on characteristics of thermal conductivity enhancement of nanofluids. Curr Appl Phys, ᅟ , ᅟ. in press.

Kamali, R, & Binesh, AR. (2010). Numerical investigation of heat transfer enhancement nanofluids. International Communications in Heat and Mass Transfer, 37 , 1153–1157.

Kannadasan, N, Ramanathan, K, & Suresh, S. (2012). Comparison of heat transfer and pressure drop in horizontal and vertical helically coiled heat exchanger with CuO/water based nano fluids. Exp Thermal Fluid Sci, 42 , 64–70.

Kayhani, MH, Soltanzadeh, H, Heyhat, MM, Nazari, M, & Kowsary, F. (2012). Experimental study of convective heat transfer and pressure drop of TiO 2 /water nanofluid. International Communications in Heat and Mass Transfer, 39 , 456–462.

Khedkar, RS, Sonawane, SS, & Wasewar, KL. (2013). Water to Nanofluids heat transfer in concentric tube heat exchanger: Experimental study. Procedia Engineering, 51 , 318–323.

Kim, D, Kwon, Y, Cho, Y, Li, C, Cheong, S, Hwang, Y, Lee, J, Hong, D, & Moon, S. (2009). Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions. Curr Appl Phys, 9 , e119–e123.

Kumaresan, V, Velraj, R, & Das, SK. (2012). Convective heat transfer characteristics of secondary refrigerant based CNT nanofluids in a tubular heat exchanger, international journal of refrigeration .

Kumaresan, V, Mohaideen Abdul Khader, S, Karthikeyan, S, & Velraj, R. (2013). Convective heat transfer characteristics of CNT nanofluids in a tubular heat exchanger of various lengths for energy efficient cooling/heating system. Int J Heat Mass Transf, 60 , 413–421.

Lazarus Godson, A, Balakrishnan, R, Dhasan Mohan, L, & Somchai, W. (2011). Convective heat transfer of nanofluids with correlations. Particuology, 9 , 626–631.

Liu, Z-H, & Liao, L. (2010). Forced convective flow and heat transfer characteristics of aqueous drag-reducing fluid with carbon nanotubes added. Int J Therm Sci, 49 , 2331–2338.

Liu, KV, Choi, US, & Kasza, KE. (1988). Measurement of pressure drop and heat transfer in turbulent pipe flows of particulate slurries, Argonne National Laboratory Report . ANL-88-15.

Lo, C-H, Tsung, T-T, & Chen, L-C. (2005). Shape-controlled synthesis of Cu based nanofluid using submerged arc nanoparticle synthesis system (SANSS). J Cryst Growth, 277 (1–4), 636–642.

Lo, C-H, Tsung, T-T, & Chen, L-C. (2006). Ni nano-magnetic fluid prepared by submerged arc nano synthesis system (sanss). JSME International Journal, Series B: Fluids and Thermal Engineering, 48 (4), 750–755.

Maré, T, Halelfadl, S, Sow, O, Estellé, P, Duret, S, & Bazantay, F. (2011). Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger. Exp Thermal Fluid Sci, 35 , 1535–1543.

Meriläinen, A, Seppälä, A, Saari, K, Seitsonen, J, Ruokolainen, J, Puisto, S, Rostedt, N, & Ala-Nissila, T. (2013). Influence of particle size and shape on turbulent heat transfer characteristics and pressure losses in water-based nanofluids. Int J Heat Mass Transf, 61 , 439–448.

Mohammed, HA, Bhaskaran, G, Shuaib, NH, & Saidur, R. (2011). Heat transfer and fluid flow characteristics in microchannels heat exchanger using nanofluids: a review. Renew Sust Energ Rev, 15 , 1502–12.

Mohammeda, HA, Al-aswadia, AA, Shuaiba, NH, & Saidur, R. (2011). Convective heat transfer and fluid flow study over a step using nanofluids: A review. Renew Sust Energ Rev, 15 , 2921–2939.

Murshed, SMS, Leong, KC, & Yang, C. (2005). Enhanced thermal conductivity of TiO 2 –water based nanofluids. Int J Therm Sci, 44 (4), 367–373.

Pandey, SD, & Nema, VK. (2012). Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger. Exp Thermal Fluid Sci, 38 , 248–256.

Philip, J, & Shima, PD. (2012). Thermal properties of nanofluids. Adv Colloid Interf Sci, 183–184 , 30–45.

Rabienataj Darzi, AA, Mousa, F, & Kurosh, S. (2013). Heat transfer and flow characteristics of Al 2 O 3 –water nanofluid in a double tube heat exchanger. International Communications in Heat and Mass Transfer, 47 , 105–112.

Rashmi, W, Ismail, AF, Sopyan, I, Jameel, AT, Yusof, F, Khalid, M, & Mubrak, NM. (2011). Stability and thermal conductivity enhancement of carbon nanotube nanofluids using gum Arabic. J Exp Nanosci, 6 (6), 567–579.

Rayatzadeh, HR, Avval-Saffar, M, Mansoukiaei, M, & Abbasi, A. (2013). Effects of continuous sonication on laminar convective heat transfer inside a tube using water- TiO 2 nanofluid, Experimental Thermal and Fluid Science .

Razi, P, Akhavan-Behabadi, MA, & Saeedinia, M. (2011). Pressure drop and thermal characteristics of CuO–base oil nanofluid laminar flow in flattened tubes under constant heat flux. International Communications in Heat and Mass Transfer, 38 , 964–971.

Rea, U, McKrell, T, Lin-wen, H, & Buongiorno, J. (2009). Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids. Int J Heat Mass Transf, 52 , 2042–2048.

Sadik, K. (2009). Anchasa Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf, 52 , 3187–3196.

Saeedinia, M, Akhavan-Behabadi, MA, & Nasr, M. (2012). Experimental study on heat transfer and pressure drop of nanofluid flow in a horizontal coiled wire inserted tube under constant heat flux. Exp Thermal Fluid Sci, 36 , 158–168.

Sahin, B, Gül Gedik, G, Eyuphan, M, & Sendogan, K. (2013). Experimental investigation of heat transfer and pressure drop characteristics of Al 2 O 3 –water nanofluid, Experimental Thermal and Fluid Science .

Sajadi, AR, & Kazemi, MH. (2011). Investigation of turbulent convective heat transfer and pressure drop of TiO 2 /water nanofluid in circular tube. International Communications in Heat and Mass Transfer, 38 , 1474–1478.

Sarkar, J. (2011). A critical review on convective heat transfer correlations of nanofluids. Renew Sust Energ Rev, 15 , 3271–3277.

Selvakumar, P, & Suresh, S. (2012). Convective performance of CuO/water nanofluid in an electronic heat sink. Exp Thermal Fluid Sci, 40 , 57–63.

Singh, AK. (2008). Thermal Conductivity of Nanofluids. Def Sci J, 58 (5), 600–607.

Sohel Murshed, SM, Nieto de Castro, CA, Lourenc, MJV, Lopes, MLM, & Santos, FJV. (2011). A review of boiling and convective heat transfer with nanofluids. Renew Sust Energ Rev, 15 , 2342–2354.

Suresh, S, Chandrasekar, M, & Chandra Sekhar, S. (2011). Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under turbulent flow in a helically dimpled tube. Exp Thermal Fluid Sci, 35 , 542–549.

Suresh, S, Venkitaraj, KP, Selvakumar, P, & Chandrasekar, M. (2012). Effect of Al 2 O 3 –Cu/water hybrid nanofluid in heat transfer. Exp Thermal Fluid Sci, 38 , 54–60.

Sureshkumar, R, Tharves Mohideen, S, & Nethaji, N. (2013). Heat transfer characteristics of nanofluids in heat pipes: A review. Renew Sust Energ Rev, 20 , 397–410.

Syam Sundar, L, & Singh, MK. (2013). Convective heat transfer and friction factor correlations of nanofluid in a tube and with inserts: A review. Renewable and Sustainable Energy Reviews, 20 , 23–35.

SyamSundar, L, Ravi Kumar, NT, Naik, MT, & Sharma, KV. (2012). Effect of full length twisted tape inserts on heat transfer and friction factor enhancement with Fe 3 O 4 magnetic nanofluid inside a plain tube: An experimental study. Int J Heat Mass Transf, 55 , 2761–2768.

Tayal, SP, Jaafar, A, & Mushtaq, A. (ᅟ). Heat transfer through heat exchanger using Al 2 O 3 nanofluid at different Concentrations. ᅟ, ᅟ , ᅟ. journal homepage: www.elsevier .com.

Tiwari, AK, Ghosh, P, & Sarkar, J. (2013). Performance comparison of the plate heat exchanger using different nanofluids. Exp Thermal Fluid Sci, 49 , 141–151.

Vajjha, RS, & Das, DK. (2012). A review and analysis on influence of temperature and concentration of nanofluids on thermophysical properties, heat transfer and pumping power. Int J Heat Mass Transf, 55 , 4063–4078.

Vajjha, RS, Das, DK, & Kulkarni, DP. (2010). Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids. Int J Heat Mass Transf, 53 , 4607–4618.

Wagener, M, Murty, BS, & Gunther, B. (1997). Preparation of metal nanosuspensions by high-pressure DC-sputtering on running liquids. In S Komarnenl, JC Parker, & HJ Wollenberger (Eds.), Nanocrystalline and Nanocomposite Materials II (Vol. 457, pp. 149–154). Pittsburgh, PA: Materials Research Society.

Wang, X-Q, & Mujumdar, AS. (2007). Heat transfer characteristics of nanofluids: A Review. Int J Therm Sci, 46 , 1–19.

Wang, X, Xu, X, & Choi, SUS. (1999). Thermal conductivity of nanoparticle–fluid mixture. J Thermophys Heat Transf, 13 (4), 474–480.

Wang, J, Zhu, J, Zhang, X, & Chen, Y. (2013). Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows. Exp Thermal Fluid Sci, 44 , 716–721.

Weerapun, D, & Somchai, W. (2009). Heat transfer enhancement and pressure drop characteristics of TiO 2 –water nanofluid in a double-tube counter flow heat exchanger. International Journal of Heat and Mass Transfer , 52 , 2059–2067.

Wen, D, & Ding, Y. (2004). Experimental investigation into convective heat transfer of nanofluid at the entrance region under laminar flow conditions. International Journal of Heat Mass Transfer, 47 , 5181–8.

Wu, Z, Wang, L, & Sundén, B. (2013). Pressure drop and convective heat transfer of water and nanofluids in a double-pipe helical heat exchanger. Appl Therm Eng, 60 , 266–274.

Xuan, Y, & Li, Q. (2000). Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Transfer, 21 , 58–64.

Xuan, Y, Li, Q, & Tie, P. (2013). The effect of surfactants on heat transfer feature of nanofluids. Exp Thermal Fluid Sci, ᅟ , ᅟ.

Ying Yang, Z, Zhang, G, Grulke, EA, Anderson, WB, & Wu, G. (2005). Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow. Int J Heat Mass Transf, 48 , 1107–1116.

Yu, L, Dong, L, & Frank, B. (2012a). Laminar convective heat transfer of alumina-polyalphaolefin nanofluids containing spherical and non-spherical nanoparticles. Exp Thermal Fluid Sci, 37 , 72–83.

Yu, W, France, DM, Timofeeva, EV, Singh, D, & Routbort, JL. (2012b). Comparative review of turbulent heat transfer of nanofluids. Int J Heat Mass Transf, 55 , 5380–5396.

Yu, W, Timofeeva, EV, Singh, D, France, DM, & Smith, RK. (2013). Investigations of heat transfer of copper-in-Therminol 59 nanofluids. Int J Heat Mass Transf, 64 , 1196–1204.

Zamzamian, A, Oskouie, SN, Doosthoseini, A, Aliakbar, J, & Pazouki, M. (2011). Experimental investigation of forced convective heat transfer coefficient in nanofluids of Al2O3/EG and CuO/EG in a double pipe and plate heat exchangers under turbulent flow. Exp Thermal Fluid Sci, 35 , 495–502.

Zeinali Heris, S, Etemad, SG, & Nasr Esfahany, M. (2006). Experimental investigation of oxide nanofluids laminar flow convective heat transfer. International Communications in Heat and Mass Transfer, 33 , 529–535.

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Gupta, M., Arora, N., Kumar, R. et al. A comprehensive review of experimental investigations of forced convective heat transfer characteristics for various nanofluids. Int J Mech Mater Eng 9 , 11 (2014). https://doi.org/10.1186/s40712-014-0011-x

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Empirical Relations for Forced Convection Heat Transfer

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Analytical solutions of some simple convection heat transfer problems, especially the convection with laminar flow, have been presented in Chap. 7 . There are a large number of convection problems, especially the convection with turbulent flow, for which the analytical solutions have not met the success. Hence, the technique of dimensional analysis has been applied to develop functional relations in terms of dimensionless numbers. Empirical relations of heat transfer and friction factor have been presented in terms of these dimensionless numbers for flat plates, tubes, annuli, rectangular and parallel plate ducts, submerged bodies and tube banks for different boundary conditions. Nusselt number correlations for fully developed turbulent flow of liquid metals have been given in Sect.  8.11 . In the end, effect of wall roughness on friction factor and heat transfer coefficient has been discussed and some correlations have been presented along with the Moody diagram.

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The fundamental dimensions are quantities such as length L , mass M , time T and temperature θ , which are directly measured. The derived dimensions are those which are measured in the terms of the fundamental dimensions. For example, area is a derived quantity with dimensions L 2 . In heat transfer, heat Q is also sometimes considered as fundamental dimension.

If the fluid is flowing in the horizontal direction, the sum of the horizontal components of these forces constitutes the drag, and the sum of their vertical components constitutes the lift. In the study of heat transfer, we are interested only in the drag, which is the resistance to the flow to be overcome in pumping of the fluid.

The Dittus-Boelter equation is widely used because of its simplicity. For greater accuracy, Gnielinski or Petukhov et al. correlation (refer Table  8.3 ) may be considered.

Bejan A, Kraus AD (eds) (2003) Heat transfer handbook. Wiley, New York

Google Scholar  

Bhatti MS, Shah RK (1987) Turbulent and transition flow convective heat transfer. In: Kakac S, Shah RK, Aung W (eds) Handbook of single-phase convective heat transfer, Chap. 4, Wiley, New York

Churchill SW (1977) Comprehensive correlating equations for heat, mass and momentum transfer in fully developed flow in smooth tubes. Ind Eng Chem Fundam 16(1):109–116

Article   MathSciNet   Google Scholar  

Churchill SW, Bernstein M (1977) A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. J Heat Transfer 99:300–306

Article   Google Scholar  

Dalle Donne M, Meerwald E (1973) Heat transfer and friction coefficients for turbulent flow in smooth annuli at high temperatures. Int J Heat Mass Transfer 16:787–809

Dippery DF, Sabersky RH (1963) Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers. Int J Heat Mass Transfer 6:329–353

Douglas WJM, Churchill SW (1956) Recorrelation of data for convective heat transfer between gases and single cylinders with large temperature differences. Chem Eng Prog Symp Ser 52(18):23–28

Ebadian MA, Dong ZF (1998) Forced convection, internal flow in ducts. In: Rohesenow WM, Hartnett JP, Cho YI (eds) Handbook of heat transfer. McGraw Hill Book Co, New York

Eckert ERG, Drake RM Jr (1972) Analysis of heat and mass transfer. McGraw-Hill Kogakusha, Tokya

MATH   Google Scholar  

Gnielinski V (2015) Turbulent heat transfer in annular spaces- a new comprehensive correlation. Heat Transfer Eng 36:787–789

Gowen RA, Smith JW (1968) Heat transfer from smooth and rough surfaces. Int J Heat Mass Transfer 11:1657–1673

Heaton HS, Reynolds WC, Kays WM (1964) Heat transfer in annular passages: simultaneous development of velocity and temperature fields in laminar flow. Int J Heat Mass Transfer 7:763–781

Hilpert R (1933) Heat transfer from cylinders. Forsch Geb Ingenieurwes 4:215–224

Holman JP (1992) Adapted for SI units by White PRS. Heat transfer. McGraw-Hill Book Co, New York

Hsu ST (1963) Engineering heat transfer. D. Van Nostrand, New York

Isachenko VP, Osipova VA, Sukomel AS (1977) Heat transfer, 2nd edn. MIR Publishers, Moscow

Kays WM, Crawford ME (1980) Convective heat and mass transfer. Tata McGraw-Hill Publishing Co., Ltd, New Delhi

Kays WM, Leung EY (1963) Heat transfer in annular passages-hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux. Int J Heat Mass Transfer 6:537–557

Kays WM, Perkins HC (1973) Forced convection, internal flow in ducts. In: Rohsenow WM, Hartnett JP (eds) Handbook of heat transfer, Chap. 7. McGraw-Hill, New York

Knudsen JD, Katz DL (1958) Fluid dynamics and heat transfer. McGraw-Hill, New York

Langhaar HL (1942) Steady flow in the transition length of a straight tube. J Appl Mech Trans ASME 64:A55–A58

Lee Y (1968) Turbulent heat transfer from the core tube in thermal entrance regions of concentric annuli. Int J Heat Mass Transfer 11:509–522

Lundgren TS, Sparrow EM, Starr JB (1964) Pressure drop due to the entrance region in ducts of arbitrary cross-section. J Basic Eng 86(3):620–626

Mikheyev M (1964) Fundamental of heat transfer. Mir Publishers, Moscow

Mills AF (1995) Heat and mass transfer. Richard D, Irwin, Chicago

Moody LF (1944) Friction factors for pipe flow. Trans ASME 66:671–684

Nikuradse J (1950) Laws of flow in rough pipes. NACA, Technical Memorandum 1292

Rajendra Karwa, Bairwa RD, Jain BP, Karwa N (2005) Experimental study of the effect of rib angle and discretization on heat transfer and friction in an asymmetrical heated rectangular duct. J Enhanced Heat Transfer 12(4):343–355

Ranz WE, Marshall WR Jr (1952a) Evaporation from drops. Parts I. Chem Eng Progr 48:141–146

Ranz WE, Marshall WR Jr (1952b) Evaporation from drops. Parts II. Chem Eng Progr 48:173–180

Rogers GFC, Mayhew YR (1967) Engineering thermodynamics work and heat transfer. English Language Book Co and Longmans, Green and Co, London

Schlichting H (1960) Boundary layer theory (trans: Kestin J), 4th edn. McGraw-Hill, New York

Schlichting H, Gersten K (2000) Boundary-layer theory (trans: Katherine Mayes). Springer, Heidelberg

Book   Google Scholar  

Seban RA, Shimazaki TT (1951) Heat transfer to a fluid flowing turbulently in a smooth pipe with walls at constant temperature. Trans ASME 73:803–807

Sieder EN, Tate CE (1936) Heat transfer and pressure drop of liquids in tubes. Ind Eng Chem 28:1429–1435

Skupinshi E, Tortel J, Vautrey L (1965) Determination des coefficients de convection a’un alliage sodium-potassium dans un tube circulaire. Int. J. Heat Mass Transfer 8:937–951

Sleicher CA, Rouse MW (1975) A convenient correlation for heat transfer to constant and variable property fluids in turbulent pipe flow. Int J Heat Mass Transfer 18:677–683

Sleicher Jr. CA (1955) Heat transfer in a pipe with turbulent flow and arbitrary wall-temperature distribution. Ph.D. Thesis, University of Michigen, p. 67

Sparrow EM, Lloyd JR, Hixon CW (1966) Experiments on turbulent heat transfer in an asymmetrically heated rectangular duct. J Heat Transfer 88:170–174

Tam LM, Ghajar AJ (2006) Transitional heat transfer in plain horizontal tubes. Heat Transfer Eng 27(5):23–28

Webb RL, Eckert ERG, Goldstein RJ (1971) Heat transfer and friction in tubes with repeated-rib roughness. Int J Heat Mass Transfer 14:601–617

Whitaker S (1972) Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and flow in packed beds and tube bundles. AIChE J 18(2):361–371

Winterton RHS (1998) Where did the Dittus and Boelter equation come from? Int J Heat Mass Transfer 41:809–810

Witte LC (1968) An experimental study of forced-convection heat transfer from a sphere to liquid sodium. J Heat Transfer 90:9–12

Zukauskas AA (1987) Convective heat transfer in cross-flow. In: Kakac S, Shah RK, Aung W (eds) Handbook of single-phase convective heat transfer, Chap. 6. Wiley, New York

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Review Questions

Explain the principle of the dimensional analysis. What are the limitations of the dimensional analysis?

What are fundamental and derived dimensions?

Express the variables in Table  8.1 in terms of M - L - T - θ and M - L - T - θ - Q systems of fundamental dimensions.

List the variables that affect the forced convection heat transfer coefficient.

Using the technique of dimensional analysis establish the following relation for forced convection heat transfer.

With the help of Buckingham pi theorem, show that for the forced convection

At low flow velocities, the free convection effect may be present in forced convection heat transfer case. Using dimensional analysis, show that the following form of correlation is obtained.

Derive the relationship (for forced convection)

What is the physical interpretation of the following non-dimensional numbers?

Define hydraulic diameter.

Discuss the effect of the heating or cooling of a fluid on velocity distribution under laminar flow condition in a tube. How does this affect the heat transfer and friction factor and how this effect is taken into account?

Enlist various heat transfer-coefficient and friction-factor correlations developed for laminar and turbulent flows in circular tubes. Discuss them.

What are the effects of thermal and hydrodynamic entry lengths on the heat transfer coefficient and friction factor in both laminar and turbulent tube flows? How is this effect taken into account?

Obtain a relation between the convective heat transfer coefficient and the friction factor when Pr = 1.

What is the effect of the following on the average value of the heat transfer coefficient in the case of fully developed turbulent flow in tubes?

Two fold increase in the fluid mass flow rate; all other parameters remaining the same.

Two fold increase in the tube diameter; all other parameters including the flow velocity are the same.

[ Ans. For fully developed turbulent flow in tubes, Dittus Boelter relation may be used, which gives \({\text{Nu}} \propto \text{Re}^{0.8} = \left( {\frac{{\rho U_{m} d}}{\mu }} \right)^{0.8} ;\) \(h = {\text{Nu}}\frac{k}{d} \propto U_{m}^{0.8} d^{ - 0.2} ;\) Two fold increase in velocity will increase h \(\left( {h \propto U_{m}^{0.8} } \right)\) by 2 0.8  = 1.741 times. A two fold increase in the diameter will reduce h \(\left( {h \propto \frac{1}{{d^{0.2} }}} \right)\) by 2 0.2 i.e., 14.86%.]

Water flows through a long electrically heated smooth tube of 30 mm diameter. If velocity and temperature profiles are fully developed at a location x  =  a , determine the heat transfer coefficient and heat flux at the location. The mass flow rate of water is 0.5 kg/s. At x  =  a , water temperature is 30°C and wall temperature is 40°C.

[ Ans. Thermo-hydraulic properties of water at bulk temperature 30°C are: ρ  = 995.6 kg/m 3 , k  = 0.617 W/(m K), μ  = 7.97 × 10 −4 N s/m 2 , Pr = 5.4; \(\text{Re} = \frac{{\rho U_{m} d}}{\mu } = \frac{4m}{\pi d\mu } = 26625;\) Turbulent flow; \(h = Nu\frac{k}{d} = 0.024\text{Re}^{0.8} \mathop {\Pr }\nolimits^{{0.4}} \frac{k}{d} = 3362\;{\text{W/(m}}^{ 2} {\text{K)}}\) ; \(\frac{q}{A} = h(t_{w} - t_{b} ) = 33.62\;{\text{kW/m}}^{ 2} .\) ]

One kg/s of water at 35°C flows through a 25 mm diameter tube whose surface is maintained at a uniform temperature of 100°C. Determine the required length of the tube for 65°C water outlet temperature.

[Ans. Water properties at the mean bulk temperature t m  = ( t i  +  t o )/2 = 50°C from Table A4:

ρ  =988.1 kg/m 3 , c  = 4182 J/(kg K), μ  = 544 × 10 −6 N s/m 2 , k  = 0.644 W/(m K) and Pr = 3.55. \(\text{Re} = \frac{md}{{(\pi /4)d^{2} \mu }} = \frac{4m}{\pi d\mu } = \frac{4 \times 1}{{\pi \times 0.025 \times 544 \times 10^{ - 6} }} = 93620;\) From Dittus and Boelter equation, \(\overline{h} = \frac{k}{d} \times 0.024\text{Re}^{0.8} \mathop {\Pr }\nolimits^{{0.4}} = \frac{0.644}{0.025} \times 0.024 \times 93620^{0.8} \times 3.55^{0.4}\) \(= 9735\) W/(m 2 K); From \(\frac{{t_{w} - t_{o} }}{{t_{w} - t_{i} }} = \exp \left( { - \frac{P}{mc}L\overline{h} } \right)\) , \(L = - \frac{mc}{{P\overline{h} }}\ln \left( {\frac{{t_{w} - t_{o} }}{{t_{w} - t_{i} }}} \right) =\) \(- \frac{1 \times 4282}{\pi \times 0.025 \times 9735}\ln \left( {\frac{100 - 65}{100 - 35}} \right) = 3.46{\text{m}}\) .]

Cold fluid is passing through a thin-walled tube 10 mm in diameter 2 m long whose surface is maintained at 100°C. The cold fluid flows at a rate of 0.05 kg/s and its inlet and outlet temperatures are 30 and 60°C, respectively. Determine the outlet temperature of the cold fluid if its flow rate is increased by 50% with all other conditions remaining the same. Given that dynamic viscosity of the fluid is 0.0004 N s/m 2 . Flow may be assumed to be fully developed.

[Ans. \(\frac{{t_{w} - t_{o} }}{{t_{w} - t_{i} }} = \exp \left( { - \frac{P}{mc}L\bar{h}} \right)\) gives \(\frac{{\bar{h}}}{c} = \frac{m}{PL} \times \ln \left( {\frac{{t_{w} - t_{i} }}{{t_{w} - t_{o} }}} \right)\) \(= \frac{0.05}{\pi \times 0.01 \times 2} \times\) \(\ln \left( {\frac{100 - 30}{100 - 60}} \right)\) \(= 0.445;\) Reynolds number \(\text{Re} = \frac{4m}{\pi d\mu } = \frac{4 \times 0.05}{\pi \times 0.01 \times 0.0004}\) \(= 15915.\) The flow is turbulent. For increase in mass flow rate by 50%, the Reynolds number will increase by 50%. Since \(h \propto \text{Re}^{0.8}\) from Dittus-Boelter relation for fully developed turbulent flow, new \(\bar{h}/c \approx 0.445 \times 1.5^{0.8} = 0.616\) . The fluid outlet temperature for increased mass flow rate \(t_{o} = t_{w} - (t_{w} - t_{i} )\exp \left[ { - \frac{PL}{m}\left( {\frac{{\bar{h}}}{c}} \right)} \right] \approx 100 - (100 - 30)\exp \left( { - \frac{\pi \times 0.01 \times 2}{1.5 \times 0.05} \times 0.616} \right) = 58.2^{\circ} {\text{C}}.\) ]

Air at 1 atmospheric pressure and 40°C is heated while it passes at a velocity of 8 m/s through a tube 1 m long and 40 mm in diameter whose surface is maintained at 120°C. Determine the outlet temperature of the air.

[ Ans . Mean bulk temperature, \(t_{m} = \frac{{t_{i} + t_{o} }}{2} = \frac{{40 + t_{o} }}{2}\) ; Assuming a trial value of t m  = 50°C, the thermophysical properties of the air are: ρ  = 1.0949 kg/m 3 , k  = 0.02799 W/(m K), μ  = 1.9512 × 10 −5  kg/(m s), c p  = 1007.2 J/(kg K) and Pr = 0.703; \(\text{Re} = \frac{{\rho U_{m} D}}{\mu } = 17957;\) Flow is turbulent. Dittus-Boelter equation gives Nu = 0.024Re 0.8 Pr 0.4  = 52.77; \(\bar{h} = Nu\frac{k}{D} = 36.93\;{\text{W/(m}}^{ 2} {\text{K)}};\) \(m = \rho \frac{\pi }{4}D^{2} U_{m} = 0.011\;{\text{kg/s;}}\) outlet temperature \(t_{o} = t_{w} - (t_{w} - t_{i} )\exp \left[ { - \frac{PL}{m}\left( {\frac{{\bar{h}}}{c}} \right)} \right]\) \(= 120 - (120 - 40)\exp \left( { - \frac{\pi \times 0.04 \times 1}{0.011} \times \frac{36.93}{1007.2}} \right) = 67.38^{\circ} {\text{C}}\) ; Revised mean temperature t m  = 53.69°C, retrial with this estimate of t m may be carried out.]

Air at atmospheric pressure and 25°C mean bulk temperature flows through a rectangular duct (height H  = 400 mm and width W  = 800 mm) with a mean velocity of 5 m/s. The duct is at an average temperature of 40°C. Determine the heat loss per unit length of the duct.

[Ans. At 25°C bulk temperature, thermophysical properties of the air are: ρ  = 1.1868 kg/m 3 , k  = 0.02608 W/(m K), μ  = 1.8363 × 10 −5 N s/m 2 , Pr = 0.709; \(D_{h} = \frac{4WH}{2(W + H)} = 0.53\;{\text{m}}\) ; \(\text{Re} = \frac{{\rho U_{m} D_{h} }}{\mu } = 1.71 \times 10^{5} ;\) \({\text{Nu}} = 0.024\text{Re}^{0.8} \mathop {\Pr }\nolimits^{{0.4}} = 321.3\) ; \(h = {\text{Nu}}\frac{k}{{D_{h} }} = 15.81\;{\text{W/(m}}^{ 2}\; {\text{K);}}\) \(\frac{q}{L} = h[2(W + H)](t_{w} - t_{b} ) = 569.2\;{\text{W/m}} .\) ]

Air at atmospheric pressure and 100°C is flowing through a 20 mm diameter tube at a velocity of 20 m/s. The wall temperature is 30°C above the air temperature all along the tube length. Calculate the heat transfer rate per unit length of the tube. Assume fully developed flow condition.

[ Ans. At 100°C bulk temperature, thermophysical properties of the air are: ρ  = 0.9452 kg/m 3 , k  = 0.0317 W/(m K), μ  = 2.172 × 10 −5 N s/m 2 , Pr = 0.693, c p  = 1.0113 kJ/(kg K); \(\text{Re} = \frac{{\rho U_{m} d}}{\mu } = 17407;\) Flow is turbulent; \(h = Nu\frac{k}{d} = 0.024\text{Re}^{0.8} \mathop {\Pr }\nolimits^{{0.4}} \frac{k}{d} = 81.11\;{\text{W/(m}}^{ 2}\; {\text{K);}}\) \(\frac{q}{L} = h(\pi d)(t_{w} - t_{b} ) = 152.85\;{\text{W/m}} .\) ]

For flow of 0.04 m 3 /s of oil at 20°C bulk temperature through a 1.5 m long tube 125 mm in diameter kept at 30°C, determine the average heat transfer coefficient. The property values are: k  = 0.14 W/(m K), μ b  = 1.2 kg/(m s), μ w  = 0.6 kg/(m s), Pr = 20000, c p  = 2000 J/(kg K), ρ  = 890 kg/m 3 .

[Ans. \(\text{Re}_{L} = \frac{{\rho U_{m} d}}{\mu } = \frac{\rho Vd}{{(\pi /4d^{2} )\mu }} = \frac{4\rho V}{\pi d\mu } = 302;\) Flow is laminar; \(L_{hy} = 0.05\text{Re} d = 1.89{\text{m}}\)  > 1.5 m; \(L_{th} = 0.05\text{Re} \Pr d = 37.75\;{\text{km > 1}} . 5\;{\text{m;}}\) Flow is simultaneously developing; Sieder-Tate relation may be used; \({\text{Nu}} = 1. 8 6\left( {\frac{d}{L} \times \text{Re} \Pr } \right)^{0.33} \left( {\frac{{\mu_{b} }}{{\mu_{w} }}} \right)^{0.14} = 156;\) \(h = {\text{Nu}} \times \frac{k}{d} = 174.7\;{\text{W/(m}}^{ 2} {\text{K)}} .\) ]

Air at atmospheric pressure and 20°C flows across a long cylinder of 50 mm diameter at a velocity of 40 m/s. The cylinder surface temperature is maintained at 100°C. Calculate the heat transfer rate per unit length of the cylinder.

[ Ans. At mean temperature t m  = 60°C, air properties: ρ  = 1.059 kg/m 3 , k  = 0.02875 W/(m K), μ  = 1.997 × 10 −5  kg/(m s), Pr = 0.701, c p  = 1008 J/(kg K); \(\text{Re}_{x} = \frac{{\rho U_{\infty } d}}{\mu } = 106059;\) From Table  8.11 , C  = 0.027, n = 0.805; \(h = Nu\frac{k}{d} = 0.027\text{Re}^{0.805} \mathop {\Pr }\nolimits^{{1/3}} \frac{k}{d} = 153.1\;{\text{W/(m}}^{ 2} {\text{K);}}\) \(\frac{q}{L} = h(\pi d)(t_{w} - t_{b} ) = 1923.9\;{\text{W}}/{\text{m}}\) .]

Air at 25°C flows at 10 m/s parallel to the surface of a highly polished aluminium plate flat plate maintained at a uniform temperature of t s  = 75°C by a series of segmented heaters. Determine the heat removed from the section between x 1  = 0.3 m and x 2  = 0.4 m. The plate width is 0.3 m. The flow is turbulent throughout.

[ Ans. For air at film temperature of 50°C from Table A5, ρ  = 1.0949 kg/m 3 , μ  = 1.9512 × 10 −5  kg/(m s), k  = 0.02799 W/(m K) and Pr = 0.703; \(h_{x} = \frac{k}{x}{\text{Nu}}_{\text{x}} = \frac{k}{x} \times 0.0296\text{Re}_{x}^{0.8} \mathop {\Pr }\nolimits^{{1/3}} =\) \(\frac{k}{x} \times 0.0296\left( {\frac{{\rho U_{\infty } x}}{\mu }} \right)^{0.8} \mathop {\Pr }\nolimits^{{1/3}}\) ; Hence, \(h_{x1} = \frac{0.02799}{0.3} \times 0.0296 \times \left( {\frac{1.0949 \times 10 \times 0.3}{{1.9512 \times 10^{ - 5} }}} \right)^{0.8} \times\) \(0.703^{1/3} = 37.25\) W/(m 2 K), Similarly h ×2  = 35.17 W/(m 2 K); The average heat transfer coefficient h ×1-×2 for distance x 1  = 0.3 m and x 2  = 0.4 m is (37.25 + 35.17)/2 = 36.21; Heat transfer rate q  =  h x1-×2  × ( x 2 – x 1 ) W  × ( t s - t ∞ ) = 54.3 W.]

Air at 1 atm, 25°C and 5 m/s is in cross flow over a long cylinder of 30 mm diameter. Determine the drag force per unit length of the cylinder.

[Ans. For air at 25°C from Table A5, ρ  = 1.1868 kg/m 3 , μ  = 1.8363 × 10 −5  kg/(m s); \(\text{Re}_{D} = \frac{{\rho U_{\infty } D}}{\mu }\) \(= \frac{1.1868 \times 5 \times 0.03}{{1.8363 \times 10^{ - 5} }} = 9694;\) From Fig.  8.10 , C D  ≈ 1; From Eq. (8.46), \(F_{D} = C_{D} A\left( {\frac{1}{2}\rho U_{\infty }^{2} } \right),\) where A  =  LD ; Substitution gives \(F_{D} = 1 \times (1 \times 0.03) \times \left( {\frac{1}{2} \times 1.1868 \times 5^{2} } \right) = 0.445\;{\text{N}}/{\text{m}}\) .]

Water at 25°C and 10 m/s flows over a sphere of 10 mm diameter. Surface temperature of the sphere is 75°C. Determine the drag force. What will be the drag force if fluid is air?

[Ans. For water at film temperature of 50°C from Table A4, ρ  = 988.1 kg/m 3 , μ  = 544 × 10 −6  kg/(m s); \(\text{Re}_{D} = \frac{{\rho U_{\infty } D}}{\mu } =\) \(= \frac{988.1 \times 10 \times 0.01}{{544 \times 10^{ - 6} }} = 1.8 \times 10^{5} ;\) From Fig.  8.10 , C D   ≈ 0.4; From Eq. (8.46), \(F_{D} = C_{D} A\left( {\frac{1}{2}\rho U_{\infty }^{2} } \right),\) where A  = frontal area = (π/4) D 2 ; Substitution gives \(F_{D} = 0.4 \times \frac{\pi }{4} \times 0.01^{2} \times \left( {\frac{1}{2} \times 988.1 \times 10^{2} } \right) = 1.55{\text{N}}\) . For air at film temperature of 50°C from Table A5, ρ  = 1.0949 kg/m 3 , μ  = 19.512 × 10 −6  kg/(m s); \(\text{Re}_{D} = \frac{{\rho U_{\infty } D}}{\mu } =\) \(\frac{1.0949 \times 10 \times 0.01}{{19.512 \times 10^{ - 6} }} = 5.6 \times 10^{3} ;\) From Fig.  8.10 , C D  ≈ 0.4; From Eq. ( 8.46 ), \(F_{D} = C_{D} A\left( {\frac{1}{2}\rho U_{\infty }^{2} } \right),\) where A  = frontal area = (π/4) D 2 ; Substitution gives \(F_{D} = 0.4 \times \frac{\pi }{4} \times 0.01^{2} \times \left( {\frac{1}{2} \times 1.0949 \times 10^{2} } \right) = 0.0017{\text{N}}\) . Comment: In the present case, drag force associated with water is significantly higher than for air because of higher density of water.]

Air at 1 atm and 25°C flows at 7.5 m/s over inline tube bundle with p  =  p t  = 25 mm. The bundle contains 10 tubes per row. The tube diameter is 12.5 mm. If air outlet temperature is 225°C and tube surface temperature is 400°C, determine the number of rows of the tubes per m length.

[Ans. Air properties at the mean bulk temperature t m [= ( t ∞i  +  t ∞o )/2 = 125°C] are: ρ  = 0.8872 kg/m 3 , c  = 1013.8 J/(kg K), μ  = 2.2776 × 10 −5  kg/(m s), k  = 0.0335 W/(m K) and Pr = 0.689. At t w  = 400°C, Pr w  = 0.683; \(U_{{max} } = U_{\infty } \times \frac{{p_{t} }}{{p_{t} - D}} = 15\;{\text{m}}/{\text{s}}\) ; \(\text{Re}_{D} = \frac{{\rho U_{{max} } D}}{\mu } = 7304;\) Assuming N  > 16, from Eq. ( 8.58c ), \({\text{Nu}} = 0.27\text{Re}_{D}^{0.63} \mathop {\Pr }\nolimits^{{0.36}} (\Pr /\Pr_{w} )^{0.25} = 64.3;\) \(\bar{h} = \frac{k}{D}{\text{Nu}} = 172.3\;{\text{W}}/\left( {{\text{m}}^{2} \,{\text{K}}} \right)\) ; From 7.16 , \(t_{\infty o} = t_{w} - \left( {t_{w} - t_{\infty i} } \right)\exp \left( { - \frac{P}{{mc_{p} }}L\overline{h} } \right)\) , or \(\ln \left( {\frac{{t_{w} - t_{\infty o} }}{{t_{w} - t_{\infty i} }}} \right)\) \(= - \frac{\pi DN}{{\rho U_{\infty } N_{t} p_{t} c_{p} }}L\overline{h}\) , which gives \(N = \ln \left( {\frac{{t_{w} - t_{\infty i} }}{{t_{w} - t_{\infty o} }}} \right)\frac{{\rho U_{\infty } N_{t} p_{t} c_{p} }}{{\pi DL\overline{h} }} = 190\) for L  = 1 m; No. of rows =  N / N t  = 190/10 = 19 > 16.]

Liquid mercury at 20°C enters a metal tube of 20 mm internal diameter at the rate of 1 kg/s and is to be heated to 30°C. The tube wall is at a constant temperature of 40°C. Determine the length of the tube. Given for the mercury: ρ  = 13560 kg/m 3 , k  = 8.7 W/(m K), μ  = 1.5 × 10 −3  kg/(m s), Pr = 0.025, c p  = 139 J/(kg K).

[Ans. Reynolds number, \(\text{Re} = \frac{{\rho U_{m} d}}{\mu } = \frac{4m}{\pi d\mu } = \frac{4 \times 1}{{\pi \times 0.02 \times 1.5 \times 10^{ - 3} }} = 42441\) ; \({\text{Pe}} = \text{Re} \Pr\) \(= 42441 \times 0.025 = 1061;\) For constant wall temperature, Seban and Shimazaki equation, Table  8.13 , gives \(\overline{h} = {\text{Nu}}\frac{k}{d} = (5.0 + 0.025{\text{Pe}}^{0.8} )\frac{k}{d}\) \(= [5.0 + 0.025 \times (1061)^{0.8} ] \times \frac{8.7}{0.02}\) \(= 5039{\text{ W/(m}}^{ 2} {\text{ K);}}\) For isothermal case, \(\ln \left( {\frac{{t_{w} - t_{o} }}{{t_{w} - t_{i} }}} \right) = - \frac{PL}{{mc_{p} }}\overline{h}\) , which gives \(L = \ln \left( {\frac{{t_{w} - t_{i} }}{{t_{w} - t_{o} }}} \right)\frac{{mc_{p} }}{{P\overline{h} }}\) \(= \ln \left( {\frac{40 - 20}{40 - 30}} \right)\) \(\times \frac{1.0 \times 139}{\pi \times 0.02 \times 5039} = 0.304{\text{m}}\) .]

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Karwa, R. (2020). Empirical Relations for Forced Convection Heat Transfer. In: Heat and Mass Transfer. Springer, Singapore. https://doi.org/10.1007/978-981-15-3988-6_8

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