Skip to main content
Log in

Analysis of Convective Heat Transfer Enhancement by Nanofluids: Single-Phase and Two-Phase Treatments

  • REVIEWS
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

Nanofluids have been investigated regarding their advantages and potentialities for the purpose of increasing convective heat transfer rates inside thermal systems where they are used as working fluids. Researchers in thermophysics have investigated these fluids experimentally and numerically. This review provides extensive theoretical information concerning nanofluids in the single-phase and two-phase treatments. Important published works on nanofluid properties and correlations are summarized and reviewed in detail. Heat transfer enhancement by nanofluids is a challenging problem due to the difficulties inherent in the model of the physical mechanism of interaction between the paricles. Here the interaction between the phases is modeled by several two-phase models, and the results are given in graphical and tabular forms. Despite the advantages of the mixture model, such as imlementation of physical properties and less computational power requirements, some studies showed that the results of the single-phase and two-phase models are very similar. The main difference consists in the effect of the drift velocities of the phases relative to each other.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Kakaç and A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf., 52, 3187–3196 (2009).

    Article  MATH  Google Scholar 

  2. S. Kakaç and A. Pramuanjaroenkij, Single-phase and two-phase treatments of convective heat transfer enhancement with nanofluids — A state-of-the-art review, Int. J. Therm. Sci., 100, 75–97 (2016).

    Article  Google Scholar 

  3. L. S. Sundar and M. K. Singh, Convective heat transfer and friction factor correlations of nanofluid in a tube and with inserts: A review, Renew. Sustain. Energy Rev., 20, 23–35 (2013).

    Article  Google Scholar 

  4. Y. Li, J. Zhou, S. Tung, E. Schneider, and S. Xi, A review on development of nanofluid preparation and characterization, Powder Technol., 196, 89–101 (2009).

    Article  Google Scholar 

  5. H. Zhu, C. Zhang, and S. Liu, Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3O4 aqueous nanofluids, Appl. Phys. Lett., 89, 23123–23126 (2006).

    Article  Google Scholar 

  6. M. S. Liu, M. C. Lin, I. T. Huang, and C. C. Wang, Enhancement of thermal conductivity with carbon nanotube for nanofluids, Int. Commun. Heat Mass Transf., 32, 1202–1210 (2005).

    Article  Google Scholar 

  7. J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, and L. J. Thompson, Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett., 78, 718–720 (2001).

    Article  Google Scholar 

  8. D. Wen and Y. Ding, Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, Int. J. Heat Mass Transf., 47, 5181–5188 (2004).

    Article  Google Scholar 

  9. A. D. Sommers and K. L. Yerkes, Experimental investigation into the convective heat transfer and system-level effects of Al2O3–propanol nanofluids, J. Nanoparticle Res., 12, 1003–1014 (2010).

    Article  Google Scholar 

  10. M. Chandrasekar, S. Suresh, and T. Senthilkumar, Mechanisms proposed through experimental investigations on thermophysical properties and forced convective heat transfer characteristics of various nanofluids — A review, Renew. Sustain. Energy Rev., 16, 3917–3938 (2012).

    Article  Google Scholar 

  11. B. C. Pak and Y. I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transf., 11, 151–170 (1998).

    Article  Google Scholar 

  12. Y. Xuan and W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transf., 43, 3701–3707 (2000).

    Article  MATH  Google Scholar 

  13. M. M. Elias, I. M. Mahbubul, R. Saidur, M. R. Sohel, I. M. Shahrul, S. S. Khaleduzzaman, and S. Sadeghipour, Experimental investigation on the thermo-physical properties of Al2O3 nanoparticles suspended in car radiator coolant, Int. Commun. Heat Mass Transf., 54, 48–53 (2014).

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. S. Kakaç, Y. Yener, and A. Pramuanjaroenkij, Convective Heat Transfer, CRC Press, Boca Raton (2013).

    MATH  Google Scholar 

  16. L. S. Sundar, K. V. Sharma, M. T. Naik, and M. K. Singh, Empirical and theoretical correlations on viscosity of nanofluids: A review, Renew. Sustain. Energy Rev., 25, 670–686 (2013).

    Article  Google Scholar 

  17. J. H. Lee, K. S. Hwang, S. P. Jang, B. H. Lee, J. H. Kim, and S. U. S. Choi, Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles, Int. J. Heat Mass Transf., 51, 2651–2656 (2008).

    Article  Google Scholar 

  18. M. Chandrasekar, S. Suresh, and B. A. C. Bose, Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid, Exp. Therm. Fluid Sci., 34, 210–216 (2010).

    Article  Google Scholar 

  19. C. T. Nguyen, F. Desgranges, N. Galanis, G. Roy, T. Mare, and S. Boucher, Viscosity data for Al2O3/water nanofluid hysteresis: Is heat transfer enhancement using nanofluids reliable, Int. J. Therm. Sci., 47, 103–111 (2008).

    Article  Google Scholar 

  20. K. B. Anoop, S. Kabelac, T. Sundararajan, and S. K. Das, Rheological and flow characteristics of nanofluids: influence of electroviscous effects and particle agglomeration, J. Appl. Phys., 106, 034909 (2009).

    Article  Google Scholar 

  21. M. J. Pastoriza-Gallego, C. Casanova, R. Páramo, B. Barbés, J. L. Legido, and M. M. Piñeiro, A study on stability and thermophysical properties (density and viscosity) of Al2O3 in water nanofluid, J. Appl. Phys., 106, 064301 (2009).

    Article  Google Scholar 

  22. M. J. Pastoriza-Gallego, C. Casanova, J. L. Legido, and M. M. Pineiroa, CuO in water nanofluid: influence of particle size and polydispersity on volumetric behaviour and viscosity, Fluid Phase Equilib., 300, 188–196 (2011).

    Article  Google Scholar 

  23. W. Duangthongsuk and S. Wongwises, Measurement of temperature-dependent thermal conductivity and viscosity of TiO2-water nanofluids, Exp. Therm. Fluid Sci., 33, 706–714 (2009).

    Article  Google Scholar 

  24. Q. Li, Y. Xuan, and J. Wang, Experimental investigations on transport properties of magnetic fluids, Exp. Therm. Fluid Sci., 30, 109–116 (2005).

    Article  Google Scholar 

  25. L. Godson, B. Raja, L. D. Mohan, and S. Wongwises, Experimental investigation on the thermal conductivity and viscosity of silver-deionized water nanofluid, Exp. Heat Transf., 23, 317–332 (2010).

    Article  Google Scholar 

  26. P. K. Namburu, D. P. Kulkarni, D. Misra, and D. K. Das, Viscosity of copper oxide nanoparticles dispersed in ethylene glycol and water mixture, Exp. Therm. Fluid Sci., 32, 397–402 (2007).

    Article  Google Scholar 

  27. E. V. Timofeeva, W. Yu, D. M. France, D. Singh, and J. L. Routbort, Base fluid and temperature effects on the heat transfer characteristics of SiC in ethylene glycol/H2O and H2O nanofluids, J. Appl. Phys., 109, 014914 (2011).

    Article  Google Scholar 

  28. W. Yu, H. Xie, Y. Li, and L. Chen, Experimental investigation on thermal conductivity and viscosity of aluminum nitride nanofluid, Particuology, 9, 187–191 (2001).

    Article  Google Scholar 

  29. W. Yu, H. Xie, L. Chen, and Y. Li, Investigation of thermal conductivity and viscosity of ethylene glycol based ZnO nanofluid, Thermochim. Acta, 491, 92–96 (2009).

    Article  Google Scholar 

  30. W. Yu, H. Xie, Y. Li, L. Chen, and Q. Wang, Experimental investigation on the thermal transport properties of ethylene glycol based nanofluids containing low volume concentration diamond nanoparticles, Colloids Surf. A: Physicochem. Eng. Asp., 380, 1–5 (2001).

    Article  Google Scholar 

  31. H. Chen, Y. Ding, and A. Lapkin, Rheological behaviour of nanofluids containing tube/rod-like nanoparticles, Powder Technol., 194, 132–141 (2009).

    Article  Google Scholar 

  32. M. A. Hachey, C. T. Nguyen, N. Galanis, and C. V. Popa, Experimental investigation of Al2O3 nanofluids thermal properties and rheology — Effects of transient and steady-state heat exposure, Int. J. Therm. Sci., 76, 155–167 (2014).

    Article  Google Scholar 

  33. L. S. Sundar, M. K. Singh, I. Bidkin, and A. C. M. Sousa, Experimental investigations in heat transfer and friction factor of magnetic Ni nanofluid flowing in a tube, Int. J. Heat Mass Transf., 70, 224–234 (2014).

    Article  Google Scholar 

  34. S. Halelfadl, P. Estellé, and T. Maré, Heat transfer properties of aqueous carbon nanotubes nanofluids in coaxial heat exchanger under laminar regime, Exp. Therm. Fluid Sci., 55, 174–180 (2014).

    Article  Google Scholar 

  35. S. Halelfadl, T. Maré, and P. Estellé, Efficiency of carbon nanotubes water based nanofluids as coolants, Exp. Therm. Fluid Sci., 53, 104–110 (2014).

    Article  Google Scholar 

  36. R. Saleh, N. Putra, R. E. Wibowo, W. N. Septiadi, and S. P. Prakoso, Titanium dioxide nanofluids for heat transfer applications, Exp. Therm. Fluid Sci., 52, 19–29 (2014).

    Article  Google Scholar 

  37. S. Manikandan, A. Shylaja, and K. S. Rajan, Thermo-physical properties of engineered dispersions of nano-sand in propylene glycol, Colloids Surf. A: Physicochem. Eng. Asp., 449, 8–18 (2014).

    Article  Google Scholar 

  38. D. Singh, E. V. Timofeeva, M. R. Moravek, S. Cingarapu, W. Yu, T. Fischer, and S. Mathur, Use of metallic nanoparticles to improve the thermophysical properties of organic heat transfer fluids used in concentrated solar power, Solar Energy, 105, 468–478 (2014).

    Article  Google Scholar 

  39. A. Einstein, A new determination of the molecular dimensions, Ann. Phys., 324, No. 2, 289–306 (1906).

    Article  Google Scholar 

  40. D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, Springer, Berlin (1999).

    Book  MATH  Google Scholar 

  41. H. C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20, 571–581 (1952).

    Article  Google Scholar 

  42. G. K. Batchelor, The effect of Brownian motion on the bulk stress in a suspension of spherical particles, J. Fluid Mech., 83, 97–117 (1977).

    Article  MathSciNet  Google Scholar 

  43. N. S. Cheng and A. W. K. Law, Exponential formula for computing effective viscosity, Powder Technol., 129, Nos. 1–3, 156–160 (2003).

    Article  Google Scholar 

  44. C. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Maré, S. Boucher, and H. A. Mintsa, Temperature and particle size-dependent viscosity data for water-based nanofluids — Hysteresis phenomenon, Int. J. Heat Fluid Flow, 28, No. 6, 1492–1506 (2007).

    Article  Google Scholar 

  45. S. E. B. Maїga, C. T. Nguyen, N. Galanis, and G. Roy, Heat transfer behaviours of nanofluids in a uniformly heated tube, Superlat. Microstruct., 35, 543–557 (2004).

    Article  Google Scholar 

  46. U. Rea, T. McKrell, L. W. Hu, and J. Buongiorno, Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids, Int. J. Heat Mass Transf., 52, 2042–2048 (2009).

    Article  Google Scholar 

  47. M. H. Esfe, S. Saedodin, and M. Mahmoodi, Experimental studies on the convective heat transfer performance and thermophysical properties of MgO–water nanofluid under turbulent flow, Exp. Therm. Fluid Sci., 52, 68–78 (2014).

    Article  Google Scholar 

  48. X. Wang, X. Xu, and S. U. S. Choi, Thermal conductivity of nanoparticle–fluid mixture, J. Thermophys. Heat Transf., 13, No. 4, 474–480 (1999).

    Article  Google Scholar 

  49. M. Ghanbarpour, E. B. Haghigi, and R. Khodabandeh, Thermal properties and rheological behavior of water based Al2O3 nanofluid as a heat transfer fluid, Exp. Therm. Fluid Sci., 53, 227–235 (2014).

    Article  Google Scholar 

  50. I. M. Krieger and T. J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol., 3, 137–152 (1959).

    Article  MATH  Google Scholar 

  51. M. Corcione, Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids, Energy Conv. Manage., 52, 789–793 (2011).

    Article  Google Scholar 

  52. L. A. Pozhar and K. E. Gubbins, Quasihydrodynamics of nanofluid mixtures, Phys. Rev. E, 56, 5367–5396 (1997).

    Article  Google Scholar 

  53. L. A. Pozhar and K. E. Gubbins, Transport theory of dense inhomogeneous fluids, J. Chem. Phys., 99, 8970–8996 (1993).

    Article  Google Scholar 

  54. L. A. Pozhar, A master equation for dynamical systems with thermal disturbances, Ukr. Phys. J., 34, 779–788 (1989).

    Google Scholar 

  55. L. A. Pozhar and K. E. Gubbins, Dense inhomogeneous fluids: functional perturbation theory, the generalized Langevin equation, and kinetic theory, J. Chem. Phys., 94, 1367–1384 (1991).

    Article  MathSciNet  Google Scholar 

  56. L. A. Pozhar, Structure and dynamics of nanofluids: Theory and simulations to calculate viscosity, Phys. Rev. E, 61, 1432–1446 (2000).

    Article  Google Scholar 

  57. H. Chen, Y. Ding, and C. Tan, Rheological behaviour of nanofluids, New J. Phys., 9, 367-1–367-24 (2007).

    Google Scholar 

  58. H. Chen, Y. Ding, and A. Lapkin, Rheological behaviour of nanofluids containing tube/rod-like nanoparticles, Powder Technol., 194, Nos. 1–2, 132–141 (2009).

    Article  Google Scholar 

  59. S. Özerinç, S. Kakaç, S. and A. G. Yazıcıoğlu, Enhanced thermal conductivity of nanofluids: A state-of-the-art review, Microfluid Nanofluid, 8, No. 2, 145–170 (2010).

  60. G. Paul, M. Chopkar, I. Manna, and P. K. Das, Techniques for measuring the thermal conductivity of nanofluids: A review, Renew. Sustain. Energy Rev., 14, 1913–1924 (2010).

    Article  Google Scholar 

  61. X. Zhang, H. Gu, and M. Fujii, Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles, Exp. Therm. Fluid Sci., 31, 593–599 (2007).

    Article  Google Scholar 

  62. X. J. Wang and X. F. Li, Influence of pH on nanofluids’ viscosity and thermal conductivity, Chin. Phys. Lett., 26, No. 5, 056601 (2009).

    Article  Google Scholar 

  63. Y. Hwang, H. S. Park, J. K. Lee, and W. H. Jung, Thermal conductivity and lubrication characteristics of nanofluids, Current Appl. Phys., 6, No. S1, 67–71 (2006).

    Article  Google Scholar 

  64. D. Lee, J. W. Kim, and B. G. Kim, A new parameter to control heat transport in nanofluids: surface charge state of the particle in suspension, J. Phys. Chem., 110, 4323–4328 (2006).

    Article  Google Scholar 

  65. M. Jahanshahi, S. F. Hosseinizadeh, M. Alipanah, A. Dehghani, and G. R. Vakilinejad, Numerical simulation of free convection based on experimental measured conductivity in a square cavity using water/SiO2 nanofluid, Int. Commun. Heat Mass Transf., 37, 687–694 (2010).

    Article  Google Scholar 

  66. W. Yu, H. Xie, L. Chen, and Y. Li, Investigation on the thermal transport properties of ethylene glycol-based nanofluids containing copper nanoparticles, Powder Technol., 197, 218–221 (2010).

    Article  Google Scholar 

  67. M. Chopkar, S. Kumar, D. R. Bhandari, P. K. Das, and I. Manna, Development and characterization of Al2Cu and Ag2Al nanoparticle dispersed water and ethylene glycol based nanofluids, Mater. Sci. Eng. B, 139, 141–148 (2007).

    Article  Google Scholar 

  68. P. Sharma, I. H. Baek, T. Cho, S. Park, and K. B. Lee, Enhancement of thermal conductivity of ethylene glycol based silver nanofluids, Powder Technol., 208, 7–19 (2011).

    Article  Google Scholar 

  69. J. C. Maxwell, Treatise on Electricity and Magnetism, Oxford University Press, London (1904).

    MATH  Google Scholar 

  70. R. L. Hamilton and O. K. Crosser, Thermal conductivity of heterogeneous two-component systems, Ind. Eng. Chem. Fund., 1, 182–191 (1962).

    Article  Google Scholar 

  71. P. Bhattacharya, S. K. Saha, A. Yadav, P. E. Phelan, and R. S. Prasher, Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids, J. Appl. Phys., 95, 6492–6494 (2004).

    Article  Google Scholar 

  72. J. Koo and C. Kleinstreuer, A new thermal conductivity model for nanofluids, J. Nanoparticle Res., 6, No. 6, 577–588 (2004).

    Article  Google Scholar 

  73. S. K. Das, N. Putra, P. Thiesen, and W. Roetzel, Temperature dependence of thermal conductivity enhancement of nanofluids, ASME J. Heat Transf., 125, 567–574 (2003).

    Article  Google Scholar 

  74. S. Özerinç, Heat Transfer Enhancement with Nanofluids, Master Thesis, Middle East Technical University, Ankara, Turkey (2010).

  75. C. Nan, R. Birringer, D. R. Clarke, and H. Gleiter, Effective thermal conductivity of particulate composites with interfacial thermal resistance, J. Appl. Phys., 81, No. 10, 6692–6699 (1997).

    Article  Google Scholar 

  76. B. Wang, L. Zhou, and X. Peng, A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles, Int. J. Heat Mass Transf., 46, No. 14, 2665–2672 (2003).

    Article  MATH  Google Scholar 

  77. R. Prasher, P. E. Phelan, and P. Bhattacharya, Effect of aggregation kinetics on the thermal conductivity of nanoscale colloidal solutions (nanofluids), Nano Lett., 6, No. 7, 1529–1534 (2006).

    Article  Google Scholar 

  78. Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang, and H. Lu, Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transf., 50, Nos. 11–12, 2272–2281 (2007).

    Article  MATH  Google Scholar 

  79. W. Evans, R. Prasher, J. Fish, P. Meakin, P. Phelan, and P. Keblinski, Effect of aggregation and interfacial thermal resistance on thermal conductivity of nanocomposites and colloidal nanofluids, Int. J. Heat Mass Transf., 51, Nos. 5–6, 1431–1438 (2008).

    Article  MATH  Google Scholar 

  80. Y. Xuan, Q. Li, and W. Hu, Aggregation structure and thermal conductivity of nanofluids, AIChE J., 49, No. 4, 1038–1043 (2003).

    Article  Google Scholar 

  81. C. Yu, A. G. Richter, A. Datta, M. K. Durbin, and P. Dutta, Observation of molecular layering in thin liquid films using X-ray reflectivity, Phys. Rev. Lett., 82, No. 11, 2326–2329 (1999).

    Article  Google Scholar 

  82. W. Yu and S. U. S. Choi, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Maxwell model, J. Nanoparticle Res., 5, 167–171 (2003).

    Article  Google Scholar 

  83. Q. Xue and W. Xu, A model of thermal conductivity of nanofluids with interfacial shells, Mater. Chem. Phys., 90, Nos. 2–3, 298–301 (2005).

    Article  Google Scholar 

  84. D. A. G. Bruggeman, The calculation of various physical constants of heterogeneous substances. I. The dielectric constants and conductivities of mixtures composed of isotropic substances, Ann. Phys., 416, No. 7, 636–664 (1935).

    Article  Google Scholar 

  85. E. Yamada and T. Ota, Effective thermal conductivity of dispersed materials, Wärme Stoffübert., 13, 27–37 (1980).

    Article  Google Scholar 

  86. C. H. Chon, K. D. Kihm, S. P. Lee, and S. U. S. Choi, Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Appl. Phys. Lett., 87, No. 15, 153107 (2005).

    Article  Google Scholar 

  87. M. Corcione, Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids, Energy Convers. Manage., 52, 789–793 (2011).

    Article  Google Scholar 

  88. A. Ghozatloo, A. M. Rashidi, and M. Shariaty-Niasar, Effects of surface modification on the dispersion and thermal conductivity of CNT/water nanofluids, Int. Commun. Heat Mass Transf., 54, 1–7 (2014).

    Article  Google Scholar 

  89. J. Lee, K. Han, and J. Koo, A novel method to evaluate dispersion stability of nanofluids, Int. J. Heat Mass Transf., 70, 421–429 (2014).

    Article  Google Scholar 

  90. M. J. Nine, H. Chung, M. R. Tanshen, N. A. B. A. Osman, and H. Jeong, Is metal nanofluid reliable as heat carrier? J. Hazard. Mater., 273, 183–191 (2014).

    Article  Google Scholar 

  91. M. Karami, M. A. Akhavan-Bahabadi, S. Delfani, and A. Ghozatloo, A new application of carbon nanotubes nanofluid as working fluid of low-temperature direct absorption solar collector, Solar Energy Mater. Solar Cells, 121, 114–118 (2014).

    Article  Google Scholar 

  92. D. Madhesh, R. Parameshwaran, and S. Kalaiselvam, Experimental investigation on convective heat transfer and rheological characteristics of Cu–TiO2 hybrid nanofluids, Exp. Therm. Fluid Sci., 52, 104–115 (2014).

    Article  Google Scholar 

  93. S. Lee, S. U. S. Choi, S. Li, and J. A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, J. Heat Transf., 121, No. 2, 280–289 (1999).

    Article  Google Scholar 

  94. D. Oh, A. Jain, J. K. Eaton, K. E. Goodson, and J. S. Lee, Thermal conductivity measurement and sedimentation detection of aluminum oxide nanofluids by using the 3ω method, Int. J. Heat Fluid Flow, 29, No. 5, 1456–1461 (2008).

    Article  Google Scholar 

  95. S. P. Jang and S. U. S. Choi, Role of Brownian motion in the enhanced thermal conductivity of nanofluids, Appl. Phys. Lett., 84, No. 21, 4316–4318 (2004).

    Article  Google Scholar 

  96. H. Xie, M. Fujii, and X. Zhang, Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle–fluid mixture, Int. J. Heat Mass Transf., 48, No. 14, 2926–2932 (2005).

    Article  MATH  Google Scholar 

  97. C. Sitprasert, P. Dechaumphai, and V. Juntasaro, A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer, J. Nanoparticle Res., 11, No. 6, 1465–1476 (2009).

    Article  Google Scholar 

  98. S. E. Ahmed, A. K. Hussein, H. A. Mohammed, and S. Sivasankaran, Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids, Appl. Math. Comput., 238, 149–162 (2014).

    Google Scholar 

  99. H. Zerradi, S. Ouaskit, A. Dezairi, H. Loulijat, and S. Mizani, New Nusselt number correlations to predict the thermal conductivity of nanofluids, Adv. Powder Technol., 25, No. 3, 1124–1131 (2014).

    Article  Google Scholar 

  100. C. Y. Tso, S. C. Fu, and Christopher Y. H. Chao, A semi-analytical model for the thermal conductivity of nanofluids and determination of the nanolayer thickness, Int. J. Heat Mass Transf., 70, 202–214 (2014).

  101. B. Lamas, B. Abreu, A. Fonseca, N. Martins, and M. Oliveira, Critical analysis of the thermal conductivity models for CNT based nanofluids, Int. J. Therm. Sci., 78, 65–76 (2014).

    Article  Google Scholar 

  102. R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts, Supplement 1 to Advances in Heat Transfer, Academic Press, New York (1978).

    Google Scholar 

  103. E. N. Sieder and G. E. Tate, Heat transfer and pressure drop of liquids in tubes, Ind. Eng. Chem., 28, No. 12, 1429–1435 (1936).

    Article  Google Scholar 

  104. Q. Li and Y. Xuan, Convective heat transfer and flow characteristics of Cu–water nanofluid, Sci. China Ser. E: Technol. Sci., 45, No. 4, 408–416 (2002).

    Google Scholar 

  105. S. Z. Heris, M. N. Esfahany, and S. G. Etemad, Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube, Int. J. Heat Fluid Flow, 28, No. 2, 203–210 (2007).

    Article  Google Scholar 

  106. S. Özerinç, A. G. Yazıcıoğlu, and S. Kakaç, Numerical analysis of laminar forced convection with temperature-dependent thermal conductivity of nanofluids and thermal dispersion, Int. J. Therm. Sci., 62, 138–148 (2012).

    Article  Google Scholar 

  107. L. Godson, B. Raja, D. M. Lal, and S. Wongwises, Enhancement of heat transfer using nanofluids — An overview, Renew. Sustain. Energy Rev., 14, 629–641 (2010).

    Article  Google Scholar 

  108. W. Williams, J. Buongiorno, and L. W. Hu, Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/water nanoparticle colloids (nanofluids) in horizontal tubes, J. Heat Transf., 130, 042412/1–7 (2008).

    Article  Google Scholar 

  109. K. B. Anoop, T. Sundararajan, and S. K. Das, Effect of particle size on the convective heat transfer in nanofluid in the developing region, Int. J. Heat Mass Transf., 52, 2189–2195 (2009).

    Article  MATH  Google Scholar 

  110. K. S. Hwang, S. P. Jang, and S. U. S. Choi, Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime, Int. J. Heat Mass Transf., 52, 193–199 (2009).

    Article  MATH  Google Scholar 

  111. S. M. Fotukian and M. N. Esfahany, Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube, Int. Commun. Heat Mass Transf., 37, 214–219 (2010).

    Article  Google Scholar 

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

    Article  Google Scholar 

  113. W. Yu, D. M. France, D. S. Smith, D. Singh, E. V. Timofeeva, and J. L. Routbort, Heat transfer to a silicon carbide/water nanofluid, Int. J. Heat Mass Transf., 2, 3606–3612 (2009).

    Article  Google Scholar 

  114. T. K. Hong, H. S. Yang, and C. J. Choi, Study of the enhanced thermal conductivity of Fe nanofluids, J. Appl. Phys., 97, 1–4 (2005).

    Article  Google Scholar 

  115. S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood, and E. A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett., 79, 2252–2254 (2001).

    Article  Google Scholar 

  116. S. Bobbo, L. Fedele, A. Benetti, L. Colla, M. Fabrizio, and C. Pagura, Viscosity of water based SWCNH and TiO2 nanofluids, Exp. Therm. Fluid Sci., 36, 65–71 (2012).

    Article  Google Scholar 

  117. M. Choi and K. Cho, Effect of the aspect ratio of rectangular channels on the heat transfer and hydrodynamics of paraffin slurry flow, Int. J. Heat Mass Transf., 44, 55–61 (2001).

    Article  Google Scholar 

  118. N. R. Karthikeyan, J. Philip, and B. Raj, Effect of clustering on the thermal conductivity of nanofluids, Mater. Chem. Phys., 109, 50–55 (2008).

    Article  Google Scholar 

  119. C. H. Lo, T. T. Tsung, and L. C. Chen, Ni nano-magnetic fluid prepared by submerged arc nano synthesis system (SANSS), JSME Int. J., Ser. B: Fluids Therm. Eng., 48, 750–755 (2006).

    Article  Google Scholar 

  120. C. Pang, J. Y. Jung, J. W. Lee, and Y. Y. Kang, Thermal conductivity measurement of methanol-based nanofluids with Al2O3 and SiO2 nanoparticles, Int. J. Heat Mass Transf., 55, 5597–5602 (2012).

    Article  Google Scholar 

  121. O. Abouali and G. Ahmadi, Computer simulations of natural convection of single phase nanofluids in simple enclosures: A critical review, Appl. Therm. Eng., 36, 1–13 (2012).

    Article  Google Scholar 

  122. A. Bejan, Convection Heat Transfer, 3rd ed., John Wiley & Sons Inc., Hoboken, New Jersey (2004).

    MATH  Google Scholar 

  123. F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A. S. Lavine, Fundamentals of Heat and Mass Transfer, 6th ed., John Wiley & Sons Inc., Hoboken, New Jersey (2007).

    Google Scholar 

  124. R. A. Kuyper, T. H. V. Dermeer, C. J. Hoogendorn, and R. A. W. M. Henkes, Numerical study of laminar and turbulent natural convection in an inclined square cavity, Int. J. Heat Mass Transf., 36, 2899–2911 (1993).

    Article  MATH  Google Scholar 

  125. T. H. Kuehn and R. J. Goldstein, Correlating equations for natural convection heat transfer between horizontal circular cylinders, Int. J. Heat Mass Transf., 19, 1127–1134 (1976).

    Article  Google Scholar 

  126. M. Itoh, T. Fujita, N. Nishiwaki, and M. Hirata, A new method of correlating heat transfer coefficients for natural convection in horizontal cylindrical annuli, Int. J. Heat Mass Transf., 13, 1364–1368 (1970).

    Article  Google Scholar 

  127. R. Kumar and M. A. Kalam, Laminar thermal convection between vertical coaxial isothermal cylinders, Int. J. Heat Mass Transf., 34, 513–524 (1991).

    Article  Google Scholar 

  128. T. Y. Chu and R. J. Goldstein, Turbulent convection in a horizontal layer of water, J. Fluid Mech., 60, 141–159 (1973).

    Article  Google Scholar 

  129. V. Bianco, F. Chiacchio, O. Manca, and S. Nardini, Numerical investigation of nanofluids forced convection in circular tubes, Appl. Therm. Eng., 29, Nos. 17–18, 3632–3642 (2009).

    Article  Google Scholar 

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

    Article  Google Scholar 

  131. Y. Xuan and Q. Li, Investigation on convective heat transfer and flow features of nanofluids, J. Heat Transf., 125, 151–155 (2003).

    Article  Google Scholar 

  132. M. H. Kayhani, H. Soltanzadeh, M. M. Heyhat, M. Nazari, and F. Kowsary, Experimental study of convective heat transfer and pressure drop of TiO2/water nanofluid, Int. Commun. Heat Mass Transf., 39, 456–462 (2012).

    Article  Google Scholar 

  133. M. H. Esfe, S. Saedodin, O. Mahian, and S. Wongwises, Heat transfer characteristics and pressure drop of COOH-functionalized DWCNTs/water nanofluid in turbulent flow at low concentrations, Int. J. Heat Mass Transf., 73, 186–194 (2014).

    Article  Google Scholar 

  134. E. B. Haghighi, M. Saleemi, N. Nikkam, R. Khodabandeh, M. S. Toprak, M. Muhammed, and B. Palm, Accurate basis of comparison for convective heat transfer in nanofluids, Int. Commun. Heat Mass Transf., 52, 1–7 (2014).

    Article  Google Scholar 

  135. M. Hajipour and A. M. Dehkordi, Mixed-convection flow of Al2O3–H2O nanofluid in a channel partially filled with porous metal foam: Experimental and numerical study, Exp. Therm. Fluid Sci., 53, 49–56 (2014).

    Article  Google Scholar 

  136. M. T. Naik, S. S. Fahad, L. S. Sundar, and M. K. Singh, Comparative study on thermal performance of twisted tape and wire coil inserts in turbulent flow using CuO/water nanofluid, Exp. Therm. Fluid Sci., 57, 65–76 (2014).

    Article  Google Scholar 

  137. Y. Abbassi, M. Talebi, A. S. Shirani, and J. Khorsandi, Experimental investigation of TiO2/water nanofluid effects on heat transfer characteristics of a vertical annulus with non-uniform heat flux in non-radiation environment, Ann. Nucl. Energy, 69, 7–13 (2014).

    Article  Google Scholar 

  138. E. Esmaeilzadeh, H. Almohammadi, A. Nokhosteen, A. Motezaker, and A. N. Omrani, Study on heat transfer and friction factor characteristics of γ-Al2O3/water through circular tube with twisted tape inserts with different thicknesses, Int. J. Therm. Sci., 82, 72–83 (2014).

    Article  Google Scholar 

  139. M. Ghobadi and Y. S. Muzychka, Fully developed heat transfer in miniscale coiled tubing for constant wall temperature, Int. J. Heat Mass Transf., 72, 87–97 (2014).

    Article  Google Scholar 

  140. C. J. Ho, W. C. Chen, and W. M. Yan, Correlations of heat transfer effectiveness in a minichannel heat sink with water-based suspensions of Al2O3 nanoparticles and/or MEPCM particles, Int. J. Heat Mass Transf., 69, 293–299 (2014).

    Article  Google Scholar 

  141. C. J. Ho, W. C. Chen, and W. M. Yan, Experiment on thermal performance of water-based suspensions of Al2O3 nanoparticles and MEPCM particles in a minichannel heat sink, Int. J. Heat Mass Transf., 69, 276–284 (2014).

    Article  Google Scholar 

  142. A. M. Hussein, R. A. Bakar, K. Kadirgama, and K. V. Sharma, Heat transfer enhancement using nanofluids in an automotive cooling system, Int. Commun. Heat Mass Transf., 53, 195–202 (2014).

    Article  Google Scholar 

  143. A. T. Utomo, E. B. Haghighi, A. I. T. Zavareh, M. Ghanbarpourgeravi, H. Poth, R. Khodabandeh, B. Palm, and A. W. Pacek, The effect of nanoparticles on laminar heat transfer in a horizontal tube, Int. J. Heat Mass Transf., 69, 77–91 (2014).

    Article  Google Scholar 

  144. H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of γ-Al2O3, SiO2 and TiO2 ultra-fine particles), Netsu Bussei, 7, No. 4, 227–233 (1993).

    Article  Google Scholar 

  145. M. N. Pantzali, A. A. Mouza, and S. V. Paras, Investigating the efficiency of nanofluids as coolants in plate heat exchangers (PHE), Chem. Eng. Sci., 64, 3290–3300 (2009).

    Article  Google Scholar 

  146. E. V. Timofeeva, D. S. Smith, W. Yu, D. M. France, D. Singh, and J. L. Routbort, Particle size and interfacial effects on thermo-physical and heat transfer characteristics of water-based α-SiC nanofluids, Nanotechnol., 21, No. 21, 215703–215713 (2010).

    Article  Google Scholar 

  147. P. Gurav, S. S. Naik, K. Ansari, S. Srinath, K. A. Kishore, Y. P. Setty, and S. Sonawane, Stable colloidal copper nanoparticles for a nanofluid: Production and application, Colloids Surf. A: Physicochem. Eng. Asp., 441, 589–597 (2014).

    Article  Google Scholar 

  148. B. Sun and D. Yang, Flow boiling heat transfer characteristics of nano-refrigerants in a horizontal tube, Int. J. Refrig., 38, 206–214 (2014).

    Article  MathSciNet  Google Scholar 

  149. D. R. Waghole, R. M. Warkhedkar, V. S. Kulkarni, and R. K. Shrivastva, Experimental investigations on heat transfer and friction factor of silver nanofliud in absorber/receiver of parabolic trough collector with twisted tape inserts, Energy Proc., 45, 558–567 (2014).

    Article  Google Scholar 

  150. N. Karami and M. Rahimi, Heat transfer enhancement in a hybrid microchannel-photovoltaic cell using boehmite nanofluid, Int. Commun. Heat Mass Transf., 55, 45–52 (2014).

    Article  Google Scholar 

  151. M. R. Sohel, S. S. Khaleduzzaman, R. Saidur, A. Hepbasli, M. F. M. Sabri, and I. M. Mahbubul, An experimental investigation of heat transfer enhancement of a minichannel heat sink using Al2O3–H2O nanofluid, Int. J. Heat Mass Transf., 74, 164–172 (2014).

    Article  Google Scholar 

  152. Y. Vermahmoudi, S. M. Peyghambarzadeh, S. H. Hashemabadi, and M. Naraki, Experimental investigation on heat transfer performance of Fe2O3/water nanofluid in an air-finned heat exchanger, Eur. J. Mech. B/Fluids, 44, 32–41 (2014).

    Article  Google Scholar 

  153. M. C. S. Reddy and V. V. Rao, Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluid in double pipe heat exchanger with and without helical coil inserts, Int. Commun. Heat Mass Transf., 50, 68–76 (2014).

    Article  Google Scholar 

  154. M. A. Khairul, M. A. Alim, I. M. Mahbubul, R. Saidur, A. Hepbasli, and A. Hossain, Heat transfer performance and exergy analyses of a corrugated plate heat exchanger using metal oxide nanofluids, Int. Commun. Heat Mass Transf., 50, 8–14 (2014).

    Article  Google Scholar 

  155. M. H. Buschmann and U. Franzke, Improvement of thermosyphon performance by employing nanofluid, Int. J. Refrig., 40, 416–428 (2014).

    Article  Google Scholar 

  156. S. Z. Heris, F. Mohammadpur, and A. Shakouri, Effect of electric field on thermal performance of thermosyphon heat pipes using nanofluids, Mater. Res. Bull., 53, 21–27 (2014).

    Article  Google Scholar 

  157. S. Z. Heris, M. N. Esfahany, and G. Etemad, Numerical investigation of nanofluid laminar convection heat transfer through a circular tube, Numer. Heat Transf., Part A, 52, No. 11, 1043–1058 (2007).

    Article  Google Scholar 

  158. A. M. Hussein, R. A. Bakar, and K. Kadirgama, Study of forced convection nanofluid heat transfer in the automotive cooling system, Case Studies Therm. Eng., 2, 50–61 (2014).

    Article  Google Scholar 

  159. A. Malvandi and D. D. Ganji, Effects of nanoparticle migration on force convection of alumina/water nanofluid in a cooled parallel-plate channel, Adv. Powder Technol., 25, No. 4, 1369–1375 (2014).

    Article  Google Scholar 

  160. A. Malvandi and D. D. Ganji, Mixed convective heat transfer of water/alumina nanofluid inside a vertical microchannel, Powder Technol., 263, 37–44 (2014).

    Article  Google Scholar 

  161. D. A. Nield and A. V. Kuznetsov, Forced convection in a parallel-plate channel occupied by a nanofluid or a porous medium saturated by a nanofluid, Int. J. Heat Mass Transf., 70, 430–433 (2014).

    Article  Google Scholar 

  162. F. Selimefendigil and H. F. Öztop, Pulsating nanofluids jet impingement cooling of a heated horizontal surface, Int. J. Heat Mass Transf., 69, 54–65 (2014).

    Article  Google Scholar 

  163. A. S. Kherbeet, H. A. Mohammed, K. M. Munisamy, and B. H. Salman, The effect of step height of microscale backward-facing step on mixed convection nanofluid flow and heat transfer characteristics, Int. J. Heat Mass Transf., 68, 554–566 (2014).

    Article  Google Scholar 

  164. H. Xu and I. Pop, Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms, Int. J. Heat Mass Transf., 75, 610–623 (2014).

    Article  Google Scholar 

  165. H. Xu and I. Pop, Fully developed mixed convection flow in a horizontal channel filled by a nanofluid containing both nanoparticles and gyrotactic microorganisms, Eur. J. Mech. B/Fluids, 46, 37–45 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  166. T. W. Ting, Y. M. Hung, and N. Guo, Field-synergy analysis of viscous dissipative nanofluid flow in microchannels, Int. J. Heat Mass Transf., 73, 483–491 (2014).

    Article  Google Scholar 

  167. S. S. Azimi and M. Kalbasi, Numerical study of dynamic thermal conductivity of nanofluid in the forced convective heat transfer, Appl. Math. Model., 38, 1373–1384 (2014).

    Article  MathSciNet  Google Scholar 

  168. M. M. Elias, I. M. Shahrul, I. M. Mahbubul, R. Saidur, and N. A. Rahim, Effect of different nanoparticle shapes on shell and tube heat exchanger using different baffle angles and operated with nanofluid, Int. J. Heat Mass Transf., 70, 289–297 (2014).

    Article  Google Scholar 

  169. A. A. Minea, Uncertainties in modeling thermal conductivity of laminar forced convection heat transfer with water alumina nanofluids, Int. J. Heat Mass Transf., 68, 78–84 (2014).

    Article  Google Scholar 

  170. M. Goharkhah and M. Ashjaee, Effect of an alternating nonuniform magnetic field on ferrofluid flow and heat transfer in a channel, J. Magnetism Magnetic Mater., 362, 80–89 (2014).

    Article  Google Scholar 

  171. V. A. A. Servati, K. Javaherdeh, and H. R. Ashorynejad, Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using lattice Boltzmann method, Adv. Powder Technol., 25, 666–675 (2014).

    Article  Google Scholar 

  172. I. O. Sert, N. S. Uzol, and S. Kakaç, Numerical analysis of transient laminar forced convection of nanofluids in circular ducts, Heat Mass Transf., 49, No. 10, 1405–1417 (2013).

    Article  Google Scholar 

  173. Z. Said, R. Saidur, N. A. Rahim, and M. A. Alim, Analyses of exergy efficiency and pumping power for a conventional flat plate solar collector using SWCNTs based nanofluid, Energy Buildings, 78, 1–9 (2014).

    Article  Google Scholar 

  174. R. Nasrin and M. A. Alim, Semi-empirical relation for forced convective analysis through a solar collector, Solar Energy, 105, 455–467 (2014).

    Article  Google Scholar 

  175. D. Lelea and I. Laza, The water based Al2O3 nanofluid flow and heat transfer in tangential microtube heat sink with multiple inlets, Int. J. Heat Mass Transf., 69, 264–275 (2014).

    Article  Google Scholar 

  176. P. Li, D. Zhang, and Y. Xie, Heat transfer and flow analysis of Al2O3–water nanofluids in microchannel with dimple and protrusion, Int. J. Heat Mass Transf., 73, 456–467 (2014).

    Article  Google Scholar 

  177. S. Parvin, R. Nasrin, and M. A. Alim, Heat transfer and entropy generation through nanofluid filled direct absorption solar collector, Int. J. Heat Mass Transf., 71, 386–395 (2014).

    Article  Google Scholar 

  178. M. Hatami and D. D. Ganji, Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu–water nanofluid using porous media approach and least square method, Energy Convers. Manage., 78, 347–358 (2014).

    Article  Google Scholar 

  179. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, Numerical study of turbulence nanofluid flow to distinguish models for in-house programming, in: Proc. AIP Conf., 1569 (2013), p. 384.

  180. J. Lee and I. Mudawar, Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels, Int. J. Heat Mass Transf., 50, 452–463 (2006).

    Article  Google Scholar 

  181. A. Behzadmehr, M. Saffar-Avval, and N. Galanis, Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach, Int. J. Heat Fluid Flow, 28, 211–219 (2007).

    Article  Google Scholar 

  182. F. Selimefendigil and H. F. Oztop, Effect of a rotating cylinder in forced convection of ferrofluid over a backward facing step, Int. J. Heat Mass Transf., 71, 142–148 (2014).

    Article  Google Scholar 

  183. M. K. H. Abdolbaqi, C. S. N. Azwadi, and R. Mamat, Heat transfer augmentation in the straight channel by using nanofluids, Int. J. Automotive Mech. Eng., 11, 2294–2305 (2015).

    Article  Google Scholar 

  184. T. Sokhansefat, A. B. Kasaeian, and F. Kowsary, Heat transfer enhancement in parabolic trough collector tube using Al2O3/synthetic oil nanofluid, Renew. Sustain. Energy Rev., 33, 636–644 (2014).

    Article  Google Scholar 

  185. S. M. Vanaki, H. A. Mohammed, A. Abdollahi, and M. A. Wahid, Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts, J. Molecular Liquids, 196, 32–42 (2014).

    Article  Google Scholar 

  186. W. I. A. Aly, Numerical study on turbulent heat transfer and pressure drop of nanofluid in coiled tube-in-tube heat exchangers, Energy Convers. Manage., 79, 304–316 (2014).

    Article  Google Scholar 

  187. I. O. Sert, N. Sezer-Uzol, and S. Kakaç, Numerical approaches for convective heat transfer with nanofluids, in: M. Rebay, S. Kakaç, and R. Cotta (Eds.), Microscale and Nanoscale Heat Transfer: Analysis, Design and Application, CRC Press, Boca Raton (2015).

    Google Scholar 

  188. Fluent 6.2 User Manual, Fluent Inc., 2006.

  189. M. Akbari, N. Galanis, and A. Behzamehr, Comparative analysis of single and two-phase models for CFD studies of nanofluid heat transfer, Int. J. Therm. Sci., 50, 1343–1354 (2011).

    Article  Google Scholar 

  190. S. Mirmasoumiand and A. Behzadmehr, Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model, Appl. Therm. Eng., 28, 717–727 (2008).

    Article  Google Scholar 

  191. R. Lotfi, Y. Saboohi, and A. M. Rashidi, Numerical study of forced convective heat transfer for nanofluids: Comparison of different approaches, Int. Commun. Heat Mass Transf., 37, 74–78 (2010).

    Article  Google Scholar 

  192. I. O. Sert, N. Sezer-Uzol, A. G. Yazicioglu, and S. Kakac, Enhancement of convective heat transfer with nanofluids — single-phase and two-phase analysis, in: Proc. 5th ICAPM, August 25–28, 2013, Cluj-Napoca, Romania (2013).

  193. D. Kim, Y. Kwon, Y. Cho, C. Li, S. Cheong, Y. Hwang, J. Lee, D. Hong, and S. Moon, Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions, Curr. Appl. Phys., 9, No. 2, 119–123 (2009).

    Article  Google Scholar 

  194. J. Buongiorno, Convective transport in nanofluids, Trans. ASME, 128, 240–250 (2006).

    Article  Google Scholar 

  195. M. M. Heyhat and F. Kowsary, Effect of particle migration on flow and convective heat transfer of nanofluids flowing through a circular pipe, J. Heat Transf., 132, 062401 (2010).

    Article  Google Scholar 

  196. M. H. Fard, M. N. Esfahany, and M. R. Talaie, Numerical study of convective heat transfer of nanofluids in a circular tube: two-phase model versus single-phase model, Int. Commun. Heat Mass Transf., 37, 91–97 (2010).

    Article  Google Scholar 

  197. Y. He, Y. Men, Y. Zhao, H. Lu, and Y. Ding, Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions, Appl. Therm. Eng., 29, 1965–1972 (2009).

    Article  Google Scholar 

  198. A. Akbarinia and R. Laur, Investigation of the diameter of solid particles effects on a laminar nanofluid flow in a curved tube using a two phase approach, Int. J. Heat Fluid Flow, 30, 706–714 (2009).

    Article  Google Scholar 

  199. M. Manninen, V. Taivassalo, and S. Kallio, On the mixture model for multiphase flow, VTT Publ., 288, Technical Research Centre of Finland, Espoo, 1–67 (1996).

  200. L. Schiller and Z. Naumann, A drag coeffi cient correlation, Z. Ver. Deutsch. Ing., 77, 318–320 (1935).

    Google Scholar 

  201. Y. Agrawal, L. Talbot, and K. Gong, Laser anemometer study of flow development in curved circular pipes, J. Fluid Mech., 85, No. 3, 497–518 (1978).

    Article  Google Scholar 

  202. C. Lareo, C. A. Branch, and P. J. Fryer, Particle velocity profiles for solid–liquid food flows in vertical pipes, J. Powder Technol., 93, 23–34 (1997).

    Article  Google Scholar 

  203. I. O. Sert, N. Sezer-Uzol, and S. Kakaç, Numerical analysis of nanofluids convective heat transfer with mixture model approaches, in: Proc. Int. Symp. Convective Heat Mass Transfer, Kusadasi, Turkey (2014).

  204. M. M. Sarafraz and F. Hormozi, Scale formation and subcooled flow boiling heat transfer of CuO–water nanofluid inside the vertical annulus, Exp. Therm. Fluid Sci., 52, 205–214 (2014).

    Article  Google Scholar 

  205. M. Goodarzi, M. R. Safaei, K. Vafai, G. Ahmadi, M. Dahari, S. N. Kazi, and N. Jomhari, Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model, Int. J. Therm. Sci., 75, 204–220 (2014).

    Article  Google Scholar 

  206. M. A. R. Sharif, Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Appl. Therm. Eng., 27, 1036–1042 (2007).

    Article  Google Scholar 

  207. H. R. Goshayshi, M. R. Safaei, and Y. Maghmoumi, Numerical simulation of unsteady turbulent and laminar mixed convection in rectangular enclosure with hot upper moving wall by finite volume method, in: Proc. 6th Int. Chemical Engineering Congress Exhibition (ICHEC 2009), Kishlsland, Iran (2009).

  208. A. Karimipour, M. Afrand, M. Akbari, and M. R. Safaei, Simulation of fluid flow and heat transfer in the inclined enclosure, in: Proc. Int. Conf. on Fluid Dynamics Thermodynamics (ICFDT 2012), Zürich, Switzerland (2012).

  209. S. Göktepe, K. Atalık, and H. Ertürk, Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube, Int. J. Therm. Sci., 80, 83–92 (2014).

    Article  Google Scholar 

  210. M. Alinia, D. D. Ganji, and M. Gorji-Bandpy, Numerical study of mixed convection in an inclined two-sided lid driven cavity filled with nanofluid using two-phase mixture model, Int. Commun. Heat Mass Transf., 38, 1428–1435 (2011).

    Article  Google Scholar 

  211. K. Hadad, A. Rahimian, and M. R. Nematollahi, Numerical study of single and two-phase models of water/Al2O3 nanofluid turbulent forced convection flow in VVER-1000 nuclear reactor, Ann. Nucl. Energy, 60, 287–294 (2013).

    Article  Google Scholar 

  212. M. K. Moraveji and E. Esmaeili, Comparison between single-phase and two-phases CFD modeling of laminar forced convection flow of nanofluids in a circular tube under constant heat flux, Int. Commun. Heat Mass Transf., 39, 1297– 1302 (2012).

    Article  Google Scholar 

  213. F. W. Dittus and L. M. K. Boelter, Heat transfer in automobile radiators of the tubular type in: Publications in Engineering, Vol. 2, Univ California, Berkeley (1930), pp. 443–461.

  214. M. K. Moraveji and R. M. Ardehali, CFD modeling (comparing single and two-phase approaches) on thermal performance of Al2O3/water nanofluid in mini-channel heat sink, Int. Commun. Heat Mass Transf., 44, 157–164 (2013).

    Article  Google Scholar 

  215. C. J. Ho and W. C. Chen, An experimental study on thermal performance of Al2O3/water nanofluid in a minichannel heat sink, Appl. Therm. Eng., 50, 516–522 (2013).

    Article  Google Scholar 

  216. S. Z. Heris, S. G. Etemad, and M. N. Esfahany, Experimental investigation of oxide nanofluid laminar flow convective heat transfer in circular tube, Int. Commun. Heat Mass Transf., 33, 529–533 (2006).

    Article  Google Scholar 

  217. O. Ghaffari, A. Behzadmehr, and H. Ajam, Turbulent mixed convection of a nanofluid in a horizontal curved tube using a two-phase approach, Int. Commun. Heat Mass Transf., 37, 1551–1558 (2010).

    Article  Google Scholar 

  218. G. W. Hogg, The Effect of Secondary Flow on Point Heat Transfer Coefficients for Turbulent Flow Inside Curved Tubes, Ph.D. Thesis, University of Idaho, USA (1968).

  219. S. V. Patankar, V. S. Pratap, and D. B. Spalding, Prediction of turbulent flow in curved pipes, J. Fluid Mech., 67, No. 3, 583–595 (1975).

    Article  MATH  Google Scholar 

  220. M. Kalteh, A. Abbassi, M. Saffar-Avval, and J. Harting, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow, 32, 107–116 (2011).

    Article  Google Scholar 

  221. M. A. Ebadian and Z. F. Dong, Forced convection, internal flow in ducts, in: W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho (Eds.), Handbook of Heat Transfer, McGraw-Hill, New York (1998), pp. 5.1–5.137.

    Google Scholar 

  222. S. Mirmasoumi and A. Behzadmehr, Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model, Appl. Therm. Eng., 28, 717–727 (2008).

    Article  Google Scholar 

  223. G. S. Barozzi, E. Zanchini, and M. Mariotti, Experimental investigation of combined forced and free convection in horizontal and inclined tubes, Meccanica, 20, 18–27 (1998).

    Article  Google Scholar 

  224. R. M. Moghari, A. Akbarinia, M. Shariat, F. Talebi, and R. Laur, Two-phase mixed convection Al2O3–water nanofluid flow in an annulus, Int. J. Multiphase Flow, 37, 585–595 (2011).

    Article  Google Scholar 

  225. M. Izadi, A. Behzadmehr, and D. Jalali-Vahida, Numerical study of developing laminar forced convection of a nanofluid in an annulus, Int. J. Therm. Sci., 48, 2119–2129 (2009).

    Article  Google Scholar 

  226. N. Islam, U. N. Gaitonde, and G. K. Sharma, Mixed convection heat transfer in the entrance region of horizontal annuli, Int. J. Heat Mass Transf., 44, 2107–2120 (2001).

    Article  MATH  Google Scholar 

  227. N. M. Natarajan and S. M. Lakshmana, Laminar flow through annuli: analytical method of pressure drop, Indian Chem. Eng., 5, No. 3, 50–53 (1973).

    Google Scholar 

  228. S. Kondaraju and J. S. Lee, Two-phase numerical model for thermal conductivity and convective heat transfer in nanofluids, Nanoscale Res. Lett., 6, 239 (2011).

    Article  Google Scholar 

  229. Y. Xuan and Q. Li, Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow, 21, 58–64 (2000).

    Article  Google Scholar 

  230. S. M. S. Murshed, K. C. Leong, and C. Yang, Thermophysical and electrokinetic properties of nanofluids — A critical review, Appl. Therm. Eng., 28, 2109–2125 (2008).

    Article  Google Scholar 

  231. V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng., 16, 359–368 (1976).

    Google Scholar 

  232. S. Kakaç, M. R. Venkataraman, A. Pramuanjaroenkij, and I. Kotcioglu, Modeling of two-phase flow instabilities in convective in-tube boiling horizontal systems, J. Therm. Sci. Technol. (Isı Bilimi ve Tekniği Dergisi), 29, No. 1, 107–116 (2009).

    Google Scholar 

  233. J. M. Wu and J. Zhao, A review of nanofluid heat transfer and critical heat flux enhancement — research gap to engineering application, Prog. Nucl. Energy, 66, 13–24 (2013).

    Article  Google Scholar 

  234. H. A. Mohammed, G. Bhaskaran, N. H. Shuaib, and R. Saidur, Heat transfer and fluid flow characteristics in microchannels heat exchanger using nanofluids: A review, Renew. Sustain. Energy Rev., 15, 1502–1512 (2011).

    Article  Google Scholar 

  235. A. M. Hussein, K. V. Sharma, R. A. Bakar, and K. Kadirgama, A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid, Renew. Sustain. Energy Rev., 29, 734–743 (2014).

    Article  Google Scholar 

  236. S. Suresh, K. P. Venkitaraj, P. Selvakumar, and M. Chandrasekar, A comparison of thermal characteristics of Al2O3/water and CuO/water nanofluids in transition flow through a straight circular duct fitted with helical screw tape inserts, Exp. Therm. Fluid Sci., 39, 37–44 (2012).

    Article  Google Scholar 

  237. W. Yu, D. M. France, E. V. Timofeeva, D. Singh, and J. L. Routbort, Comparative review of turbulent heat transfer of nanofluids, Int. J. Heat Mass Transf., 55, 5380–5396 (2012).

    Article  Google Scholar 

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

    Article  Google Scholar 

  239. M. Molana and S. Banooni, Investigation of heat transfer processes involved liquid impingement jets: A review, Brazilian J. Chem. Eng., 30, No. 3, 413–435 (2013).

    Article  Google Scholar 

  240. H. A. Mohammed, A. A. Al-Aswadi, N. H. Shuaib, and R. Saidur, Convective heat transfer and fluid flow study over a step using nanofluids: A review, Renew. Sustain. Energy Rev., 15, 2921–2939 (2011).

    Article  Google Scholar 

  241. O. Mahian, A. Kianifar, S. A. Kalogirou, I. Pop, and S. Wongwises, A review of the applications of nanofluids in solar energy, Int. J. Heat Mass Transf., 57, 582–594 (2013).

    Article  Google Scholar 

  242. S. S. Ashrafmansouri and M. N. Esfahany, Mass transfer in nanofluids: A review, Int. J. Therm. Sci., 82, 84–99 (2014).

    Article  Google Scholar 

  243. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, The permeability effects of copper-nanofluid flow with using the porous media model, in: Proc. Int. Symp. Advances in Computational Heat Transfer, Piscataway, USA (2015).

  244. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, The development of mathematical modeling for nanofluid as a porous media in heat transfer technology, in: Proc. IX Minsk Int. Seminar on Heat Pipes, Heat Pumps, Refrigerators, Power Sources, Minsk, Belarus (2015).

  245. A. A. Mohamad, Myth about nano-fluid heat transfer enhancement, Int. J. Heat Mass Transf., 86, 397–403 (2015).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Kakaç.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 89, No. 3, pp. 752–788, May–June, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kakaç, S., Pramuanjaroenkij, A. Analysis of Convective Heat Transfer Enhancement by Nanofluids: Single-Phase and Two-Phase Treatments. J Eng Phys Thermophy 89, 758–793 (2016). https://doi.org/10.1007/s10891-016-1437-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-016-1437-1

Keywords

Navigation