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Numerical Study of Mixing Thermal Conductivity Models for Nanofluid Heat Transfer Enhancement

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Researchers have paid attention to nanofluid applications, since nanofluids have revealed their potentials as working fluids in many thermal systems. Numerical studies of convective heat transfer in nanofluids can be based on considering them as single- and two-phase fluids. This work is focused on improving the single-phase nanofluid model performance, since the employment of this model requires less calculation time and it is less complicated due to utilizing the mixing thermal conductivity model, which combines static and dynamic parts used in the simulation domain alternately. The in-house numerical program has been developed to analyze the effects of the grid nodes, effective viscosity model, boundary-layer thickness, and of the mixing thermal conductivity model on the nanofluid heat transfer enhancement. CuO–water, Al2O3–water, and Cu–water nanofluids are chosen, and their laminar fully developed flows through a rectangular channel are considered. The influence of the effective viscosity model on the nanofluid heat transfer enhancement is estimated through the average differences between the numerical and experimental results for the nanofluids mentioned. The nanofluid heat transfer enhancement results show that the mixing thermal conductivity model consisting of the Maxwell model as the static part and the Yu and Choi model as the dynamic part, being applied to all three nanofluids, brings the numerical results closer to the experimental ones. The average differences between those results for CuO–water, Al2O3–water, and CuO–water nanofluid flows are 3.25, 2.74, and 3.02%, respectively. The mixing thermal conductivity model has been proved to increase the accuracy of the single-phase nanofluid simulation and to reveal its potentials in the single-phase nanofluid numerical studies.

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

    Article  Google Scholar 

  3. S. Kakaç and A. Pramuanjaroenkij, Analysis of convective heat transfer enhancement by nanofluids: Single-phase and two-phase treatments, J. Eng. Phys. Thermophys., 89, No. 3, 758–793 (2016).

    Article  Google Scholar 

  4. S. E. B. Maïga, C. T. Nguyen, N. Galanis, and G. Roy, Heat transfer behaviors of nanofluids in a uniformly heated tube, Superlatt. Microstruct., 35, 543–557 (2004).

    Article  Google Scholar 

  5. 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 

  6. A. P. Santra, S. Sen, and N. Chakraborty, Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates, Int. J. Therm. Sci., 48, 391–400 (2009).

    Article  Google Scholar 

  7. M. Haghshenas Fard, M. Nasr 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 

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

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

    Article  Google Scholar 

  10. V. Bianco, O. Manca, and S. Nardini, Numerical investigation on nanofluids turbulent convection heat transfer inside a circular tube, Int. J. Therm. Sci., 50, 341–349 (2010).

    Article  Google Scholar 

  11. 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 

  12. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, Numerical study of turbulence nanofluid flow to distinguish models for in-house programming, in: AIP Conf. Proc., 1569 (1), 384–388 (2013), DOI: https://doi.org/10.1063/1.4849299.

  13. A. Tongkratoke, A. Pramuanjaroenkij, and S. Kakaç, Numerical study of turbulence nanofluid flow to distinguish multiphase flow models for in-house programming, in: Proc. ASME 2016 Int. Conf. on Nuclear Engineering (Congress and Exposition, IMECE 2016-66606), November 11–17, 2016, Phoenix, Arizona, USA (2016).

  14. H. H. Ting and S. S. Hou, Investigation of laminar convective heat transfer for Al2O3–water nanofluids flowing through a square cross-section duct with a constant heat flux, J. Mater., 8, 5321–5335 (2015).

    Article  Google Scholar 

  15. M. R. Safaei, A. H. Jahanbin, A. Kianifar, S. Gharehkhani, A. S. Kherbeet, M. Goodarzi, and M. Dahari, Mathematical modeling for nanofluids simulation: a review of the latest works, in: N. S. Akbar (Ed.), Modeling and Simulation in Engineering Sciences, InTech (2016), DOI: 10.5772/64154.

  16. G. Sekrani, S. Poncet, and M. Bouterra, Numerical simulations of Al2O3 nanofluid flows in laminar and turbulent regimes in a uniformly heated pipe, in: Proc. 3rd Int. Conf. on Fluid Flow, Heat and Mass Transfer (FFHMT’ 16), May 2–3, 2016, Ottawa, Canada (2016).

  17. M. Ismail, S. Fotowat, and A. Fartaj, Numerical simulation of Al2O3/automatic transmission fluid and Al2O3/water nanofluids in a compact heat exchanger, J. Fluid Heat Mass Transf., 3, 34–43 (2016).

    Google Scholar 

  18. M. Marzougui, M. Hammami, and R. B. Maad, Numerical simulation into the convective heat transfer of Al2O3 and CuO nanofluids flowing through a straight tube using two-phase modeling, Nanosci. Nanotechnol., 6, No. 1A, 122–131 (2016) .

    Google Scholar 

  19. L. Qiang and X. Yimin, Convective heat transfer and flow characteristics of Cu–water nanofluid, Sci. China, Ser. E, 45, 408 (2002).

    Google Scholar 

  20. S. Zeinali Heris, M. Nasr Esfahany, and S. Gh. Etemad, Experimental investigation of convective heat transfer of Al2O3–water nanofluid in circular tube, Int. J. Heat Fluid Flow, 28, 203–210 (2007).

    Article  Google Scholar 

  21. T. H. Nassan, S. Zeinali Heris, and S. H. Noie, A comparison of experimental heat transfer characteristics for Al2O3/water and CuO/water nanofluids in square cross-section duct, Int. Commun. Heat Mass Transf., 37, 924–928 (2010).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. 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 

  25. N. Putra, W. Roetzel, and S. K. Das, Natural convection of nanofluids, Heat Mass Transf., 39, 775–784 (2003).

    Article  Google Scholar 

  26. J. C. Maxwell, Treatise on Electricity and Magnetism, Oxford Univ. Press, London (1940).

    MATH  Google Scholar 

  27. J. Koo and C. Kleinstreuer, A new thermal conductivity model for nanofluids, J. Nanopart. Res., 6, 577–588 (2004).

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, Numerical study of nanofluid heat transfer enhancement with mixing thermal conductivity models, Comput. Therm. Sci., 6, 1–12 (2014).

    Article  Google Scholar 

  30. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, Nanofluids flow simulation as the flow through the porous media, in: Proc. Int. Symp. on Convective Heat and Mass Transfer, June 8–13, 2014, Kusadasi, Turkey (2014).

  31. 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. on Advances in Computational Heat Transfer (CHT-15-106), May 25–29, 2015, Piscataway, USA (2015).

  32. A. Tongkratoke, A. Pramuanjaroenkij, A. Chaengbamrung, and S. Kakaç, The development of mathematical modeling for nanofluid as a porous media in heat transfer technology, Heat Pipe Sci. Technol. Int. J., 6, No. 3, 1–13 (2015).

    Google Scholar 

  33. A. Tongkratoke, A. Pramuanjaroenkij, and S. Kakaç, The development of mathematical modeling for Al2O3 nanofluid as a porous medium in heat transfer technology, in: Proc. 12th Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics, July 11–13, 2016, Costa del Sol, Spain (2016).

  34. A. Tongkratoke, A. Pramuanjaroenkij, and S. Kakaç, In-house mathematical modeling for nanofluids as porous media in a heat exchanger, in: Proc. 2nd Int. Conf. on Machining, Materials and Mechanical Technologies (IC3MT2016), October 7–11, 2016, Matsue, Japan (2016).

  35. B. C. Pak and Y. I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transf., 11, No. 2, 151–170 (1998).

    Article  Google Scholar 

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

    MATH  Google Scholar 

  37. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Corporation, New York, USA (1980).

    MATH  Google Scholar 

Download references

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Correspondence to S. Kakaç.

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Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 1, pp. 112–122, January–February, 2018.

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Pramuanjaroenkij, A., Tongkratoke, A. & Kakaç, S. Numerical Study of Mixing Thermal Conductivity Models for Nanofluid Heat Transfer Enhancement. J Eng Phys Thermophy 91, 104–114 (2018). https://doi.org/10.1007/s10891-018-1724-0

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  • DOI: https://doi.org/10.1007/s10891-018-1724-0

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