International Scientific Journal


Laminar incompressible mixed-convective heat transfer in two-dimensional lid-driven cavity, filled with nanofluid CuO-water, is studied numerically. Eight different viscosity models are compared to investigate the enhancement in the heat transfer and the increase in the average Nusselt number. The point of view of each model essentially differs in terms of whether it takes various parameters such as temperature effects, Brownian motion of the nanoparticles, the radii of aggregated particles, and the volume-fraction of nanoparticles into account or not. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The main sensitive parameters of interest to investigate the viscosity models are chosen as volume fraction of the nanoparticles φ, and Richardson number Ri. The performance study of the viscosity models and the interpretation of the corresponding results of velocity components are done in a different range of φ and Ri.
This article has been corrected with 10.2298/TSCI160418084E.
PAPER REVISED: 2014-03-20
PAPER ACCEPTED: 2014-04-14
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 1, PAGES [347 - 358]
  1. Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, ASME Fluids Engineering Division 231 (1995), pp. 99-105.
  2. Putra, N., Roetzel, W., Das, S.K., Natural convection of nanofluids, Heat and Mass Transfer 39 (2003), pp. 775-784.
  3. Daungthongsuk, W., Wongwises, S., A critical review of convective heat transfer nanofluids, Renewable & Sustainable Energy Reviews 11 (2007), pp. 797-817.
  4. Trisaksri, V., Wongwises, S., Critical review of heat transfer characteristics of nanofluids, Renewable & Sustainable Energy Reviews 11 (2007), pp. 512-523.
  5. Kakac, S., Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer 52 (2009), pp. 3187-3196.
  6. Saidur, R., Leong, K.Y., Mohammad, H.A., A review on applications and challenges of nanofluids, Renewable & Sustainable Energy Reviews 15 (2011), pp.1646-1668.
  7. Mahbubul, I.M., Saidur, R., Amalina, M.A., Latest developments on the viscosity of nanofluids, International Journal of Heat and Mass Transfer 55 (2012), pp. 874-885.
  8. Mukesh Kumar, P.C., Kumar, J., Suresh, S., Review on nanofluid theoretical viscosity models, International Journal of Engineering Innovation and Research 1(2) (2012), pp. 128-134.
  9. Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer 46 (2003), pp. 3639-3653.
  10. Abu-Nada, E., et al., Effect of nanofluid variable properties on natural convection in enclosures, International Journal of Thermal Science 49 (2010), pp. 479-491.
  11. Talebi, F., Mahmoudi, A.H., Shahi, M., Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid, International Communications in Heat and Mass Transfer 37 (2010), pp. 79-90.
  12. Mahmoodi, M., Numerical simulation of free convection of a nanofluid in L-shaped cavities, International Journal of Thermal Science 50 (2011), pp. 1731-1740.
  13. Pourmahmoud, N., Ghafouri, A., Mirzaee, I., Numerical study of mixed convection heat transfer in lid-driven cavity using nanofluid; effect of type and model of nanofluid, Journal of thermal Science (2013), doi:10.2298/TSCI120718053P.
  14. Brinkman, H.C., The viscosity of concentrated suspensions and solutions, Journal of Chemical Physics 20 (1952), pp. 571-581.
  15. Nguyen, C.T., et al., Temperature and particle-size dependent viscosity data for water based nanofluids- hysteresis phenomenon, International Journal of Heat and Fluid flow 28 (2007), pp.1492-1506.
  16. Nasrin, R., Alim, M.A., Chamkha, A.J., Combined convection flow in triangular wavy chamber filled with water-CuO nanofluid: Effect of viscosity models, International Communications in Heat and Mass Transfer 39 (2012), pp. 1226-1236.
  17. Pak, B.C., Cho, Y., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle, Experimental Heat Transfer 11 (1998), pp. 151-170.
  18. Sheikhzadeh, G.A., et al., Numerical study of mixed convection flows in a lid-driven enclosure filled with nanofluid using variable, Results in Physics 2 (2012), pp. 5-13.
  19. Chamkha, A.J., Abu-Nada, E., Mixed convection flow in single and double-lid driven square cavities filled with water-Al2O3 nanofluid: effect of viscosity models, European Journal of Mechanics - B/Fluids 36 (2012), pp. 82-96.
  20. Abu-Nada, E., Rayleigh-Bénard convection in nanofluids: effect of temperature dependent properties, International Journal of Thermal Science 50 (2011), pp. 1720-1730.
  21. Chon, C.H., et al., Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Applied Physics Letters 87 (15) (2005), pp. 153107-1-3.
  22. Angue Minsta, H., et al., New temperature and conductivity data for water- based nanofluids, International Journal of Thermal Science 48 (2) (2008), pp. 363-373.
  23. Haddad, Z., et al., Natural convection in nanofluids: Are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement?, International Journal of Thermal Science 57 (2012), pp. 152-162.
  24. Krieger, I.M., Dougherty, T.J., A mechanism for non-Newtonian flow in suspensions of rigid spheres, Transactions of the Society of Rheology 3 (1959), pp. 137-152.
  25. Chen, H., Ding, Y., Tan, C., Rheological behavior of nanofluids, New Journal of Physics 9 (10) (2007), pp. 267.
  26. Nielsen, L.E., Generalized equation for the elastic moduli of composite materials, Journal of Applied Physics 41 (1970), pp. 4626-4627.
  27. Wang, X., Xu, X., Choi, S.U.S., Thermal conductivity of nanoparticle-fluid mixture, Journal of Thermophysics and Heat Transfer 13 (4) (1999), pp. 474-480.
  28. Azmi, W. H., Sharma, K. V., Mamat, R., Alias, A. B. S., Misnon, I. I., Correlations for thermal conductivity and viscosity of water based nanofluids, Materials Science and Engineering 36 (2012) 012029, doi:10.1088/1757-899X/36/1/012029.
  29. Koo, J., Kleinstreuer, C., Laminar nanofluid flow in micro heat-sinks, International Journal of Heat and Mass Transfer 48 (13) (2005), pp. 2652-2661.
  30. Abu-Nada, E., Effects of variable viscosity and thermal conductivity of CuO-water nanofluid on heat transfer enhancement in natural convection: mathematical model and simulation, Journal of Heat Transfer132 (2010), pp. 052401.
  31. Krane, R.J., Jessee, J., Some detailed field measurements for a natural convection flow in a vertical square enclosure, Proceedings of 1st ASME-JSME Thermal Engineering Joint Conference, 1983, Vol. 1, pp. 323-329.
  32. Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid flow 29 (2008), pp. 1326-1336.
  33. Fusegi, T.,et al., A numerical study of three dimensional natural convection in a differentially heated cubical enclosure, International Journal of Heat and Mass Transfer 34 (1991), pp.1543-1557.
  34. Markatos, N.C., Pericleous, K.A., Laminar and turbulent natural convection in an enclosed cavity, International Journal of Heat and Mass Transfer 27 (1984), pp. 772-775.
  35. Vahl Davis, G. De., Natural convection of air in a square cavity, a benchmark numerical solution, International Journal for Numerical Methods in Fluids 3 (1983), pp. 249-264.

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence