Numerical study of different conduction models for Al2O3-water nanofluid with variable properties inside a trapezoidal enclosure

Natural convection in enclosures containing nanofluids is important in physical and environmental applications. Different models for conduction have been developed because of the importance of this phenomenon in natural convection in enclosures. In this study, effects of conduction models of Chon, Corcione, Khanafer, and Koo and Kleinstreuer on the natural convection inside a trapezoidal enclosure with hot and cold walls are evaluated numerically. The enclosure contains Al2O3-water nanofluid with variable properties. Effects of the conduction models on fluid flow, natural convection, variations in volume fraction, and diameter of nanoparticles in the models, as well as the variations in the Rayleigh number, are examined. Results show that at Rayleigh numbers of 105 and 106, the maximum and minimum values of the average Nusselt number are obtained using the models of Khanafer and Chon, respectively. In all models, the average Nusselt number presents upward and downward trends when the volume fraction of nanoparticles increases but decreases when the diameter of the nanoparticles increases. At Ra = 105 in all models, as the volume fraction of nanoparticles increases, the nanofluid provides a higher average Nusselt number compared with the base fluid. By contrast, at Ra = 106, at volume fractions larger than 0.01 and using the model of Chon, the average Nusselt number of the nanofluid is lower compared with that of the base fluid.