COMPUTATION OF THE NATURAL CONVECTION OF NANOFLUID IN A SQUARE CAVITY WITH HOMOGENEOUS AND NONHOMOGENEOUS MODELS

A numerical study of a laminar natural convection of the CuO-water nanofluid in a square cavity using homogeneous and nonhomogeneous models is presented. All the governing equations including the volume fraction equation are discretized on a cell-centered, nonuniform grid employing the finite-volume method with a primitive variable formulation. Calculations are performed over a range of Rayleigh numbers (Ra-f=10(4)-10(7)) and volume fractions of the nanoparticle (0.01 phi 0.1). From the computed results, it is shown that both the homogeneous and nonhomogeneous models predict the deterioration of the natural convection heat transfer well with an increase of the volume fraction of nanoparticle at the same Rayleigh number, which was observed in the previous experimental studies. It is also shown that the differences in the computed results of the average Nusselt number at the wall between the homogeneous and nonhomogeneous models are very small, and this indicates that the slip mechanism of the Brown diffusion and thermophoresis effects are negligible in the laminar natural convection of the nanofluid. The degradation of the heat transfer with an increase of the volume fraction of the nanoparticle in the natural convection of nanofluid is due to the increase of the viscosity and the decrease of the thermal expansion coefficient and the specific heat. It is clarified in the present study that the previous controversies between the numerical and experimental studies are owing to the different definitions of the Nusselt number.