Analytical and numerical study of buoyancy-driven convection in a vertical enclosure filled with nanofluids

This paper presents an analytical and numerical study of natural convection of nanofluids contained in a rectangular enclosure subject to uniform heat flux along the vertical sides. Governing parameters of the problem under study are the thermal Rayleigh number Ra, the Prandtl number Pr, the aspect ratio of the cavity A and the solid volume fraction of nanoparticles, Phi. Three types of nanoparticles are taken into consideration: Cu, Al2O3 and TiO2. Various models are used for calculating the effective viscosity and thermal conductivity of nanofluids. In the first part of the analytical study, a scale analysis is made for the boundary layer regime situation. In the second part, an analytical solution based on the parallel flow approximation is reported for tall enclosures (A >> 1). In the boundary layer regime a good agreement is obtained between the predictions of the scale analysis and those of the analytical solution. Solutions for the flow fields, temperature distributions and Nusselt numbers are obtained explicitly in terms of the governing parameters of the problem. A numerical study of the same phenomenon, obtained by solving the complete system of the governing equations, is also conducted. A good agreement is found between the analytical predictions and the numerical simulations.