Three-dimensional natural convection in a porous enclosure filled with a nanofluid using Buongiorno’s mathematical model

Steady-state natural convection heat transfer in a three-dimensional porous enclosure filled with a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account two important slip mechanisms in nanofluids like Brownian diffusion and thermophoresis. The study is formulated in terms of the dimensionless vector potential functions, temperature and concentration of nanoparticles. The governing equations were solved by finite difference method on non-uniform mesh and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of six types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter and the aspect ratio on the fluid flow, heat and mass transfer. Three-dimensional velocity, temperature and nanoparticle volume fraction fields, average Nusselt numbers are presented. It is found that low Rayleigh and Lewis numbers and high thermophoresis parameter reflect essential non-homogeneous distribution of nanoparticles inside the cavity, hence a non-homogeneous model is more appropriate for the description of the system.