Double diffusive convection in a vertical enclosure filled with anisotropic porous media

Abstract

This paper summarises a numerical study of double-diffusive natural convection in a rectangular cavity filled with a saturated anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, while the horizontal walls are adiabatic and impermeable. The buoyancy forces that induce the fluid motion are assumed to be cooperative. Numerical results are presented for 10 2≤ R T≤10 4, 0≤ N≤30, 10 −5≤ K≤10 3, 1≤ Le≤10, and A=1, where R T, N, K, Le and A denote the thermal Rayleigh number, buoyancy ratio, permeability ratio, Lewis number and the aspect ratio. In the two extreme cases of heat-driven ( N≪1) and solute-driven ( N≫1) natural convection, scale analysis is applied to predict the order of magnitudes involved in the boundary layer regime. Also, based on the numerical results, correlations for the average Nusselt and Sherwood numbers are proposed for the range of parameters considered in this study. It is demonstrated that the anisotropic properties of the porous medium considerably modify the heat and mass transfer rates from that expected under isotropic conditions. The Brinkman's extension of Darcy's law is also used in this study to investigate double-diffusive convection in anisotropic porous media with high porosity.