Multiple solutions for double-diffusive convection in a vertical porous enclosure

Abstract

A numerical study is made of double-diffusive natural convection in a rectangular fluid-saturated vertical porous enclosure. The flows are driven by conditions of uniform heat and mass fluxes imposed along the two vertical side walls of the cavity where the two buoyancy effects can either augment or counteract each other. An extensive series of numerical simulations is conducted in the range 1 ⩽ R T ⩽ 165, 1 ⩽ Le ⩽ 10 3, −20 ⩽ N ⩽ 20 and A = 1, where R T , Le, N and A are the Darcy-modified Rayleigh number, Lewis number, buoyancy ratio and aspect ratio of the enclosure, respectively. For aiding flows ( N > 0) the behaviour of the resulting double-diffusive convection is in qualitative agreement with the available numerical results. For opposing flows ( N < 0) the existence of multiple steady states is demonstrated. It is determined that, for a given value of N, both Lewis and Rayleigh numbers have an influence on the domain of existence of these multiple steady states. Comprehensive Nusselt and Sherwood number data are presented as functions of the governing parameters mentioned above. The effects of the buoyancy ratio are found to be rather significant on the flow pattern and heat and mass transfer, especially for the opposing flows.