Multiple Natural Convection Solution in Porous Media Under Cross Temperature and Concentration Gradients

Abstract

Double-diffusive natural convection is of interest in several natural and industrial fields, for example, oceanography, nuclear waste, transformation processes, and crystal growth techniques. This work focuses on double-diffusive natural convection in a square cavity filled with porous media heated and cooled along vertical walls by uniform heat fluxes when a solutal flux is imposed vertically. The formulation of the problem is based on the Darcy?Brinkman model, and the density variation is taken into account by the Boussinesq approximation. W e found three distinct regimes. The first is a fully thermal convective regime in which the flow is essentially due to thermal buoyancy forces. The second is a diffusive one where the solutal forces are strong enough to produce a stable solutal stratification with no significant convective flows. The third is an intermediate regime where competition between the two buoyancy forces takes place. In the intermediate regime a hysterisys is observed and two different solutions can be obtained depending on the initial state. The effects of Rayleigh, Lewis, and Darcy numbers are analyzed.