Multiple natural convection solution in porous media under cross temperature and concentration gradients

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 tire Darcy-Brinkman model, and the density variation is taken into account by the Boussinesq approximation, We found three distinct regimes, The first is a fully thermal convective regime in which the pow 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 tire initial state, The effects of Rayleigh, Lewis, and Darcy numbers are analyzed.