Analytical and numerical study of double diffusive parallel flow induced in a vertical porous layer subjected to constant heat and mass fluxes

Multiplicity of solutions induced by opposing thermal and solutal buoyancy forces hi a vertical porous layer subject to horizontal fluxes of heat and mass is studied analytically and numerically using the Darcy model. The governing parameters for the problem are the Rayleigh number, RT, the Lewis number, Le, the buoyancy ratio, N and the aspect ratio of the porous matrix, A. The analytical solution developed is based on the parallel flow approximation. Thr effect of the parameters Le and N oil the multiplicity of solutions is studied. It is demonstrated, in this study, that numerical multiple steady stale solutions, that agree very well with the analytical ones, are possible when the aspect ratio of the porous layer is large enough. IL is also found that the heat and mass transfer depend strongly on the solution considered when multiple steady stales are existing.