Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies

Fluid flow and heat and mass transfer induced by double-diffusive natural convection in a horizontal porous layer subjected to vertical gradients of temperature and concentration are studied analytically and numerically using the Brinkman-extended Darcy model. Both cases of rigid and free horizontal boundaries are examined in the present study. The parameters governing the problem are the Rayleigh number R-T, the Lewis number Le, the buoyancy ratio N, the Darcy number Da and the aspect ratio Ar. The analytical solution is based on the parallel flow approximation. The critical Rayleigh number corresponding to the onset of the parallel flow in this system is determined analytically as a function of Le, N and Da. For sufficiently small Da, both free and rigid boundaries yield results which are identical to those predicted by the Darcy model. The present investigation shows that there exists a region in the plane (N, Le) where the convective flow is not possible in the layer regardless of the Rayleigh and Darcy numbers considered.