Onset of thermosolutal convection in a shallow porous layer heated and salted from below and subject to a horizontal heat flux balanced by a Soret mass flux

In the present paper, a thorough analytical and numerical investigation is carried out to examine the double-diffusive convective instability within a horizontal porous layer heated and salted from below. A situation is considered where a lateral perturbing heat flux applied to the system is balanced by the horizontally induced Soret mass flux. The parameters governing this problem are the thermal Rayleigh number, R-T; the Lewis Number, Le; the buoyancy ratio, N; the Soret parameter, M; the ratio of the horizontal to vertical heat flux, alpha; and the aspect ratio, A(r); of the porous layer. The present investigation is focused on the situation where MN = 1, which describes an equilibrium state between the induced Soret mass flux and the imposed heat flux. For this situation, a rest state solution is possible. The analytical solution, derived on the basis of the parallel flow approximation, is validated numerically using a finite difference method by solving the full governing equations. In the M*-Le plane (M* = 1/M), five distinct regions, describing different flow behaviors, are delineated and their location depends on the lateral heat flux parameter alpha. It is also demonstrated that supercritical and/or subcritical bifurcations are possible for specific ranges of M* and Le. The effect of the lateral heating and the Soret parameter on the critical Rayleigh number, corresponding to the onset of parallel flow convection, is examined. The parameter alpha affects the flow and the heat transfer considerably, but its effect on the mass transfer is negligible. (c) 2006 Elsevier Ltd. All rights reserved.