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, RT; the Lewis Number, Le; the buoyancy ratio, N; the Soret parameter, M; the ratio of the horizontal to vertical heat flux, a; and the aspect ratio, Ar; 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 a. 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 a affects the flow and the heat transfer considerably, but its effect on the mass transfer is negligible.