Multiplicity of Solutions Induced by Thermosolutal Convection in a Square Porous Cavity Heated from Below and Submitted to Horizontal Concentration Gradient in the Presence of Soret Effect

Abstract

ABSTRACT Soret effect on fluid flow and heat and mass transfer induced by double-diffusive natural convection in a square porous enclosure, submitted to cross gradients of temperature and concentration, is studied numerically. The cavity is heated from below and cooled from the top, while its vertical walls are adiabatic and maintained at constant but different concentrations. Numerical results are presented for governing parameters varying in the following ranges: 40 ≤ R T ≤ 1,000, Le = 10, − 0.2 ≤ N ≤ 0.2 and − 30 ≤ M ≤ 30, where R T , Le, N, and M are the thermal Rayleigh number, the Lewis number, the buoyancy ratio, and the Soret parameter, respectively. The effect of the buoyancy ratio and the Soret parameter on the maintenance and disappearance of the multiple steady-state solutions obtained in the case of purely thermal convection is analyzed. It is found that only one monocellular flow mode persists at large values of N (or − N), both in the presence and in the absence of the Soret effect. Some flow modes are destroyed by the solutal buoyancy forces in the absence of the Soret effect (M = 0) but reappear in some range of the parameter M. The Soret effect may affect considerably the heat and mass transfer in the medium; it leads to an enhancement or to a reduction of the mass transfer, depending on the flow structure and the sign of M. There are situations where a solution transfers the solute toward the wall with the highest concentration. Such behavior is observed when the temperature gradient and the magnitude of the Soret parameter M are such that the thermodiffusion flux opposes and overcomes the convection flux, resulting in a net mass flux directed from the least concentrated wall toward the most concentrated one.