The Horton Rogers Lapwood Problem Under Soret Influence In A Bounded Darcy Medium: Stability Analysis

The purpose of this paper is to investigate the influence of the Soret effect on natural convection in a porous horizontal rectangular cavity, filled with a fluid binary-mixture. Vertical temperature gradient is applied on the two horizontal surfaces of the cavity, while the other bounds are adiabatic. All the bounds of the cell are impermeable for mass flux. The Darcy model with Boussinesq approximation is used. The considered fluid is binary mixture and the Soret influence is taken into account. The motivation being to explain the mechanisms of transition towards complex modes, in the Horton-Rogers-Lapwood convection or also designed by HRL -which is the counterpart of Rayleigh Benard problem in clear fluid media. The supercritical Rayleigh for the onset of convection is predicted based on a numerical linear stability analysis based on Galerkin and finite element methods. The subcritical values of convection are obtained using a direct finite volume resolution of the problem. Since the flow is confined, the aspect ratio effect is taken into account and analyzed. We present a technique, which consists in building a linear operator via reducing the problem, to a base form of eigenvectors corresponding to the classical Rayleigh Benard in porous media, and a perturbation growth rate due to the horizontal flow. Thus, the approximate solution of the system will be in the form of a base of eigenvectors, and a perturbation growth rate. We show that the planes (R, N) and (R, Le) are, according to the parameters of the problem, shared into zones with subsequent convective flow behaviors, and we also quantify the influence of the Lewis number, the separation rate, and the Soret effect.