Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: the effect of conducting bounding plates

The aim of this study was to investigate the effect of conducting boundaries on the onset of convection in a binary fluid-saturated porous layer. The isotropic saturated porous layer is bounded by two impermeable but thermally conducting plates, subjected to a constant heat flux. These plates have identical conductivity. Moreover, the conductivity of the plates is generally different from the porous layer conductivity. The overall layer is of large extent in both horizontal directions. The problem is governed by seven dimensionless parameters, namely the normalized porosity of the medium epsilon, the ratio of plates over the porous layer thickness delta and their relative thermal conductivities ratio d, the separation ratio delta, the Lewis number Le and thermal Rayleigh number Ra. In this work, an analytical and numerical stability analysis is performed. The equilibrium solution is found to lose its stability via a stationary bifurcation or a Hopf bifurcation depending on the values of the dimensionless parameters. For the long- wavelength mode, the critical Rayleigh number is obtained as Ra-cs = 12(1 + 2d delta)/[1 + psi (2d delta Le + Le + 1)] and k(cs) = 0 for psi > psi(uni) > 0. This work extends an earlier paper by Mojtabi and Rees (2011 Int. J. Heat Mass Transfer 54 293-301) who considered a configuration where the porous layer is saturated by a pure fluid.