Convection of a binary fluid in a shallow porous cavity heated and salted from the sides

This paper investigates natural convection in a shallow porous cavity filled with a binary fluid. Constant fluxes of heat and concentration are imposed on the vertical walls of the enclosure. Both double-diffusive convection and Soret-induced convection are considered. An analytical solution, valid for shallow enclosures, is derived on the basis of the parallel flow approximation. The work focuses, among other things, on the existence of multiple solutions when the buoyancy ratio is in the vicinity of phi = -1, for which a trivial steady state solution corresponding to the rest state exists. For this particular value of phi, it is well known that the onset of motion occurs above a subcritical Rayleigh number. The present analytical model reveals that, under certain conditions, such a subcritical Rayleigh number also exists when phi < -1. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. Heat, solute and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations. (C) 2013 Elsevier Ltd. All rights reserved.