Natural convection in a horizontal fluid layer bounded by thin porous boundaries

This paper reports an analytical and numerical study of natural convection in a horizontal binary fluid layer confined between two horizontal porous walls. The cavity is heated from the bottom by a constant heat flux while the long side walls are impermeable and adiabatic. The Beavers-Joseph slip condition on velocity is applied at the interface between the fluid and porous layers. Both double-diffusive convection and Soret-induced convection are considered. An analytical model, based on the parallel flow approximation, is proposed for the case of a shallow layer. The flow and heat and mass transfer variables are obtained in terms of the governing parameters of the problem. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted for various hydrodynamic boundary conditions. The results for a fluid layer bounded by solid walls and free surfaces emerge from the present analysis as limiting cases. The study is completed by a numerical solution of the full governing equations.