Convection in superposed fluid and porous layers

This paper reports an analytical study of the stability and natural convection in a system consisting of a horizontal fluid layer over a layer of saturated porous medium. Neumann thermal boundary conditions are applied to the horizontal walls of the enclosure while the vertical walls are impermeable and adiabatic. At the interface between the fluid and the porous layers the empirical slip condition, suggested by Beavers and Joseph, is employed. An analytical solution is obtained using a parallel flow approximation, for constant-flux thermal boundary conditions, for which the onset of supercritical cellular convection occurs at a vanishingly small wavenumber and can thus be predicted by the present theory. The critical Rayleigh number, Ra (c) , and Nusselt number, Nu, are found to depend on the depth ratio, eta, the Darcy number, Da, the thermal conductivity ratio, gamma and the slip parameter alpha. Results are presented for a wide range of each of the governing parameters. The results are compared with limiting cases of the problem and are found to be in agreement.