The effect of conducting bounding plates on the onset of Horton–Rogers–Lapwood convection

We present an analytical and numerical stability analysis of the onset of natural convection in a horizontal fluid-saturated porous cavity. The cavity is bounded by thin horizontal plates with uniform thickness whose outer surfaces are subject to a constant heat flux. The main aim is to determine the effect of the presence of the bounding plates on the onset of convection. The onset criterion is found to be sensitively dependent on the relative thickness of the plates and the porous layer, δ, and their relative conductivities, d. For the long wavelength mode it is precisely Rac = 12(1 + 2δd).