The effect of conducting boundaries on Lapwood-Prats convection

We investigate the onset of convection in a uniform, constant-thickness, horizontal porous layer which is heated from below. The layer is bounded above and below by thermally conducting but impermeable layers. Our aim is to determine the effect on the onset of convection of the interaction between the presence of these outer conducting layers and a horizontal background flow. A linear stability analysis is performed and a dispersion relation is derived from which the stability characteristics of the layer are computed. Convection cells are found move along the layer at a speed which is lower than that of the imposed flow due to a thermal drag caused by the presence of the bounding solid layers. Neutral curves and streamline/isotherm patterns are presented in order to understand the physical role played by the governing nondimensional parameters. When the diffusivity of the solid layers is much lower than the diffusivity of the porous layer there exists a regime where the neutral curve can exhibit two minima, and at one point in parameter space there exists a neutral curve with a quartic minimum.