Thermally driven shallow cavity flows in porous media: the merged-layer régime

Abstract

An analysis is given of convective motions generated in a shallow rectangular cavity by an applied horizontal temperature gradient; the cavity is filled with a fluid-saturated porous medium. For large Rayleigh numbers R , and for large aspect ratios L , a distinguished limit arises when R = O ( L 2 ). In this limit the boundary layers on the horizontal walls merge and completely fill the cavity. The régime is characterized by a non-parallel core flow that provides the dominant structure over a surprisingly wide range of the parameter R / L 2 . New results for the merged layer core are compared with the parallel flow convection-dominated boundary layer limit R / L 2 → ∞, and with the parallel flow diffusion-dominated limit R / L 2 → 0. Heat transfer calculations, which define the dependence of the Nusselt number on R / L 2 , have also been carried out.