Convection in a composite air-porous layer with an internal heat source depending on a solid volume fraction

In the paper we apply a linear stability analysis to a horizontal air layer partially filled with a heat-generating porous matrix. The porous matrix divides the layer into two sublayers and is a heat source with the strength depending on the volume fraction of solid phase linearly. The two-layered media are bounded by the perfectly thermal conductive plates that have equal temperatures. We simulate convective air flow by the two-domain model where convection equations are written in each of the sublayers separately and air filtration in the porous medium obeys Darcy's law. The numerical modeling is based on the method for constructing a fundamental system of solutions. The attention is paid to the onset of the up-and-down local and large-scale flows with varying the solid volume fraction and relative thickness of the air sublayer. The flows enhance the heat transfer rate across the sublayers.