Natural convection in fluid-superposed porous layers heated locally from below

A numerical study of two-dimensional natural convection in fluid-superposed porous layers heated locally from below is reported based on the one-domain formulation of the conservation equations. The effects of five dimensionless parameters on overall Nusselt number are investigated: Rayleigh number based on overall layer height, heater-to-cavity length ratio, porous layer-to-cavity height ratio, domain aspect ratio, and Darcy number. Streamline and isotherm patterns indicate that convective motion is restricted to the overlying fluid layer with some penetration into the porous layer. Nusselt numbers increase with a decrease in the heater length and height ratio, and increase with the Darcy number. The size of the heat source does not affect the dependence of the heat transfer coefficient on height ratio and Darcy number. For domains with large aspect ratios, complex flow restructuring is observed with an increase in Rayleigh number. The present results represent an extension of the well studied problem of buoyant convection in fluid-superposed porous layers with a fully heated lower surface.