Conjugate free convection above a heated finite horizontal flat plate embedded in a porous medium

In this paper, we investigate the phenomenon of conjugate free convection in a semi-infinite porous medium above a heated finite plate. Numerical solutions of the full governing equations for the fluid region, coupled to the heat conduction equation in the finite plate, are obtained for a wide range of the non-dimensional parameters appearing in the problem, which are the Rayleigh number, Ra, the ratio of the thermal conductivities of the finite plate and the fluid, k, and the aspect ratio of the finite plate, λ, and a detailed description of the effects of these parameters on the characteristics of the fluid flow and the heat-transfer in the fluid is provided. For the high Rayleigh number regime, when a convective boundary-layer is assumed, the number of the non-dimensional parameters reduce to two and the results provided by this formulation show good agreement with the numerical results. In addition, for Ra≫1 a formulation which assumes one-dimensional heat conduction in the plate, is developed and provides computationally inexpensive results for the average conjugate boundary temperature and Nusselt number which compare well with the results obtained by the boundary-layer formulation.