FREE-CONVECTION IN A POROUS-MEDIUM ADJACENT TO HORIZONTAL SURFACES

The free convection in a porous medium adjacent to a horizontal surfac e subjected to special wall temperature spatial distributions is analy sed. In the steady case. when the wall temperature is a quadratic func tion along the surface, it is suggested form a numerical investigation that a steady free convective boundary-layer flow solution exists if and only if the quadratic wall temperature is a convex function. This is also confirmed from the unsteady case for which in a concave parabo lic wall temperature prescription, the flow reveals a singular behavio ur at a finite time. In order to over-come this modelled singularity, in the steady case, spatially periodic wall temperature functions are considered. In this new situation, the full numerical solution obtaine d from solving the non-similar free convective boundary-layer equation s is in very good agreement with a 5 terms approximate small solution and reveals interesting features of the flow which are discussed in de tail.