Free convection in a porous medium adjacent to horizontal surfaces

The free convection in a porous medium adjacent to a horizontal surface subjected to special wall temperature spatial distributions is analysed. In the steady case. when the wall temperature is a quadratic function 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 parabolic wall temperature prescription, the flow reveals a singular behaviour 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 obtained from solving the non-similar free convective boundary-layer equations is in very good agreement with a 5 terms approximate small solution and reveals interesting features of the flow which are discussed in detail.