Free Convection in a Porous Medium Adjacent to Horizontal Surfaces
D. Lesnic, Ioan Victor Pop · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1998
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 from 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 overcome 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.