On a Free Convection Problem Over a Vertical Flat Surface in a Porous Medium

Abstract

The problem of the free convection boundary-layer flow over a semi-infinite vertical flat surface in a porous medium is considered, in which the surface temperature has a constant value T 1 at the leading edge, where T 1 is above the ambient temperature, and takes a value T 2 at a given distance L along the surface, varying linearly between these two values and remaining constant afterwards. Numerical solutions of the boundary-layer equations are obtained as well as solutions valid for both small and large distance along the surface. Results are presented for the three cases, when the temperature T 2 is greater, equal or less than the ambient temperature T ∞. In the first case, T 2 > T ∞, a boundary-layer flow develops along the surface starting with a flow associated with the temperature difference T 1 − T ∞ at the leading edge and approaching a flow associated with the temperature difference T 2 − T ∞ at large distances. In the second case, T 2 = T ∞, the convective flow set up on the initial part of the surface drives a wall jet in the region where the surface temperature is the same as ambient. In the final case, T 2 < T ∞, a singularity develops in the numerical solution at the point where the surface temperature becomes T ∞. The nature of this singularity is discussed.