Free convection boundary-layer flow along a vertical surface in a porous medium with Newtonian heating

Abstract

In this paper the steady free convection boundary-layer flow along a vertical surface embedded in a porous medium with Newtonian heating is investigated. The mathematical problem reduces to a pair of coupled partial differential equations for the temperature and the streamfunction, and full numerical, asymptotic and matching solutions are obtained for a wide range of values of the coordinate along the plate. The results for the temperature profiles on the plate and in the convective fluid are presented. A comparison between the full finite-difference solution and the small and large series expansion solutions illustrates that the full numerical solution is accurate. Furthermore, a matching closed form of solution for the scaled temperature on the wall is fitted to the theoretical results and this will be useful in numerous engineering practical applications.