Free convection from a horizontal surface in a porous medium with Newtonian heating

A very effective solution method is proposed to solve the steady free conve ction boundary-layer flow on a horizontal surface embedded in a porous medi um in which the flow is generated by Newtonian heating. Asymptotic solution s, which are valid for small and large values of x, the coordinate along th e plate, as well as a very accurate numerical solution of the full governin g equations that matches the asymptotic solutions have been obtained. It is found that for small values of x the first-order flow is driven by a const ant heat flux form the surface, and the higher order terms are then perturb ations of the standard uniform heat flux solution, which is the same behavi or seen in the corresponding conjugate problem. However, ther is an essenti al difference between the present situation and the conjugate problem when the solution far downstream is considered. For the conjugate problem, the f low far downstream approaches the standard isothermal wall solution, wherea s in the present situation, the flow far downstream at large values of x gi ves rise to a new similarity solution in which the wall fluid velocity and temperature are almost linear and quadratic functions of x, respectively.