Solar radiation assisted natural convection in uniform porous medium supported by a vertical flat plate

Natural convection flow of an absorbing fluid up a uniform porous medium supported by a semi-infinite, ideally transparent, vertical pat plate due to solar radiation is considered. Boundary-layer equations are derived using the usual Boussinesq approximation and accounting for applied incident radiation flux. A correlation type boundary condition is used at the plate surface. These equations exhibit no similarity solution. However, the local similarity method is employed for the solution of the present problem so as to allow comparisons with previously published work. The resulting approximate nonlinear ordinary differential equations are solved numerically by a standard implicit iterative finite-difference method. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed.