Mixed Convection Boundary Layer Flow Over A Vertical Permeable Plate In A Porous Medium: Opposing Flow Case

The opposing flow case of steady mixed convection boundary layer flow over a vertical permeable surface in a porous medium with uniform thermal wall conditions, i.e. when both the wall temperature and the wall heat flux are constants, is considered. The Rayleigh number for the porous medium is assumed to be large so that the boundary layer approximation can be considered. Under these assumptions, it is found that the problem depends both on the mass transfer parameters and the mixed convection parameters. It is shown that the governing equations can be reduced to a similarity form, i.e. to ordinary differential equations. These equations are solved numerically using a very efficient implicit finite difference scheme known as the Keller-box method. Numerical results for the reduced skin friction and non-dimensional wall temperature are presented and discussed in detail for various values of the parameters of interest. An important finding of this problem is that there are dual solutions of the governing boundary layer equations and the separation of boundary layer occurs for certain cases.