Final Steady Flow near a Stagnation Point on a Vertical Surface in a Porous Medium¤

This paper investigates the large time (¯nal steady °ow) solutions for unsteady mixed convection boundary layer °ow near a stagnation point on a vertical sur-face embedded in a Darcian °uid-saturated porous medium. Through numerical computations Nazar et. al. [1] concluded that for values of the mixed convection parameter ¸> ¡1, the governing boundary value problem (BVP) had a unique solution. If ¸c ¡1:4175 < ¸ · ¡1 two solutions were reported, and if ¸ < ¸c then no solutions were found. The purpose of this note is to provide further mathematical and numerical analysis of this problem. We prove existence of a solution to the governing BVP for all ¸> ¡1. We also present numerical ev-idence that a second solution exists for ¸> ¡1, thus giving dual solutions for all ¸> ¸c. It is also proven that if ¸ < ¡2:9136 no solution to the BVP exists. Finally, a stability analysis is performed to show that solutions on the upper branch are linearly stable while those on the lower branch are linearly unstable