Final steady flow near a stagnation point on a vertical surface in a porous medium

This paper investigates the large time (final state flow) solutions for unsteady mixed convection boundary layer flow near a stagnation point on a vertical surface embedded in a Darcian fluid-saturated porous medium. Through numerical computations Nazar et al. [R. Nazar, N. Amin, I. Pop, Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium, Int. J. Heat Mass Transfer 47 (2004) 2681-2688] concluded that for values of the mixed convection parameter lambda > -1, the governing boundary value problem (BVP) had a unique solution. If lambda(c) approximate to -1.4175 < lambda <= -1 two solutions were reported, and if lambda < lambda(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 lambda > -1. We also present numerical evidence that a second solution exists for lambda > -1, thus giving dual solutions for all lambda > lambda(c). It is also proven that if lambda < -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. (c) 2006 Elsevier Ltd. All rights reserved.