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 λ > -1, the governing boundary value problem (BVP) had a unique solution. If λ_c ≈ -1.4175 < λ ≤ -1 two solutions were reported, and if λ < λ_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 λ > -1. We also present numerical evidence that a second solution exists for λ > -1, thus giving dual solutions for all λ > λ_c. It is also proven that if λ < -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.