Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium

The unsteady mixed convection boundary layer flow near the region of a stagnation point on a vertical surface embedded in a Darcian fluid-saturated porous medium is studied in this paper. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature. The problem is reduced to a single partial differential equation, which is solved numerically using the Keller–Box method. The small time (initial unsteady flow) as well as the large time (final steady state flow) solutions are also included in the analysis. The asymptotic behavior of the solution for small and large values of the mixed convection parameter λ is also examined when the flow becomes steady. It is shown that there is a smooth transition from the small time solution to the large time solution. It is also shown that there is an excellent agreement between the numerical and analytical solutions. The uniqueness of this problem lies on the fact that we have been able to show that in the case of steady state flow, solutions are possible for all values of λ>0 (assisting flow) and for λ<0 (opposing flow), solutions are possible only for a limited range of λ.