The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

Abstract

The natural convection boundary-layer flow near a stagnation point on a permeable surface embedded in a porous medium is considered when there is local heat generation within the boundary layer at a rate proportional to (T-T_infty )^p, p ge 1, where T is the fluid temperature and T_infty the ambient temperature. There is mass transfer through the surface characterized by the dimensionless parameter gamma, with gamma >0 for fluid injection and gamma <0 for fluid withdrawal. The steady states are considered where it is found that, for p >1, there is a critical value gamma _c of gamma with solutions existing for gamma ge gamma _c if 1<p<2 and for gamma le gamma _c if p>2. The initial-value problem reveals that, for 1 le p<2, the nontrivial steady states are stable and the solution evolves to this state at large times. However, for p>2 these steady states are unstable and the solution either approaches the trivial state with the local heating dying out or a finite-time singularity develops for sufficiently large initial inputs.