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

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 , where T is the fluid temperature and the ambient temperature. There is mass transfer through the surface characterized by the dimensionless parameter , with for fluid injection and for fluid withdrawal. The steady states are considered where it is found that, for , there is a critical value of with solutions existing for if and for if . The initial-value problem reveals that, for , the nontrivial steady states are stable and the solution evolves to this state at large times. However, for 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.