THE EFFECTS OF AN OUTER FLOW ON THE UNSTEADY FREE CONVECTION BOUNDARY LAYER NEAR A STAGNATION POINT IN A HEAT-GENERATING POROUS MEDIUM

The unsteady mixed convection boundary-layer flow near a forward stagnation point in a porous medium is considered when there is local heat generation within the boundary layer at a rate proportional to (T - T-infinity)(p), (p >= 1), where T is the fluid temperature and T-infinity the ambient temperature. The solution to the initial-value problem is seen to depend on the exponent p and the dimensionless parameter lambda that characterizes the strength of the outer flow. For p = 1 the solution approaches a non-trivial state at large times when lambda < 1 and a trivial state if lambda > 1. When 1 < p < 2 there is a critical value lambda(crit) arising in the steady state solutions, dependent on p and decreasing to zero as p -> 2. When lambda < lambda(crit), the solution approaches the corresponding steady state and when lambda > lambda(crit), it approaches the trivial state. When p > 2, there is a critical value for lambda, above which the trivial state is reached at large times and below which a finite-time singularity with thermal runaway develops in the solution, the details of which are discussed. A critical initial input strength is seen to be required to generate non-trivial solutions a larger times.