FREE-CONVECTION STAGNATION POINT BOUNDARY-LAYERS DRIVEN BY CATALYTIC SURFACE-REACTIONS .2. TIMES TO IGNITION

The steady states of a combustion model, derived in a previous paper, were shown to have critical points (turning points in the bifurcation diagram) for certain ranges of parameter values. Here attention is fix ed on the heat release parameter lambda and the time evolution for the solution for values of lambda just above its critical value lambda(c) ((1)) is discussed. It is shown that the solution develops a three-sta ge structure, with the solution both approaching and leaving the criti cal point on a relatively short time scale. However, the majority of t he time is spent in moving slowly past the critical point, on an O((la mbda - lambda(c)((1)))(-1/2)) time scale. The solution finally attains its values on the upper solution branch, except in the special case o f the exponential approximation and when reactant consumption is negle cted. Here the temperature develops a singularity at a finite time t(B ), of O(log(t(B) - t)), though the fluid velocity remains finite at t( B).