Quenching of Flame Propagation with Heat Loss

The steady propagation of a planar laminar premixed flame, with a one-step exothermic reaction and linear heat loss, is studied. The corresponding travelling wave equations are solved numerically. The dependence of the flame velocity on the heat loss parameter is determined and compared with known results obtained by asymptotic expansion and other approximations. Due to the introduction of an ignition temperature the problem can be reduced to a bounded interval (of length L) and the graph of flame speed versus heat loss parameter can be parametrised by L. The numerical method is tested in the case of a step function nonlinearity when the exact solution of the differential equations can also be calculated.