The effect of ambient temperature on the propagation of nonadiabatic combustion waves

In this paper, we undertake an analytical and numerical investigation of the linear stability and properties of travelling nonadiabatic combustion wave for the case of nonzero ambient temperature. Here we consider premixed fuel with one-step exothermic reaction described by Arrhenius law. The speed of the front is estimated analytically by employing the matched asymptotic expansion approach and numerically using the shooting and relaxation methods. It is shown that increasing the ambient temperature results in the growth of both the flame speed and the region of existence of the travelling wave solutions in the parameter space. The linear stability of the travelling wave solution is investigated analytically by using the matched asymptotic expansion method and numerically by employing the Evans function approach. We demonstrate that by increasing the ambient temperature the stability of the propagating wave can also be increased.