The effect of heat loss on the propagation of strongly exothermic combustion waves

We study the propagation in one spatial dimension of combustion waves in a strongly exothermic, premixed fuel. After using numerical methods to determine the form of the combustion waves, we use the method of matched asymptotic expansions to obtain asymptotic approximations for the permanent form travelling wave solutions. This allows us to determine the leading-order behaviour of the maximum temperature, the residual concentration of fuel behind the wave, the wave speed and the maximum heat transfer coefficient that allows the propagation of waves, along with the qualitative form of the wave. In all cases, good agreement is found between numerical and asymptotic results.