Combustion waves for gases (Le = 1) and solids (Le→∞)

The traditional combustion problems of calculating flame speeds for a premixed gaseous fuel and for a premixed solid fuel are revisited using a simpler (than previously) non–dimensional temperature. It turns out to be possible to carry out asymptotic calculations for flame speed and the agreement with corresponding numerical calculations is remarkably good. In each case the uniqueness of the speed is considered using phase plane methods, with a little effort to determine the nature of the ‘cold’ critical point. Consideration of the stability of the travelling combustion wave fronts suggests a period doubling route to chaos for the premixed solid fuel (as the exothermicity is decreased) and corresponds with previous work using different non–dimensional temperature and parameters.