Asymptotic Analysis of Laminar Flame Propagation for General Lewis Numbers

The structure of a steady one-dimensional isobaric deflagration is examined for the case of a direct first-order one-step irreversible exothermic unimolecular decomposition under Arrhenius kinetics. In particular, the eigenvalue giving the speed of propagation of the laminar flame into the unburned gas is sought for constant Lewis number of order unity. The method of matched asymptotic expansion is invoked in the physically interesting limit of activation temperature large relative to the adiabatic flame temperature. The leading approximation for the eigenvalue is found to be a generalization of the result given by Zeldovich, Frank-Kamenetski, and Semenov for Lewis number unity. The first two terms in the asymptotic expansion for the eigenvalue yield an expression superior to any previously published.