Analytical solution of a near-equidiffusional flame problem

The near-equidiffusional flame problem for determining the effect of acoustic disturbances having a time scale comparable with the diffusion time is reduced to a set of nonlinear Volterra equations for a pair of functions related to the burning rate and the flame temperature perturbation. Further analysis yields a small-time approximation of general validity and an explicit solution for arbitrary small-amplitude disturbances. A numerical method for solving the Volterra-equation problem is described. Numerical examples are exhibited to compare the behaviour of the linear approximation to the solution of the full model. Slowly decaying oscillatory behaviour for flames with Lewis number near the right stability boundary is predicted by the linear approximation and observed in numerical examples for the nonlinear model.