Steady-state solutions for strongly exothermic ignition in symmetric geometries

We consider the steady-state solutions for the strongly exothermic decompos ition of a combustible material under Arrhenius kinetics in symmetric geome tries, neglecting the consumption of the material. We solve the nonlinear b oundary-value problem for the dimensionless temperature, u, d(2)u/dr(2) + N - 1/r du/dr + lambdaH(u)e(-1/u) = 0, subject to du/dr = 0 at r = 0, and Bi(u(a) - u) = du/dr at r = 1, for lambd a >> 1, using both numerical and asymptotic methods. All of the features of the bifurcation diagram and the steady-state solutions that we determine n umerically, including multiplicity of steady-state solutions and the existe nce in certain cases of a boundary layer at the centre of the material, can be explained using asymptotic techniques.