Theory of Ignition of a Reactive Solid by Constant Energy Flux

A formula for the ignition time, that Bradley obtained empirically, is derived analytically by a rigorous asymptotic analysis of the limit of large activation energy. Two terms in the expansion must be retained. The second term reveals the existence—just prior to ignition—of a reactive-diffusive zone at the surface of the solid and a transient-diffusive zone in the interior. The analysis also exhibits a universal correction factor for Bradley's formula, of order unity.