Ignition of a Rectangular Solid by an External Heat Flux

The influence of corners on the ignition of a solid exposed to a surface energy flux is analyzed with large activation energy asymptotics. We begin with the analysis of the ignition of semi-infinite wedges by a constant heat flux. Two stages and two spatial zones, reactive and inert, are found. The ignition stage can be described by a slowly convergent asymptotic expansion for the increment in temperature due to the chemical reaction or, more accurately, by a simplified nonlinear parabolic equation to be solved numerically. This analysis applies to the ignition of two-dimensional finite bodies with corners if the external heat flux is large enough for the size of the reaction zone to be much smaller than that of the solid. The ignition of bodies with rectangular shape for small heat fluxes, when the reaction zone extends to the whole solid, is also analyzed. K e y words, combustion, ignition, thermal runaway, hot spot, activation energy asymptotics, Arrhenius kinetics A M S subject classifications. 35C20, 35K57, 80A25