Radiant ignition of a reactive solid with in-depth absorption

Abstract

An asymptotic analysis of the limit of large activation energy is presented for radiant ignition of a solid that experiences a one-step Arrhenius reaction in the condensed phase. Both constant and time-dependent radiant-energy fluxes arc considered, and the complete range of values is covered for the absorption coefficient ji. It is shown that as » increases, the structure of the transition stage, which follows the inert heat-conduction stage, passes from a thermal explosion without heat conduction, to a single transient heat-conduction zone with distributed chemical heat release, to a two-zone structure composed of a reactive-diffusive-absorptive zone near the surface and a transient-diffusive zone in the interior. For very high values of u, the reactive-diffusive-absorptive zone further splits into a surface absorption zone and an interior reactive-diffusive zone, thereby reproducing results obtained previously for ignition by a surface-applied energy flux. The analysis shows that contrary to earlier expectation, the nondimensional absorption coefficient must be at least as large as the nondimensional activation energy for in-depth absorption to affect the ignition time negligibly.