IGNITION OF AN ABSORBING EMITTING MEDIUM BY AN IMPOSED RADIANT-HEAT FLUX/

We consider the unsteady ignition of a reactive slab subjected to exte rnal heating, in conditions where all the heat transfers are of radiat ive origin and, consequently, introduce a reference length L (Planck's ). Radiant exchanges in the bulk are modelled by the Eddington equatio n, and an Arrhenius law with a large activation temperature is postula ted for the rate of heat release. The problem is thus solved by activa tion energy asymptotics. Similarly to ignitions by conductive heating, one can distinguish two main stages: an inert stage, followed by an i gnition stage. As is first shown upon use of a simplified source funct ion, different situations must be distinguished depending on the ignit ion time t(ig): 1) for early ignition, the thermal runaway occurs in a n optically-thin surface layer where the excess-emission due to heat r elease may be neglected. 2) moderately late ignitions still take place in optically-thin layers but excess emission must be retained. 3) lat e ignitions occur in reaction layers of O(1) optical thicknesses, impl ying fully nonlocal exchanges. 4) very late ignitions are governed by the optically-thick approximation and the problem assumes a structure encountered in conductive ignitions. In any case asymptotic estimates of t(ig) are provided analytically. In the last parts of the paper we show that the aforementioned reaction layers have rather universal str uctures, in the sense that they are also encountered when nonlinearize d radiative transfer and/or, in some instances, when reactive bodies o f more complicated shapes are considered. In the case of finite reacti ve bodies, ignition may not occur and generalized Semenov-Frank-Kamene tskii problems define the conditions for the existence of a thermal ru naway.