MICROWAVE-INDUCED COMBUSTION - A ONE-DIMENSIONAL MODEL

A model for the heating and ignition of a combustible solid by microwa ve energy is formulated and analysed in the limit of small inverse act ivation energy epsilon and small Riot number B. The high activation en ergy limit implies that the heating process is effectively inert until the temperature within the material reaches a critical ignition value , while the small Riot number limit implies that during this stage spa tial variations in temperature throughout the material are always smal l. Analysis of the inert stage includes determination of the dynamics of inert hot-spots. As the ignition temperature is approached chemical energy is released rapidly in the form of heat, and the evolution the n enters an ignition stage which develops on a fast timescale. A reduc ed system is derived governing small-amplitude departures of the tempe rature from the inert value during the ignition stage under the signif icant scaling relation between the expansion parameters, which is show n to be <epsilon similar to B. This reduced system recovers both of th e familiar canonical systems describing (i) localized ignition by in-d epth absorption of radiation and (ii) spatially homogeneous blow-up, i n the limits of small and large values of mu = epsilon/B, respectively . Numerical integration of the reduced system in parameter regimes rel evant to production of materials by combustion synthesis shows that ig nition can occur either on the boundary or in the interior of a solid sample, and that there are regimes where the ignition site changes abr uptly with variation of system parameters.