Initiation of combustion waves in solids, and the effects of geometry

In a recent paper Weber et al. [9] examined the propagation of combustion w aves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate he re on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their form ation. The investigation includes calculations for finite systems. The resu lts for a slab, cylinder and sphere are compared. Critical conditions for initiation of ignition by a power source are establ ished. For a slab the energy input is spread uniformly over one boundary su rface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the ex ception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to th e present study, with very simple adaptation, it has been possible to repro duce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries wit h various initial and boundary conditions.