Critical conditions for conjugate thermal explosion

The thermal explosion problem is considered within the two thermally interacting regions with different thermal and kinetic properties. Thermal exchange with the surroundings is assumed to obey Newton's law. Critical conditions for such a problem are established for the planar, cylindrical and spherical geometries. The major conclusion of the present paper is that critical conditions in the two-media system differ both quantitatively and qualitatively from that of the single-media system. In particular, thermal runaway may occur in the composite system at the parameters that are subcritical for both regions, considered as a single media. On the other hand, under certain conditions where a single-media system would experience thermal explosion, conjugate thermal explosion is preventable by adjusting the properties of the neighboring material and the rate of heat exchange with the surroundings. Different scenarios of thermal explosion development are presented for a typical (cylindrical geometry) case by way of unsteady numerical simulations.