Friction and localized heat initiation of ignition: The asymmetrical slab and cylindrical annulus

Certain chemical compunds, including powders not normally classified as deflagrating or denoting explosives, can nevertheless decompose with violence. Surface heat-sources that arise in the handling and transport of these materials are considered here. When reactant consumption is ignored and thermal conduction controls heat-flow, explicit solutions can be obtained for the dependence of temperature on position in the steady state so long as the shapes are simple. The present paper extends our previous work to the asymmetrical slab and the cylindrical annulus with localized heating at the inner surface and/or internal heating within the inner core. Surface heating decreases the range of stability in a simple way and explicit expressions are derived for the effects in the case of the cylindrical annulus. The asymmetrical slab gives rise to a set of transcendental equations from which the critical conditions are computed. For the asymmetrical slab a condition for which the maximum occurs within the reacting material can be obtained analytically.