Critical conditions for thermal explosion in conductive heat transfer in the reaction zone and the surrounding medium

The critical conditions for thermal explosion are examined for plane, sphere, and cylinder in an unbounded medium with convective heat transfer in the internal and external regions. Criteria are used in integro-differential equations in the form of a Duhamel integral, which allow the conjugate problem to be reduced to a boundary one. Critical conditions are calculated by computer, with analysis for the cases of greatest practical interest.Notation c thermal capacity - density - thermal conductivity - a thermal diffusivity - Q heat of reaction - E activation energy - k₀ the preexponential factor - extent of reaction - T temperature - T₀ temperature of surrounding medium - r₀ characteristic dimension of bodyWe are indebted to B. I. Khaikin and V. V. Barzykin for valuable advice.