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.

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

: An analysis was made and a solution was found with the aid of an electronic computer for a system of equations for thermal explosions; it is given in partial derivatives for reactions of the zero and first order with heat transfer by conduction in the zone of the reaction and a Newton heat exchange at the boundary. The basic characteristics of thermal explosions are exactly determined. The obtained results are presented in the form of approximate expressions connecting the characteristics of the thermal explosion with all parameters of the problem for a wide range of changes. A criterion is given for the applicability of the averaged volume of the equation for calculating the period of induction, in case the heat transfer in the reacting volume takes place by conduction. A method is offered for averaging the system of equations of thermal explosions. (Author)

S. I. Khudyaev

Papers

Concerning the theory of unsteady thermal explosions