Conditions for a Thermal Explosion in the Plate under Convective-Radiation Heat Transfer

The processes of obtaining and storing energy-saturated substances are characterized by energy release in their volume. The intensity of this energy release increases with increasing temperature. The stability of the stationary temperature state of a solid with a temperature-dependent intensity of volumetric energy release is directly related to the conditions of heat transfer of this body with the environment. If the heat energy released in the volume of the body can no longer be diverted into the environment, the steady temperature state of the body becomes impossible. The paper studies the conditions for a thermal explosion in a solid in the form of a plate with a temperature-dependent coefficient of thermal conductivity and convective-radiation heat transfer on its surfaces. The statement of the nonlinear problem of steady-state thermal conductivity in the plate is represented by a system of integral relations. The limits of integration of the integrals included in these relations are the desired functions and parameters which determine the temperature state of the plate. A quantitative analysis of these relationships makes it possible to establish the influence of the parameters which determine the intensity of heat transfer and the dependence of the thermal conductivity of the plate material on the conditions for a thermal explosion with an arbitrary law of variation with temperature of the volumetric power of the energy release in the plate. The results of such an analysis are presented in the framework of a one-parameter model of the stationary theory of thermal explosion