Critical conditions for thermal explosion in a plate with a nonlinear heat source

Abstract

The exact analytical solution of the nonstationary heat conduction problem with a nonlinear internal heat source at the nonsymmetric third-type boundary conditions was obtained by the method of variable separation. The relations between the boundary condition parameters and a heat source separating the stationary processes from processes of an unlimited temperature increase (thermal explosion) were found. For known physical properties of medium, the maximum allowable value of the specific power of a heat source has been found. If nonsymmetric boundary conditions are exceeded on wall surfaces, it can lead to thermal destruction.