Thermal explosion of a hollow cylinder under third-kind boundary conditions

The problem of the thermal explosion of a reactant in the shape of a hollow cylinder under third-kind boundary conditions is solved by an inverse method. Methods for determining the critical parameters in the general and particular cases are given. Transcendental equations are derived whose roots are used to determine the critical values of the Frank-Kamenetskii parameter. The results of a numerical analysis are presented and approximating functions are given to determine the critical Frank-Kamenetskii parameter as a function of the Biot number.