Thermal explosion of an annular layer with boundary conditions of the third kind

An analytical solution of the problem of thermal explosion of an annular layer is obtained for two cases: 1) the inner cylinder is thermally insulated (heat exchange with the environment through the surface of the outer cylinder follows Newton's law); 2) the outer cylinder is thermally insulated (heat exchange through the surface of the inner cylinder follows the same law). The dependence of the critical value of the Frank-Kamenetskii parameter on the ratio of the radius of the inner cylinder to the radius of the outer cylinder is constructed for various values of the Biot number. The limiting cases where this ratio tends to zero and unity are considered.