The thermal explosion revisited.

The classical problem of the thermal explosion in a long cylindrical vessel is modified so that only a fraction alpha of its wall is ideally thermally conducting while the remaining fraction 1-alpha is thermally isolated. Partial isolation of the wall naturally reduces the critical radius of the vessel. Most interesting is the case when the structure of the boundary is a periodic one, so that the alternating conductive alpha and isolated 1-alpha parts of the boundary occupy together the segments 2pi/N (N is the number of segments) of the boundary. A numerical investigation is performed. It is shown that at small alpha and large N, the critical radius obeys a scaling law with the coefficients depending on N. For large N, the result is obtained that in the central core of the vessel the temperature distribution is axisymmetric. In the boundary layer near the wall having the thickness approximately 2pir0/N (r0 is the radius of the vessel), the temperature distribution varies sharply in the peripheral direction. The temperature distribution in the axisymmetric core at the critical value of the vessel radius is subcritical.