A comparison of some hot spot theories

Abstract In considering the extension of hot spot theory to take into account, for example, the difference between the thermal properties of a hot spot and its surroundings (one of many differences between real hot spots and the idealized hot spots of existing theoretical models) some of the approximate theories for the critical conditions for a thermally explosive spherical hot spot have been compared with each other and with numerical solutions obtained by Merzhanov et al. Certain of the mathematical approximations are in effect physical approximations and these are also briefly discussed. The initially adiabatic self-heating of the centre of the hot spot is an important feature of its behaviour and Zinn's simple treatment allows for this and gives no worse a result for the spherical hot spot than some of the more elaborate approximate models.