THE INFLUENCE OF INITIAL TEMPERATURE-EXCESS ON CRITICAL CONDITIONS FOR THERMAL-EXPLOSION

In the conductive theory of thermal explosion, an exothermic system is considered to be an ignition hazard only if the numerical value of the dimensionless group exceeds a critical value. This paper considers the temperature evolution in bodies subject to Frank-Kamenetskii boundary conditions but which are assembled with a positive, uniform temperature-excess. It is shown that in the usual exponential approximation, any system with delta less than equivalent to delta //c//r has a critical initial temperature, above which thermal runaway occurs. Exact numerical results for the critical conditions are presented for the three class A geometries (infinite slab, infinite cylinder, and sphere). Very accurate analytical approximations are also provided.