A linear relationship between dimensionless crossing-point-temperature and Frank-Kamenetskii reactivity parameter in self-heating test at infinite Biot number for slab geometry

Self-heating/ignition is one of the well-known practical causes for fires and explosions in industry and in nature. The Transient Method (or Chen Method) is a cost-effective approach for determining the thermal ignition parameters of packed particulate or loose materials (activation energy E, the product of the heat of reaction and the pre-exponential constant QA). The crossing-point-temperature (CPT) method to establish the ignition kinetics was initiated by the first author in 1994. A finite difference solution obtained in 1998 showed that for Biot number approaching infinity the dimensionless CPT, θcpt (when the conduction term becomes zero at symmetry), is proportional to the Frank-Kamenetskii reactivity parameter δ, i.e.θcpt=0.1δ. In this study, this relationship has been re-confirmed firstly by new Matlab simulations, and secondly, derived analytically with the characteristic transport dimension concept and a new simple idea of a three-region approximation. The dimensionless thickness of the third region (next to the solid-gas boundary), defined as (1−β2)self-heat, is remarkably similar to that for the heat conduction (1−β2)cond=0.333 which leads to θcpt=0.093δ. A small adjustment of (1−β2)self-heat to 0.339 leads to the exact relationship. This work shows a general applicability of the approximate linear relationship, making the method more useful.