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

作者：Chen, Xiao Dong^*; Sidhu, Harvinder; Nelson, Mark

来源：Fire Safety Journal, 2013, 61: 138-143.

DOI：10.1016/j.firesaf.2013.08.002

• Self-ignition kinetics
• Crossing-point temperature
• Transient method
• Slab geometry
• Infinite Blot number
• Frank-Kamenetskii reactivity parameter

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 Blot number approaching infinity the dimensionless CPT, Ocpt (when the conduction term becomes zero at symmetry), is proportional to the Frank-Kamenetskii reactivity parameter 5, Le.Ocpt = 0.15. 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 (1,82),fiheat, is remarkably similar to that for the heat conduction (1 132)cond =0.333 which leads to Ocpt = 0.0935. A small adjustment of (1 132)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.

• 出版日期2013-10
• 单位苏州大学