The relationship between thermal diffusivity, energy of activation and temperature rise in subcritical self heating of fuels in simple geometries

Abstract

Abstract Fuels or other substrates prone to oxidation or exothermic decomposition may experience an extreme behavior, known as supercritical behavior (i.e. when internal heat generation due to exothermic reactions overcomes heat transfer to surrounding environment), that lead to such a severe internal temperature rise that will ultimately cause a fire or an explosion. On the contrary, under subcritical conditions, self heating of the reacting mass will ultimately produce only a limited temperature rise, whose intensity is dictated by the reactivity of the substrate and by the heat transfer conditions. The experimental characterization of self heating behavior of fuels and of other substrate prone to self heating may be performed by analyzing the thermal history of samples of known size and geometry, exposed to controlled thermal environments. The experimental determination of critical temperature for samples of different sizes or the characterization of the rate of temperature rise in selected points of the sample domain are the working principles of the experimental methods used for estimating thermal and kinetic properties of the substrate. The application of the last procedure may be extended to the analysis of subcritical experiments that still produce a measurable temperature rise. In this work the analytical solution of an approximate form of the heat transfer equation with internal heat generation term has been developed and used to identify the relationship between thermal diffusivity, energy of activation of the exothermic reactions and maximum temperature rise in subcritical self heating of fuels in simple geometry. Finally comparison with the numerical solutions of the exact form of the heat transfer equation with internal heat generation term for three different substrate confirmed the previously identified functional dependence and enabled to obtain closed form correlations, in term of dimensionless variables, between the thermal diffusivity, the energy of activation, the temperature rise rate and the maximum temperature rise in subcritical self heating of fuels in simple geometries. The closed forms relationships developed in this work may be useful for estimating the thermal diffusivity of a material that is subject to the self heating oven experiments and that under sub critical conditions exhibit measurable steady state temperature rise or possibly even to estimate activation energy of the substrate from (even a single) subcritical oven heating experiment(s), once its thermal diffusivity is known with precision from a different kind of experiment.