Semi-Analytical Modeling of Pyrolysis Front and Ignition Temperatures of Thermally Reactive Single Solid Particles

A semi-analytical approach is developed for predicting pyrolysis front temperature in a charring solid undergoing thermal decomposition. The pre-reaction heating stage is described using an analytical formulation and invoking the concept of thermal penetration depth. The solution for the solid conversion stage accounts for decomposition enthalpy, the convective flow of volatiles, and a reaction front characterized by a uniform temperature that progresses toward the inner layers. This method incorporates empirical relations into the analytical model. Two scenarios are considered. First, the solution of the pyrolysis model combined with the data of conversion time versus external heat flux leads to an algebraic expression that reveals the existence of a maximum pyrolysis-front temperature. Explicit relations are derived for both the extremum pyrolysis temperature and optimum applied heat flux. In the second case, an expression is derived for the ignition temperature of a solid fuel (e.g., wood) by incorporating ignition delay time measurements into the heating stage model. The newly derived expression allows the ignition temperature to be described as a function of the Biot number and external heat flux. The relation obtained for the ignition temperature explains the experimental trends reported in some previous studies where two local extremums were observed for the ignition temperature in the absence of volatile reactions.