Asymptotic, approximate, and numerical solutions for the heatup and pyrolysis of materials including reradiation losses

Abstract

In this work, we emphasize a thorough theoretical analysis and derivation of asymptotic, approximate, and numerical solutions for the heat-up and pyrolysis of noncharring material. These results have been and/or can be used for the derivation of material flammability pyrolysis properties by using measurements in existing apparatus. Specifically, we derive and study integral equations describing heating followed by pyrolysis of a material subjected to an external heat flux. Surface reradiation losses, which are included during the heating period, make the surface temperature integral equation nonlinear. We develop for this equation (a) asymptotic expansions for large and small times by using the Mellin transform, and (b) uniformly valid approximate solutions that are compared with exact solutions. Such asymptotic and approximate solutions have already been used to extract material thermal properties from surface temperature measurements. We extend the analysis to the pyrolysis of a material, which is assumed to be described as an ablation (Stefan) problem. We have derived a new integral equation for the pyrolysis rate and we have used it to find asymptotic and validated approximate solutions. These solutions have been proven essential for deriving material pyrolysis properties from standard tests as is briefly described in each section.