When a HE is subjected to significant heating it reacts, i.e. it burns to form gaseous products.
When an explosive burns, gaseous products are formed as a result. The interaction of the burning solid and gas is not well understood. More specifically, the process of the gaseous product heating the explosive is yet to be explored in detail. The present work does much to fill that gap using mathematical modelling: this aims to track the temperature profile in the explosive and the response of the gas.

This work begins by modelling single step reactions using the simple Arrhenius model. An alternative asymptotic approach is also employed. There is close agreement between results from the full reaction-diffusion problem and the asymptotic problem. The model is then extended to include three step reaction kinetics, where we again apply asymptotic analysis.
Further work includes of gas being incorporated in the existing model with temperature and pressure distributions considered. We also consider the effects of the gas on the solid explosive temperature. This is achieved by first allowing the gas to heat the boundaries of the solid. Later we incorporate internal heating of the solid by the gas into the model. An asymptotic approach is also considered here and successfully captures the behaviours of interest. Finally, we address a second heating method; mechanical stimulus provided by a wedge-like squeezing of an explosive material. Here sensitive effects within thin shear layers are predicted. The study finds major events take place in thin boundary layers, a highlight which holds for mechanical as well as thermal events.