Combustion waves have been studied for some time. They have been observed in numerous experiments and play an important role in industrial processes, such as the production of advanced materials using Self-propagating High-temperature Synthesis (SHS). One-step irreversible reaction models have contributed greatly to our understanding of these phenomena. These models have proven their usefulness since they are relatively simple and allow analytical investigation which have led to many useful and qualitatively correct predictions for phenomena such as: ignition, extinction, propagating and stability of premixed flames, etc. However, in the overwhelming majority of cases, chemical reactions in flames proceed through a complex mechanism, that involves a variety of steps. In this work we analyse the travelling wave solutions of an non-adiabatic model of combustion with a two-step chain branching reaction mechanism.

The properties of these solutions are investigated, in particular the combustion wave speed and the residual amount of fuel that is left behind after the flame has propagated through the medium. These properties are analysed as various control parameters are varied. We also compare the results for this reaction with its one-step counterpart to determine the differences between the two mechanisms.