Modelling a slow smoldering combustion process

We present a mathematical model for the slow and partial combustion process of a sheet of paper ignited on one side and in the presence of a flow of air confined in a narrow gap above the paper. The model includes mass and thermal balance for the various components. After having introduced some simplifications, a suitable rescaling is performed and some limit cases are examined. Two classes of travelling wave solutions are analyzed, corresponding to the opposite cases of a sufficiently large or of a moderate air flow.