Propagation and extinction of forced opposed flow smolder waves

Smoldering is a slow combustion process in a porous medium in which heat is released by oxidation of the solid. If the material is sufficiently porous to allow the oxidizer to easily filter through the pores, a smolder wave can propagate through the interior of the solid. We consider samples closed to the surrounding environment except at the ends, with gas forced into the sample through one of the ends. A smolder wave is initiated at the other end and propagates in a direction opposite to the flow of the oxidizer. Previous experimental results show that for opposed flow smolder, decomposition of the solid fuel into char is the chemical process which drives the smolder process. We model this decomposition as a one step reaction. The model suggests that extinction occurs when decomposition is complete. We employ large activation energy asymptotic methods to find uniformly propagating, planar smolder wave solutions. We determine their propagation velocity, burning temperature, final degree of fuel decomposition, and extinction limits. We also determine spatial profiles of gas flux, oxidizer concentration, temperature, and degree of decomposition of the solid. Comparison is made with previous experimental results.