In a recent paper B. J. Matkowsky and G. I. Sivashinsky employed asymptotic methods to derive a simplified model in flame theory from the general equations of combustion. The model was derived under the assumptions of (i) large activation energy, (ii) closeness to similarity and (iii) weak thermal expansion, and the resulting model was associated with the constant density approximation. In this paper, assumption (iii) is relaxed somewhat and in addition a more general temperature dependence of the thermal conductivity, heat capacity and diffusivity is assumed. The new model now exhibits nonconstant density effects. A number of solutions of the model, representing various types of flames are presented, and their stability is analyzed.
ASJC Scopus subject areas
- Applied Mathematics