Stationary wave of a chemical reaction in a deformable medium with finite relaxation time of the heat flux

We propose a model for the propagation of the stationary front of a chemical reaction in a deformable medium taking into account thermal relaxation. In the model we consider possible deformations of the material due to thermal expansion and the difference between the properties of the reagent and the product and their effect on the temperature field. We show that relaxation of the heat flux and “coupling” of the temperature and strain fields are manifested through a change in the heat capacity, the effective thermal conductivity of the material, and the overall heat of the chemical reaction. In the model of a zero-order reaction, there are two velocities of the front: one of them is close to the velocity of the “thermal” self-excited wave, the other is higher than the velocity of sound and is connected with the effect of the deformation forces. Additional solutions appear in the model in the case of a first-order reaction when relaxation effects are present.