Steady regimes of conversion in a viscoelastic medium

The problem of propagation of a steady conversion front in a viscoelastic medium is solved by the method of matched asymptotic expansions in the approximation of low strains. The heat flux is assumed to satisfy the Fourier law, and the components of the stress and strain tensors are related by the Maxwell relations including the shear coefficient of viscosity. The temperature of the products and the velocity of propagation of the steady reaction front are found. The solution of the problem is obtained for the limiting cases of the small and large times of relaxation of viscous stresses. It is demonstrated that the model contains different regimes of reaction-front propagation, like the coupled models of solid-phase combustion for a thermoelastic body, and viscous stresses insert additional features.