Several-temperature systems: extended irreversible thermodynamics and thermal wavefront propagation

We develop an extension of local-equilibrium thermodynamics for systems with components at different temperatures. The description includes heat conduction, diffusion, a chemical reaction and heat losses. The ensuing equations are applied to the problem of thermal wavefront propagation. There is satisfactory agreement between the predicted and the experimental values for the speed of combustion flames over cellulosic fuels. Heat losses cause a decrease of the front speed. This generalizes Zeldovich's result. For radiative losses, the effect can easily be about 15%. When the finite speed of thermal signals is taken into account, an additional lowering of the thermal wavefront speed results.