Nonequilibrium thermodynamics of autowaves of laminar combustion

Within the framework of the Zel'dovich–Frank-Kamenetskii theory of thermal propagation of flame, thermodynamic properties of an open nonlinear system are considered, and nonequilibrium entropy of a steady combustion wave is constructed. The nonequilibrium dynamic system is analyzed qualitatively and quantitatively, and the distribution functions of local entropy production in terms of the spatial variable are constructed. It is shown that total entropy production in the system is a functional on integral curves that possess extreme properties, and its minimum corresponds to a unique physically sustainable solution of the problem. The procedure of “cutting” (vanishing) of the reaction rate is justified by methods of nonequilibrium thermodynamics. A variational formulation of the problem is presented for calculation of a steady combustion wave.