Abstract
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.
Similar content being viewed by others
REFERENCES
V. A. Vasil'ev, Yu. M. Romanovskii, and V. G. Yakhno, Autowave Processes [in Russian], Nauka, Moscow (1987).
R. A. Fisher, "The wave of advance of advantageous genes," Ann. Eugenics, 7, 335–369 (1937).
A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, "Investigation of the diffusion equation combined with an increase in the amount of the substance, and the use of this equation in one biological problem," Byul. Mosk. Gos. Univ., 1, Ser. A, No. 6, 1–26 (1937).
Ya. B. Zel'dovich and D. A. Frank-Kamenetskii, "Theory of uniform propagation of ame," Dokl. Akad. Nauk SSSR, 19, No. 9, 693–697 (1938).
Ya. B. Zel'dovich and D. A. Frank-Kamenetskii, "Theory of thermal propagation of ame," Zh. Fiz. Khim., 12, No. 1, 100–105 (1938).
P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley Intersciences, New York (1971).
L. Onsager, "Reciprocal relations in irreversible processes. I," Phys. Rev., 37, 405–426 (1931).
L. Onsager, "Reciprocal relations in irreversible processes. II," Phys. Rev., 38, 2265–2279 (1931).
I. Dyarmati, Non-Equilibrium Thermodynamics. Field Theory and Variational Principles, Springer-Verlag, Berlin-Heidelberg-New York (1970).
I. P. Vyrodov, "Variational principles of phenomenological thermodynamics of irreversible processes in the aspect of a closed system of axioms," Zh. Fiz. Khim., 56, No. 6, 1329–1342 (1982).
I. P. Vyrodov, "Extreme properties of nonequilibrium thermodynamic systems and their dissipative functionals," Zh. Fiz. Khim., 62, No. 4, 865–882 (1988).
I. P. Vyrodov, "Generalization of the Onsager theorem and construction of nonequilibrium entropy in nonlinear phenomenological thermodynamics of irreversible processes," Zh. Fiz. Khim., 72, No. 2, 225–228 (1998).
A. P. Gerasev, "Nonequilibrium thermodynamics of propagation of heat waves in a catalytic bed," Dokl. Ross. Acad. Nauk, 359, No. 4, 495–498 (1998).
A. P. Gerasev, "Nonequilibrium thermodynamics of heat waves in a catalytic bed. Functional of an autowave solution," Fiz. Goreniya Vzryva, 36, No. 3, 51–59 (2000).
A. P. Gerasev, "Propagation of heat waves in a catalytic bed upon oxidation of sulphur dioxide," Zh. Fiz. Khim., 74, No. 7, 1174–1180 (2000).
A. I. Karpov, "Minimal entropy production as an approach to the prediction of the stationary rate of ame propagation," J. Non-Equilib. Thermodyn., 17, No. 1, 1–9 (1992).
Ya. B. Zel'dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, The Mathematical Theory of Combustion and Explosions, Plenum, New York (1985).
S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam (1962).
I. Prigogine and R. Defei, Chemical Thermodynamics, Longmans-Green, London-New York-Toronto (1954).
A. P. Aldushin, V. D. Lugovoi, A. G. Merzhanov, and B. I. Khaikin, "Degeneration conditions for a steady combustion wave," Dokl. Akad. Nauk SSSR, 243, No. 6, 1434–1437 (1978).
A. G. Merzhanov and B. I. Khaikin, Theory of Combustion Waves in Homogeneous Media [in Russian], Inst. of Struct. Macrokinetics, Russian Acad. of Sci., Chernogolovka (1992).
A. P. Aldushin, Ya. B. Zel'dovich, and S. I. Khudyaev, "Numerical investigation of ame propagation in a mixture reacting at the initial temperature," Fiz. Goreniya Vzryva, 15, No. 6, 20–27 (1979).
A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Qualitative Theory of Second-Order Dynamic Systems [in Russian], Nauka, Moscow (1966).
N. N. Bautin and E. A. Leontovich, Methods and Procedures of Qualitative Investigation of Dynamic Systems on a Plane [in Russian], Nauka, Moscow (1976).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gerasev, A.P. Nonequilibrium Thermodynamics of Autowaves of Laminar Combustion. Combustion, Explosion, and Shock Waves 37, 626–633 (2001). https://doi.org/10.1023/A:1012967811989
Issue Date:
DOI: https://doi.org/10.1023/A:1012967811989