Abstract
It is shown that the well-known Hirschfelder-Euken correction to the thermal conductivity of a polyatomic gas mixture given by the first approximation in Sonine polynomials can be less than the corresponding exact value (for a Lorentz mixture of light and heavy molecules interacting in accordance with Coulomb's law) by a factor of 3.4. Fairly high accuracy is achieved in the second approximation in Sonine polynomials. Within the framework of the latter, similar corrections to the nonequilibrium heat and diffusion fluxes are found. On the basis of the generalized Chapman-Enskog method a more general case is studied. In this case some of the nonelastic collision integrals is also taken into account in calculating the transport coefficients. The transport coefficients are either represented in terms of the well-known formulas for fast and retarded internal molecular energy exchange or convenient approximate expressions are obtained.
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References
V. S. Galkin, M. N. Kogan, and N. K. Makashev, “The generalized Chapman-Enskog method. P.2. Nonequilibrium gas dynamic equations,”Uch. Zap. TsAGI,5, 66 (1974).
V. S. Galkin, M. N. Kogan, and N. K. Makashev, “The generalized Chapman-Enskog method,”Dokl. Akad. Nauk SSSR,220, 304 (1975).
M. N. Kogan, V. S. Galkin, and N. K. Makashev, “Generalized Chapman-Enskog method: derivation of the nonequilibrium gas-dynamic equations,”Rarefied Gas Dynamics. Pap. 11th Symp. Cannes 1978, Vol. 2, Paris (1979), p. 693.
V. A. Matsuk and V. A. Rykov, “The Chapman-Enskog method for a gas mixture,”Dokl. Akad. Nauk SSSR,233, 49 (1977).
V. A. Matsuk and V. A. Rykov, “The Chapman-Enskog method for a multivelocity multitemperature reacting gas mixture,”Zh. Vychisl. Mat. Mat. Fiz.,18, 1230 (1978).
B. V. Alekseev,Mathematical Kinetics of Reacting Gases [in Russian], Nauka, Moscow (1982).
N. K. Makashev, “On the methods of derivation of gasdynamic equations in the case of high-threshold reactions,”Zh. Vychisl. Mat. Mat. Fiz.,26, 1512 (1986).
V. S. Galkin and N. K. Makashev, “Calculation of transport properties of polyatomic gases for arbitrary flow nonequilibrium,”Zh. Vychisl. Mat. Mat. Fiz.,29, 867 (1989).
V. S. Galkin and N. K. Makashev, “Modification of the first approximation of the Chapman-Enskog method for a gas mixture,”Izv. Akad. Nauk SSSR, Mekh. Zhidk, Gaza, No. 4, 178 (1992).
J. O. Hirschfelder, C. F. Curtis, and R. B. Bird,Molecular Theory of Gases and Liquids, New York (1965).
J. Kestin and W. A. Wakeham, “Thermal conductivity of mixtures of polyatomic gases at low and moderate density,”Intern. J. Thermophys.,4, 295 (1983).
F. J. Uribe, E. A. Mason, and J. Kestin, “Composition dependence of the thermal conductivity of low-density polyatomic gas mixtures,”Intern. J. Thermophys.,12, 43 (1991).
S. Chapman and T. G. Cowling,The Mathematical Theory of Non-uniform Gases, University Press, Cambridge (1952).
L. Monchick, K. S. Yun, and E. A. Mason, “Formal kinetic theory of transport phenomena in polyatomic gas mixtures,”J. Chem. Phys.,39, 654 (1963).
Additional information
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–189, March–April, 1995.
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Galkin, V.S. Transport properties of nonequilibrium polyatomic gas mixtures. Fluid Dyn 30, 310–316 (1995). https://doi.org/10.1007/BF02029845
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DOI: https://doi.org/10.1007/BF02029845