Exact Hydrodynamic Equations and Transport Coefficients in Higher-Order Approximations for Partially-Ionized Gases

  • G. A. Tirskiy
Conference paper


The derivation of the hydrodynamic set of equations and transport coefficients with diffusion and heat transfer in a multicomponent partially ionized gas in the presence also or the absence of an external magnetic field is considered by the methods of the kinetic theory of gases. Expressions for heat and diffusion fluxes and formulas for transport coefficients have been obtained by the Chapman-Enskog and Grad methods. The latter formulas are fairly elaborate for practical calculations. The aim of this paper is to obtain mass and heat transfer equations, and also exact formulas for transport coefficients in a simpler form, convenient for the solution of hydrodynamics problems.

Key words

Hydrodynamics equations Multicomponent partially ionized gases Transport equa¬tions and coefficients 


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  1. Armaly BF, Sutton K (1980) Viscosity of multicomponent partially ionized gas mixtures. AIAA Paper N80-1495.Google Scholar
  2. Armaly BF, Sutton K (1982) Thermal conductivity of partially ionized gas mixtures. AIAA Paper N82-0469.Google Scholar
  3. Devoto RS (1966) Transport properties of ionized monatomic gases. Phys. Fluids 9: 1230–40.CrossRefADSGoogle Scholar
  4. Ferziger TH, Kaper HG (1972) Mathematical Theory of Transport Processes in Gases. Elzevier, Amsterdam - LondonGoogle Scholar
  5. Kolesnikov AF (1975) Transport equations for high temperature ionized mixtures of gases in an electromagnetic field. In: Tirskiy GA (ed) Trudy Inst. Mech. MGU, Moscow 39:39 (in Russian)Google Scholar
  6. Kolesnikov AF, Tirskiy GA (1982) Hydrodynamic equations of partially ionized multicomponent mixture of gases with transport coefficients in higher - order approximations. In Struminskiy VV (ed) Molecular Gasdynamics, pp. 20–44. Moscow, Nauka (in Russian)Google Scholar
  7. Kolesnichenko AV, Tirskiy GA (1976) Stefan-Maxwell Relations and heat transfer in the non-ideal multicomponent continuous media. Chislen. Metody Mech. Sploshnoy Sredy 7: 106–121 (in Russian)Google Scholar
  8. Sokolova IA, Tirskiy GA (1981) Ohm’s law for multicomponent chemically reacting gas mixtures. In: Grigorian SS (ed) Izbran. Voprosy Sovremen. Mekh., pp. 91–109, Moscow Inst. Mech. Moscow Univ. (in Russian)Google Scholar
  9. Tirskiy GA (1993) Up-to-date gasdynamic models of hypersonic aerodynamics and heat transfer with real gas properties. Ann. Rev. Fluid Mech. 25: 151–181CrossRefADSGoogle Scholar
  10. Vasil’evskiy SA, Sokolova IA, Tirskiy GA (1984) Exact equations and transport coefficients for multicomponent gas mixtures and partially ionized plasmas. Zh. Prikl. Mech. Tehn. Fiz. 4: 15–24 (in Russian)Google Scholar
  11. Vasil’evskiy SA, Sokolova IA, Tirskiy GA (1984) The determination and calculation of effective transport coefficients for chemically equilibrium flows of partially ionized and dissociated gas mixtures. Zh. Prikl. Mech. Tehn. Fiz. 1: 68–79 (in Russian)Google Scholar
  12. Vasil’evskiy SA, Tirskiy GA (1991) The effect of element diffusion in chemical equilibrium flows of multicomponent gases. In: Sedov LI (ed) Sovrem. Gasodinamich. I Fizikokhimich. Modeli Giperzvuk. Aerodinamiki I Teploobmena,, pp. 195 - 230. Moscow Inst. Mech. Moscow Univ. (in Russian)Google Scholar
  13. Zhluktov SV, Sokolova IA, Tirskiy GA (1990) Simplified formulas for the viscosity and thermal conductivity coefficients of the multicomponent partially dissociated and ionized air. Zh. Prikl. Mech. Tehn. Fiz. 1: 41–50 (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • G. A. Tirskiy
    • 1
  1. 1.Laboratory of Physics and Chemical GasdynamicsInstitute of Mechanics of Moscow State UniversityMoscowRussia

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