Slow Flows in a Slab

Part of the Progress in Mathematical Physics book series (PMP, volume 41)


Hard Sphere Collision Frequency Knudsen Number Trial Function Slow Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Abramowitz, Evaluation of the integral \( \int_0^\infty {e^{ - u^2 - x/u} du} \) , J. Math. Phys. 32, 188–192 (1953).zbMATHMathSciNetGoogle Scholar
  2. 2.
    M. Abramowitz and I.A. Stegun, Handbook of mathematical functions, Applied Mathematical Series, National Bureau of Standards, Washington (1964).Google Scholar
  3. 3.
    P. Andries, P. Le Tallec, J.P. Perlat, and B. Perthame, The Gaussian-BGK model of Boltzmann equation with small Prandtl number, Euro. J. of Mechanics B 19, 813–830 (2000).zbMATHCrossRefGoogle Scholar
  4. 4.
    P.L. Bhatnagar, E.P. Gross and M. Krook, A model for collision processes in gases. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511–525 (1954).zbMATHCrossRefGoogle Scholar
  5. 5.
    C. Cercignani, The Boltzmann equation and its applications, (Springer, New York, 1988).Google Scholar
  6. 6.
    C. Cercignani, Mathematical Methods in Kinetic Theory, (Plenum Press, New York, 1990).Google Scholar
  7. 7.
    C. Cercignani, On the general solution of the steady linearized Boltzmann equation, in Rarefied Gas Dynamics, M. Becker and M. Fiebig eds., Vol. I, A.9-1-11, DFLVR Press, Porz-Wahn (1974).Google Scholar
  8. 8.
    C. Cercignani, Plane Couette flow according to the method of elementary solutions, J. Math. Anal. Appl. 11, 93–101 (1965).MathSciNetCrossRefGoogle Scholar
  9. 9.
    C. Cercignani, A variational principle for boundary value problems in kinetic theory, J. Stat. Phys. 1, 297–311 (1969).CrossRefGoogle Scholar
  10. 10.
    C. Cercignani, Plane Poiseuille flow and Knudsen minimum effect, in Rarefied Gas Dynamics, J. A. Laurman ed., Vol II, 92–101, Academic Press, New York (1963).Google Scholar
  11. 11.
    C. Cercignani, Plane Poiseuille flow according to the method of elementary solutions, J. Math. Anal. Appl. 12, 254–262 (1965)MathSciNetCrossRefGoogle Scholar
  12. 12.
    C. Cercignani and A. Daneri, Flow of a rarefied gas between two parallel plates, Jour. Appl. Phys. 34, 3509–3513 (1963).MathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Cercignani and C. D. Pagani, Variational approach to boundary-value problems in kinetic theory, Phys. of Fluids 9, 1167–1173 (1966).CrossRefGoogle Scholar
  14. 14.
    C. Cercignani and G. Tironi, Nonlinear heat transfer between two parallel plates at large temperature ratios, in Rarefied Gas Dynamics, C.L. Brundin, Ed., Vol. I, 441–453, Academic Press, New York (1967).Google Scholar
  15. 15.
    L.H. Holway, Jr., Approximation procedures for kinetic theory, Ph.D. Thesis, Harvard (1963).Google Scholar
  16. 16.
    M. Knudsen, Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren, Ann. der Physik, 28, 75–130 (1909).zbMATHGoogle Scholar
  17. 17.
    J.L. Lebowitz, H.L. Frisch and E. Helfand, Nonequilibrium distribution functions in a fluid, Phys. Fluids 3, 325–338 (1960).zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    L. Sirovich, Kinetic modeling of gas mixtures, Phys. Fluids 5, 908–918, (1962).MathSciNetCrossRefGoogle Scholar
  19. 19.
    Y. Sone, S. Takata, and T. Ohwada, Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules, Eur. J. Mech., B: Fluids 9, 273–288 (1990).zbMATHGoogle Scholar
  20. 20.
    P. Welander, On the temperature jump in a rarefied gas, Arkiv Fysik 7, 507–553 (1954).zbMATHMathSciNetGoogle Scholar
  21. 21.
    D.R. Willis, Comparison of kinetic theory analyses of linearized Couette flow, Phys. Fluids, 5, 127–135 (1962).zbMATHCrossRefGoogle Scholar
  22. 22.
    W. Dong, University of California Report UCRL 3353 (1956).Google Scholar

Copyright information

© Birkhäuser Verlag 2006

Personalised recommendations