Abstract
In this chapter we shall study a single non-degenerate relativistic gas in a non-equilibrium state, and determine from the Boltzmann equation the linear constitutive equations for the dynamic pressure wr, pressure deviator p <αß> and heat flux qα that correspond to the laws of Navier-Stokes and Fourier of a single viscous and heat conducting relativistic fluid. The corresponding transport coefficients of bulk viscosity, shear viscosity and thermal conductivity will be determined in terms of the interaction law between the relativistic particles. For didactical purposes we shall present first a simplified version of the Chapman-Enskog method.
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References
C. Cercignani, The Boltzmann equation and its applications (Springer, New York, 1988).
S. Chapman and T. G. Cowling, The mathematical theory of nonuniform gases, 3rd. ed. (Cambridge Univ. Press, Cambridge, 1970).
D. Enskog, Kinetische Theorie der Vorgänge in mässig verdünnten Gasen, Diss. Uppsala (Almqvist & Wiksells, Uppsala, 1917).
I. S. Gradshteyn and I. M. Ryzhik, Tables of integrals,series and products 5th ed. (Academic Press, San Diego, 1994).
S. R. de Groot, W. A. van Leeuwen and Ch. G. van Weert, Relativistic kinetic theory (North-Holland, Amsterdam, 1980).
D. Hilbert, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen (B. G. Teubner, Leipzig, 1912).
W. Israel, Relativistic kinetic theory of a simple gas, J. Math. Phys. 4 11631181 (1963).
D. C. Kelly, The kinetic theory of a relativistic gas, unpublished report (Miami University, Oxford, 1963).
G. M. Kremer, Urna introdução à teoria cinética relativística (Editora da UFPR, Curitiba, 1998).
H. Margenau and G. M. Murphy, The mathematics of physics and chemistry, 2nd. ed. (D. van Nostrand, Princeton, 1956).
S. Pennisi, Some representation theorems in a 4-dimensional inner product space, Suppl. B. U. M. I. Fisica Matematica 5, 191–214 (1986).
J. M. Stewart, Non-equilibrium relativistic kinetic theory, Lecture Notes in Physics, vol. 10 (Springer, Heidelberg, 1971).
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© 2002 Birkhäuser Verlag
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Cercignani, C., Kremer, G.M. (2002). Chapman-Enskog Method. In: The Relativistic Boltzmann Equation: Theory and Applications. Progress in Mathematical Physics, vol 22. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8165-4_5
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DOI: https://doi.org/10.1007/978-3-0348-8165-4_5
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8165-4
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