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Transport in Dilute Media

  • Rémi Carminati
Chapter
  • 1.5k Downloads
Part of the Topics in Applied Physics book series (TAP, volume 107)

Abstract

This Chapter is an introduction to the kinetic theory of gases. As part of a book on micro and nanoscale heat transfer, the aims are twofold:
  • To introduce the necessary concepts and tools, and in particular, the idea of a distribution function and the Boltzmann equation, to describe heat transfer in dilute gases on short length and time scales.

  • To introduce general notions in the theory of transport, based on the kinetic approach, which will prove useful in later Chapters of the book, especially for describing the transport of electrons and phonons in solids.

The Chapter is organised as follows. We begin by introducing the ideas of distribution function, average and flux. We then discuss the particular context of thermodynamic equilibrium and show that, to describe systems that are out of equilibrium, which provide the conditions for macroscopic transfer, one must be able to calculate the distribution function in the most general situation. We introduce the underlying formalism of the Boltzmann equation and a highly simplified model based on the relaxation time. We can then discuss the idea of local thermodynamic equilibrium (LTE), and also situations that are close enough to LTE to be treated by perturbation methods. We shall show in particular how to demonstrate the Fourier law in this regime and obtain an expression for the thermal conductivity of a gas. We then turn to non-LTE regimes and in particular the ballistic transport regime which arises when the characteristic size of the system is smaller than the mean free path (or the observation time is shorter than the average time elapsed between two collisions). We end with a concrete example in which we compare and comment upon the orders of magnitude of exchanged fluxes in different regimes (convection, Fourier-type conduction, ballistic transport).

Keywords

65.80.+n 82.53.Mj 81.16.-c 44.10.+i 44.40.+a 82.80.Kq 

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References

  1. L. D. Landau, E. M. Lifshitz: Cin'etique Physique, vol. 10, Cours de Physique Th'eorique (Mir, Moscow 1990) Google Scholar
  2. L. D. Landau, E. M. Lifshitz: Statistical Physics, vol. 5, part I, Course of Theoretical Physics (Pergamon Press, Oxford 1980) Google Scholar
  3. H. B. Callen: Thermodynamics (Wiley, New York 1985) zbMATHGoogle Scholar
  4. L. Boltzmann: Leçons sur la Th'eorie des Gaz (Editions J. Gabay, Paris 1987) reprint of the French translation (1902) of the original work by Boltzmann (1895) Google Scholar
  5. J. H. Ferziger, H. G. Kaper: Mathematical Theory of Transport Processes in Gases (North Holland, Amsterdam 1972) Google Scholar
  6. R. J. Coruccini: Vacuum 7–8, 19 (1959) CrossRefGoogle Scholar
  7. J. Taine, J.-P. Petit: Heat Transfer (Prentice Hall 1993) section entitled Data Google Scholar
  8. B. Diu, G. Guthmann, D. Lederer, B. Roulet: Physique Statistique (Hermann, Paris 1989) Google Scholar

Authors and Affiliations

  • Rémi Carminati
    • 1
  1. 1.Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion (EM2C), Centre National de la Recherche ScientifiqueEcole Centrale ParisChâtenay-Malabry Cedex

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