Continuum Mechanics and Thermodynamics

, Volume 17, Issue 1, pp 61–81 | Cite as

Consistently ordered extended thermodynamics - a proposal for an alternative method

  • E. BarberaEmail author
Original article


Ordinary Thermodynamics provides reliable results for problems with fairly smooth and slowly varying fields. For rapidly changing fields or steep gradients Extended Thermodynamics (ET) [1] provides better results. The new version of ET, the so-called Consistently Ordered Extended Thermodynamics [2], assigns an order of magnitude in steepness to the variables. In [2] the authors use as variables the moments G, constructed from the irreducible parts of Hermite polynomials in the components c i of the atomic velocity. With this choice of variables the closure is automatic once an order is assigned to a process. But, in terms of the G‘s, the equations look complicated and it is quite difficult to derive them. In this paper we consider the equations in terms of the usual F-moments, constructed with simple polynomials in c i . By assigning an order to the variables, we derive the field equations appropriate to two different one-dimensional processes: heat conduction in a gas at rest and heat conduction with one-dimensional motion. Comparison with [2] shows that the sets of the field equations coincide, but, in terms of the F‘s, the equations are less complicated and they may be obtained easily.


extended thermodynamics rarefied gases 


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  1. 1.
    Müller, I., Ruggeri, T.: Rational extended thermodynamics, 2nd ed. Springer tracts in natural philosophy, vol. 37, Springer, New York, 1998Google Scholar
  2. 2.
    Müller, I., Reitebuch, D., Weiss W.: Extended thermodynamics - consistent in order of magnitude. Cont. Mech. Thermodyn. 15(2), 113-146 (2002)Google Scholar
  3. 3.
    Dreyer, W.: Maximization of the Entropy in Non-Equilibrium. J. Phys. A 20, 6505 (1987)CrossRefGoogle Scholar
  4. 4.
    Grad, H.: On the kinetic Theory of Rarefied Gases. Comm. Pure Appl. Math. 2, 331 (1949)Google Scholar
  5. 5.
    Bhatnagar, P.L., Gross, E.P., Krook M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (1954)Google Scholar
  6. 6.
    Chapman, S.C., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, 1961Google Scholar
  7. 7.
    Barbera, E., Müller I., Reitebuch D., Zhao N.: Determination of the Boundary Conditions in Extended thermodynamics via Fluctuation Theory. Cont. Mech. Thermodyn. 16(5), 411 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MessinaMessinaItaly

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