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Rational Extended Thermodynamics beyond the Monatomic Gas pp 245–269Cite as

Non-linear ET6 and the Role of the Dynamic Pressure: Phenomenological Approach

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Abstract

In this chapter, we present ET of real gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtain the symmetric hyperbolic system with respect to the main field. The correspondence between the ET 6-field (ET6) theory and the Meixner theory of relaxation processes is discussed. The internal variable and the nonequilibrium temperature in the Meixner theory are expressed in terms of the quantities of the ET6 theory, in particular, the dynamic pressure. As an example, we present the case of rarefied polyatomic gases and study the monatomic-gas limit where the system converges to the Euler system of a perfect fluid.

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Authors and Affiliations

  1. Dept. of Mathematics and Res. Center of Applied Mathematics AM², University of Bologna, Bologna, Italy

    Tommaso Ruggeri

  2. Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

    Masaru Sugiyama

Authors
  1. Tommaso Ruggeri
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  2. Masaru Sugiyama
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Ruggeri, T., Sugiyama, M. (2015). Non-linear ET6 and the Role of the Dynamic Pressure: Phenomenological Approach. In: Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, Cham. https://doi.org/10.1007/978-3-319-13341-6_11

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