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Phenomenological Nonlinear RET with 6 Fields

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Classical and Relativistic Rational Extended Thermodynamics of Gases

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Abstract

In this chapter, we present a RET theory of rarefied polyatomic gases with 6 independent fields (ET6), i.e., the mass density, the velocity, the temperature, and the dynamic pressure, without adopting the near-equilibrium approximation. This model takes into account the dissipation process in a gas only through the dynamic pressure. By ignoring both the shear viscosity and the heat conductivity, it can highlight specifically the role of the dynamic pressure. We prove its compatibility with the universal principles (the Galilean invariance, the entropy principle, and the stability), and obtain the symmetric hyperbolic system with respect to the main field. The correspondence between the 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 adopted in the ET6 theory, in particular, the dynamic pressure. We study the monatomic-gas limit where the system of ET6 converges to the Euler system of a perfect fluid. Lastly the nature of dynamic pressure is discussed in the case of rarefied polyatomic gas.

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Authors and Affiliations

  1. Department of Mathematics and Research Center on Applied Mathematics, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

  2. 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. (2021). Phenomenological Nonlinear RET with 6 Fields. In: Classical and Relativistic Rational Extended Thermodynamics of Gases. Springer, Cham. https://doi.org/10.1007/978-3-030-59144-1_12

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