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RET of Rarefied Monatomic Gas: Non-relativistic Theory

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Classical and Relativistic Rational Extended Thermodynamics of Gases

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Abstract

We make a survey about RET of rarefied monatomic gases. In addition to some results that have been already given in the Müller-Ruggeri book (Müller and Ruggeri: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)), many others obtained recently are presented.

We start from the phenomenological RET theory with 13 fields. We prove that the closure of RET coincides with both the closure proposed by Grad using the kinetic-theoretical arguments and the closure by the MEP procedure. The closure here is newly adopted by restyling the closure used in the Liu-Müller paper (Liu and Müller (Arch. Rat. Mech. Anal. 83:285, 1983)).

The RET theory with m moments obtained by the MEP closure is also presented together with the nesting theory that emerges from the concept of principal subsystem. We present the ET\(^\alpha _m\) theory, i.e., m-moment theory where the closure by using the terms up to order α with respect to the nonequilibrium variables is adopted. The domain of hyperbolicity is studied. We discuss, in particular, the results due to Brini and Ruggeri (Continuum Mech. Thermodyn. 32:23, 2020) concerning the extension of the hyperbolicity domain when we move our viewpoint from ET\(^1_{13}\) to ET\(^2_{13}\).

A problematic point concerning a bounded domain in RET is also discussed. A simple example in heat conduction is explained to show explicitly that the prediction of the RET theory is appreciably different from the counterpart of the Navier-Stokes and Fourier theory.

A lower bound for the maximum characteristic velocity is obtained as a function of the truncation tensor index N. The velocity increases as the number of moments grows, and it becomes unbounded when N →∞.

The chapter contains also a brief comparison of the RET predictions with experimental data concerning sound wave and light scattering.

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Notes

  1. 1.

    We remark that the dimensionless quantities introduced here are different from those in [25, 56]. In the previous papers \(c=\sqrt {(5/3)} \, c_s\) was used instead of c s.

  2. 2.

    The values of the dimensionless radius \(\tilde {r}^{(1)}\) calculated in [25, 56] is different from the present one since, as mentioned above, different dimensionless variables are used.

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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). RET of Rarefied Monatomic Gas: Non-relativistic Theory. In: Classical and Relativistic Rational Extended Thermodynamics of Gases. Springer, Cham. https://doi.org/10.1007/978-3-030-59144-1_4

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