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Recent Developments in Extended Thermodynamics of Dense and Rarefied Polyatomic Gases

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Abstract

We summarize the recent results and current open problems in extended thermodynamics (ET) of both dense and rarefied polyatomic gases. (i) We review, in particular, extended thermodynamics with 14 independent fields (ET14), that is, the mass density, the velocity, the temperature, the shear stress, the dynamic pressure, and the heat flux. (ii) We explain that, in the case of rarefied polyatomic gases, molecular extended thermodynamics with 14 independent fields (MET14) basing on the kinetic moment theory with the maximum entropy principle can be developed. ET14 and MET14 are fully consistent with each other. (iii) We show that the ET13 theory of rarefied monatomic gases is derived from the ET14 theory as a singular limit. (iv) We discuss briefly some typical applications of the ET14 theory. (v) We study the simple case of ET theory with 6 independent fields (ET6). (vi) The METn theories (n>14) are presented briefly. We analyze, in particular, the dependence of the characteristic velocities for increasing number of moments.

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Notes

  1. The entropy density used in the mathematical community has usually opposite sign to the present one. As a consequence, they speak about convexity instead of concavity.

  2. For the definition of the temperature T in nonequilibrium, see the reference [19].

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Acknowledgements

The authors thank T. Arima, E. Barbera, F. Brini, A. Mentrelli, M. Pavić, S. Simić, and S. Taniguchi for sharing the pleasant joint works. This work was partially supported by the National Group of Mathematical Physics GNFM-INdAM and by University of Bologna: FARB 2012 Project Extended Thermodynamics of Non-Equilibrium Processes from Macro- to Nano-Scale (T.R.) and by Japan Society of Promotion of Science (JSPS) No. 25390150 (M.S.).

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  1. Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna, Bologna, Italy

    Tommaso Ruggeri

  2. Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, 466-8555, Japan

    Masaru Sugiyama

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  1. Tommaso Ruggeri
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  2. Masaru Sugiyama
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Ruggeri, T., Sugiyama, M. Recent Developments in Extended Thermodynamics of Dense and Rarefied Polyatomic Gases. Acta Appl Math 132, 527–548 (2014). https://doi.org/10.1007/s10440-014-9923-y

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