THE GENERAL EXACT SOLUTION FOR THE MANY MOMENTS MACROSCOPIC APPROACH TO EXTENDED THERMODYNAMICS OF POLYATOMIC GASES

M.C. Carrisi, R.E. Tchame, M. Obounou, S. Pennisi

IJPAM: Volume 112, No. 4 (2017)

Title

THE GENERAL EXACT SOLUTION FOR THE MANY
MOMENTS MACROSCOPIC APPROACH TO EXTENDED
THERMODYNAMICS OF POLYATOMIC GASES

Authors

M.C. Carrisi

, R. Enoh Tchame

,
M. Obounou

, S. Pennisi

$^{1,4}$ Department of Mathematics and Informatics
University of Cagliari
Via Ospedale 72, 09124 Cagliari, ITALY
$^{2,3}$ Department of Physics
University of Yaoundé I
Yaoundé, CAMEROON

Abstract

A new model for Polyatomic and for Dense Gases has been proposed in literature in the last five years in the framework of Extended Thermodynamics. The case with an arbitrary but fixed number of moments has been recently studied, both with the kinetic approach than with the macroscopic approach; this last one is more general and includes the results of the kinetic approach only as a particular case.

Scope of the ``closure problem" is to find the expression of some arbitrary functions which appear in the balance equations. Up to now only a recurrence procedure has been published which outlines how to find the solution of this problem with the macroscopic approach; by using this procedure, a numberable set of solutions has been found and written explicitly, while we find here the most general exact solution. It is determined except for some arbirary terms and it is interesting that these terms appear also in the 24 moments model; so we find here that they are transmitted from the model with 24 moments to those with an arbitrary number of moments, without any further arbitrary term.

History

Received: October 15, 2016
Revised: February 15, 2017
Published: February 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 74A15, 76N15, 80A17
Key Words and Phrases: thermodynamics, gas dynamics, thermodynamics of continua

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1: M.C. Carrisi, S. Pennisi, J.M. Sellier, Extended Thermodynamics of Dense Gases with many moments - The macroscopic approach, Int. Journal of Non-Linear Mech., 84 (2016), 12-22, doi: https://doi.org/10.1016/ijnonlinmec.2016.04.003.
2: M.C. Carrisi, R. E. Tchame, M. Obounou, S. Pennisi, An exact solution for the macroscopic approach to extended Thermodynamic of Dense gases with many moments, IJPAM., 106 (2016), 171-189, doi: https://doi.org/10.12732/ijpam.v106i1.13.
3: M.C. Carrisi, S. Pennisi, J.M. Sellier, A kinetic type exact solution for Extended Thermodynamics of Dense Gases with many Moments, Journal of Computational and Theoretical Transport., 45 (2016), 162-173, doi: https://doi.org/10.1080/23324309.2016.1149079.
4: M.C. Carrisi, R. Enoh Tchame, M. Obounou, S. Pennisi, A numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments, Advances in Mathematical Physics., 17 (2016), doi: https://doi.org/10.1155/2016/1307813.
5: T. Arima, A. Mentrelli, T. Ruggeri, Molecular Extended Thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments, Ann. Phys., 345 (2014), 111-132, doi: https://doi.org/10.1016/j.aop.2014.03.011.
6: G. Boillat, T. Ruggeri, Hyperbolic principal subsystems: Entropy convexity and subcharacteristic conditions, Arch. Rat. Mech. Anal., 137 (1997), 305-320, doi: https://doi.org/10.1007/s002050050030.
7: I-S. Liu, I. Müller, Extended Thermodynamics of Classical and Degenerate Ideal Gases, Arch. Rat. Mech. Anal., 83 (1993), 285-332, doi: https://doi.org/10.1007/BF00963838.
8: I-S. Liu, I. Müller, T. Ruggeri, Relativistic thermodynamics of gases, Ann. Phys. (N.Y.), 169 (1986), 191-219, doi: https://doi.org/10.1016/0003-4916(86)90164-8.
9: I. Müller, T. Ruggeri, Rational Extended Thermodynamics, 2nd edn. Springer Tracts in Natural Philosophy. Springer, New York (1998), doi: https://doi.org/10.1007/978-1-4612-2210-1.
10: T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended Thermodynamics of dense gases, Continuum Mech. Thermodyn., 24 (2012), 271-292, doi: https://doi.org/10.1007/s00161-011-0213-x.
11: T. Ruggeri, M. Sugiyama, Rational Extended Thermodynamics beyond the Monatomic Gas, Springer Verlag (2015), doi: https://doi.org/10.1007/978-3-319-13341-6.
12: T. Arima, T. Ruggeri, M. Sugiyama, S. Taniguchi, Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments, Annals of Physics, 372 (2016), 83-109, doi: https://doi.org/10.1016/j.aop.2016.04.015.
13: M.C. Carrisi, S. Pennisi, T. Ruggeri, M. Sugiyama, Extended thermodynamics of dense gases in the presence of dynamic pressure, Ricerche di Matematica, 64 (2015), 403-419, doi: https://doi.org/10.1007/s11587-015-0247-7.
14: M.C. Carrisi, S. Pennisi, An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions, Entropy., 17 (2015), 214-230, doi: https://doi.org/10.3390/e17010214.
15: M.C. Carrisi, S. Pennisi, Extended thermodynamics for dense gases up to whatever order, Int. Journal of Non-Linear Mech., 77 (2015), 74-84, doi: https://doi.org/10.1016/ijnonlinmec.2015.07.011.
16: M.C. Carrisi, R. E. Tchame, M. Obounou, S. Pennisi, Extended Thermodynamics for dense gases up to whatever order and with only some symmetries, Entropy., 17 (2015), 7052-7075, doi: https://doi.org/10.3390/e17107052.
17: M.C. Carrisi, S. Pennisi, J.M. Sellier, Extended Thermodynamics of Dense Gases with at least 24 Moments, Ricerche di Matematica, 65 (2016), 505-522, doi: https://doi.org/10.1007/s11587-016-02171-2.
18: I-S. Liu, Method of Lagrange Multipliers for Exploitation of the Entropy Principle, Arch. Rat. Mech. Anal., 46 (1972), 131-148, doi: https://doi.org/10.1007/BF00250688.
19: T. Ruggeri, A. Strumia, Main Field and Convex Covariant Density for Quasi-Linear Hyperbolic Systems. Relativistic Fluid Dynamics, Ann. Inst. H. Poincaré., 34 (1981), 65-84.

How to Cite?

DOI: 10.12732/ijpam.v112i4.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 4
Pages: 827 - 849

Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).