Non-linear extended thermodynamics of real gases with 6 fields

Received 5 February 2015 Accepted 5 February 2015 Available online 13 February 2015 Keywords: Extended thermodynamics Non-equilibrium thermodynamics of gases Meixner's theory Dynamic pressure 1. Introduction Rational extended thermodynamics [1] (hereafter referred to as ET)1 is a thermodynamic theory that is applicable to non-equilibrium phenomena with steep gradients and rapid changes in space–time, which may be out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations. As ET has been strictly related to the kinetic theory with the closure method of the hierarchy of moment equations, the applic- ability range of the theory has been restricted within rarefied monatomic gases. Only recently, however, the ET theory of dense gases and of polyatomic rarefied gases has been successfully devel- oped by the present authors obtaining a 14-field theory that, in the limit of small relaxation times (parabolic limit), reduces to the Navier– Stokes–Fourier classical theory [2]. This new approach to the case of polyatomic rarefied gases, in particular, is in perfect agreement with the closure procedure using the Maximum Entropy Principle (MEP) at the kinetic level in which the distribution function depends on an extra variable that takes into account the influence of degrees of freedom of a molecule on energy transfer during collisions [3]. n Corresponding author. E-mail addresses: arima@kanagawa-u.ac.jp (T. Arima), tommaso.ruggeri@unibo.it (T. Ruggeri), sugiyama@nitech.ac.jp (M. Sugiyama), taniguchi.shigeru@kct.ac.jp (S. Taniguchi). 1 Rational extended thermodynamics is sometimes referred to as RET in order to distinguish it from other approaches in extended thermodynamics. However, in this paper, we use, for simplicity, the acronym ET for indicating rational extended thermodynamics. http://dx.doi.org/10.1016/j.ijnonlinmec.2015.02.005 0020-7462/& 2015 Elsevier Ltd. All rights reserved. abstract We establish extended thermodynamics (ET) of real gases with 6 independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approxima- tion. 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. In near- equilibrium we recover the previous results. The correspondence between the ET 6-field theory and Meixner's theory of relaxation processes is discovered. The internal variable and the non-equilibrium temperature in Meixner's theory are expressed in terms of the quantities of the ET 6-field theory, in particular, the dynamic pressure. As an example, we present the cases of a rarefied polyatomic gas and study the monatomic-gas limit where the system converges to the Euler system of a perfect fluid.