Recent Developments in Extended Thermodynamics of Dense and Rarefied Polyatomic Gases

We summarize the recent results and current open problems in extended thermo- dynamics (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 maxi- mum 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.