The general exact solution for the many moments macroscopic approach to extended thermodynamics of polyatomic gases

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

An Exact Solution for the Macroscopic Approach to Extended Thermodynamics of Dense Gases with Many Moments

Extended Thermodynamics of Dense Gases with an arbitrary but fixed number of moments has been recently studied in literature; the arbitrariness of the number of moments is linked to a number N and the resulting model is called an (N)−Model. As usual in Extended Thermodynamics, in the field equations some unknown functions appear; restriction on their generalities are obtained by imposing the entropy principle, the Galilean relativity principle and some symmetry conditions. The solution of these conditions is called the ”closure problem” and it has not been written explicitly because an hard notation is necessary, but it has been shown how the theory is selfgenerating in the sense that, if we know the closure of the (N) −Model, than we will be able to find that of the (N + 1) − Model. Instead of this, we find here an exact solution which holds for every number N