A Kinetic type Exact Solution for 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. As usual in Extended Thermodynamics, in the field equations some unknown functions appear; restriction on their generalities is obtained by imposing the entropy principle, the Galilean relativity principle, and some symmetry conditions. The solution of these conditions has been obtained by using a Taylor expansion around equilibrium, without proving its convergence but only assuming it. In this article, we find an exact solution without Taylor’ s expansion so avoiding the problem of proving convergence. It will be found through a kinetic type approach. It is not a pure kinetic approach because we do not know the distribution function, but the techniques that are used are similar. If we expand this exact solution around equilibrium, we find the most significative part of the closure previously obtained with the macroscopic approach.