Abstract
The many moments model for dense gases and macromolecular fluids is considered here, where the upper order moment is chosen in accordance to the suggestions of the non-relativistic limit of the corresponding relativistic model. The solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were, until now, obtained in the literature by using Taylor expansions around equilibrium and without proving convergence. Here, an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in the literature in a completely different way. Here, it is proven that this particular closure is included in the presently more general one.
Highlights
Extended Thermodynamics takes the first steps from the suggestions of kinetic theory of monatomic gases; here, the state of a gas is described by the phase density, f (⃗x, ⃗c, t), such that f (⃗x, ⃗c, t)d ⃗c are the number density of atoms at the point, ⃗x, and at time, t, that have velocities between ⃗c and ⃗c + d ⃗c
A corresponding definition can be formulated in the relativistic framework taking, after that, their non-relativistic limit
We hope that this will be a great spur for other researchers
Summary
Extended Thermodynamics takes the first steps from the suggestions of kinetic theory of monatomic gases; here, the state of a gas is described by the phase density, f (⃗x, ⃗c, t), such that f (⃗x, ⃗c, t)d ⃗c are the number density of atoms at the point, ⃗x, and at time, t, that have velocities between ⃗c and ⃗c + d ⃗c. In [30], Ugawa and Cordero obtained extended hydrodynamic equations derived from Enskog’s equation by using Grad’s moment expansion method in the bi-dimensional case; among other results, they discussed the nature of a simple one-dimensional heat conduction problem and were able to show that, not too far from equilibrium, the non-equilibrium pressure in this case depends on the density, temperature and heat flux vector Another model in this context can be found in [31], and this will surely be the object of further investigations in the future
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