On the non-equilibrium thermodynamics of rarefied gases: Relationships between the Chapman-Enskog and moment methods
- Conference date: 9–13 July 2012
- Location: Zaragoza, Spain
The assumptions are discussed under which the equations of the generalized non-equilibrium thermodynamics obtained by the moment and the Chapman-Enskog methods agree. The Chapman-Enskog method is known to be based on the perturbation theory with the Knudsen number as a small parameter. The parameter is introduced in the kinetic equation and the distribution function is expanded into a series in the small Knudsen number. We apply this procedure not to the distribution function, but to the expansion coefficients of the moment series. It can be shown that under special convolution of the resulting system of equations, one can pass from the moment equations to the Chapman-Enskog equations both in hydrodynamic and Burnett approximations. Here is exactly the same transition in the equations of generalized non-equilibrium thermodynamics. The structure of the heat and momentum fluxes, and non-physical fluxes entered into the Chapman-Enskog method is reproduced from the moment equations.
- Nonequilibrium thermodynamics
- Cumulative distribution functions
- Perturbation theory
- Rarefied gas dynamics
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