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June  2010, 3(2): 353-372. doi: 10.3934/krm.2010.3.353

Fluid modeling for the Knudsen compressor: Case of polyatomic gases

Shigeru Takata 1, , Hitoshi Funagane 1, and  Kazuo Aoki 2,

1. 

Department of Mechanical Engineering and Science and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan, Japan
2. 

Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501

Received  October 2009 Revised  October 2009 Published  May 2010

A fluid-dynamic system describing the behavior of a polyatomic gas in a Knudsen compressor, based on a periodic arrangement of narrower and wider two-dimensional channels and on a periodic saw-tooth temperature distribution, is derived, using the polyatomic version of the ellipsoidal statistical (ES) model of the Boltzmann equation, under the assumption that the channel width is much smaller than the length of a unit of the compressor (narrow channel approximation). The difference from the corresponding fluid-dynamic system for a monatomic gas is shown to be confined in the transport coefficients occurring in the fluid-dynamic equation. It is also shown that these coefficients in the present polyatomic-gas case are readily obtained by a simple conversion from the corresponding coefficients for the BGK model for a monatomic gas. Some numerical simulations based on the fluid-dynamic model are carried out, the results of which show that the properties of the Knudsen pump are little affected by the internal structure of a molecule.
Keywords: kinetic theory of gases, Poiseuille flow., thermal transpiration, Boltzmann equation, Knudsen pump, diffusion model.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Shigeru Takata, Hitoshi Funagane, Kazuo Aoki. Fluid modeling for the Knudsen compressor: Case of polyatomic gases. Kinetic and Related Models, 2010, 3 (2) : 353-372. doi: 10.3934/krm.2010.3.353
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