Thermal transpiration for the linearized Boltzmann equation |
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| Authors: | Chiun‐Chuan Chen I‐Kun Chen Tai‐Ping Liu Yoshio Sone |
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| Institution: | 1. National Taiwan University, 10617 Taipei, Taiwan;2. Academia Sinica;3. University of Maryland, College Park, MD 20742;4. Mathematics, Bldg. 380, 450 Serra Mall, Stanford, CA 94305;5. 230‐133 Iwakura‐Nagatani‐cho Sakyo‐ku, Kyoto 606‐0026, Japan |
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| Abstract: | The phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard‐sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation. © 2006 Wiley Periodicals, Inc. |
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