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Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics

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Abstract

Four basic flow configurations are employed to investigate steady and unsteady rarefaction effects in monatomic ideal gas flows. Internal and external flows in planar geometry, namely, viscous slip (Kramer’s problem), thermal creep, oscillatory Couette, and pulsating Poiseuille flows are considered. A characteristic feature of the selected problems is the formation of the Knudsen boundary layers, where non-Newtonian stress and non-Fourier heat conduction exist. The linearized Navier–Stokes–Fourier and regularized 13-moment equations are utilized to analytically represent the rarefaction effects in these boundary-value problems. It is shown that the regularized 13-moment system correctly estimates the structure of Knudsen layers, compared to the linearized Boltzmann equation data.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada

    P. Taheri, A. S. Rana & H. Struchtrup

  2. Seminar for Applied Mathematics, ETH Zürich, Zürich, 8092, Switzerland

    M. Torrilhon

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  1. P. Taheri
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  2. A. S. Rana
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  3. M. Torrilhon
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  4. H. Struchtrup
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Correspondence to P. Taheri.

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Taheri, P., Rana, A.S., Torrilhon, M. et al. Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics. Continuum Mech. Thermodyn. 21, 423–443 (2009). https://doi.org/10.1007/s00161-009-0115-3

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