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Rarefied flow in a channel and a periodic system of channels

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Abstract

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated.

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References

  1. C. Cercignani,Theory and Applications of the Boltzmann Equations, Scott. Acad. Press (1975).

  2. M. N. Kogan,Rarefied Gas Dynamics, Plenum Press, New York (1969).

    Google Scholar 

  3. C. Cercignani and J. Neudachin, “Rarefied gas flow through long slots,”Zeitschr. Angew. Math. Phys.,30, 943 (1979).

    Article  MATH  ADS  Google Scholar 

  4. V. D. Akin’shin, A. I. Makarov, V. D. Seleznev, and F. M. Sharipov, “Rarefied gas flow in a two-dimensional finite-length channel over a wide Knudsen number range,”Zh. Prikl. Mekh. Tekhn. Fiz., No. 1, 105 (1988).

  5. V. D. Akin’shin, A. I. Makarov, V. D. Seleznev, and F. M. Sharipov, “Rarefied gas flow in a two-dimensional finite-length channel over the entire Knudsen number range,”Zh. Prik. Mekh. Tekhn. Fiz., No. 4, 48 (1989).

  6. E. M. Shakhov, “Two-dimensional nonlinear problem of rarefied gas flow between two parallel planes,”Zh. Vych. Mat. Mat. Fiz.,35, 83 (1995).

    MathSciNet  Google Scholar 

  7. I. N. Larina and V. A. Rykov, “Calculation of two-dimensional rarefied gas flows at low Knudsen numbers,”Zh. Vych. Mat. Mat. Fiz.,36, 135 (1996).

    MathSciNet  Google Scholar 

  8. F. Sharipov and V. Seleznev, “Data on internal rarefied gas flows,”J. Phys. Chem. Ref. Data,27, 657 (1998).

    Article  ADS  Google Scholar 

  9. N. E. Kochin, I. A. Kibel’, and N. N. Roze,Theoretical Hydromechanics, Vol. 2 [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

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Authors
  1. E. M. Shakhov
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Additional information

Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000.

The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).

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Shakhov, E.M. Rarefied flow in a channel and a periodic system of channels. Fluid Dyn 35, 449–456 (2000). https://doi.org/10.1007/BF02697759

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  • DOI: https://doi.org/10.1007/BF02697759

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