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Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

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Abstract

An analytic (in the form of a Neuman series) solution to the problem of the Couette flow in a plane channel with infinitely large parallel walls is constructed using the kinetic approach in the isothermal approximation. For the basic equation, the Bhatnagar-Gross-Krook (BGK) model of the kinetic Boltzmann equation is used, while the boundary condition is determined by the diffuse reflection model. The mass flux through half the channel thickness in the direction parallel to the channel walls as well as the nonzero component of the viscous stress tensor are calculated taking into account the constructed distribution function. The results are compared with analogous data obtained by numerical methods.

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References

  1. E. M. Lifshitz and L. P. Pitaevsky, Physical Kinetics (Nauka, Moscow, 1979; Pergamon, Oxford, 1981).

    Google Scholar 

  2. F. M. Sharipov and V. D. Seleznev, Movement of Rarefied Gas in Channels and Microchannels (UrO RAN, Yekaterinburg, 2008) [in Russian].

    Google Scholar 

  3. C. E. Sievert, Eur. J. Mech. B. Fluids 21, 579 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  4. C. E. Sievert, Zeitschriff Angewandte Mathematic Physik 54, 273 (2003).

    Article  ADS  Google Scholar 

  5. C. E. Sievert and D. Valougeorgis, Eur. J. Mech. B. Fluids 22, 645 (2004).

    Google Scholar 

  6. R. D. M. Garcia and C. E. Sievert, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 67, 1041 (2007).

    Article  MATH  Google Scholar 

  7. R. D. M. Garcia and C. E. Sievert, Eur. J. Mech. B. Fluids 28, 387 (2009).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. A. V. Latyshev and A. A. Yushkanov, Analytical Solution of Boundary-Value Problems of Kinetic Theory (MGOU, Moscow, 2004 [in Russian].

    Google Scholar 

  9. A. V. Latyshev, V. N. Popov, and A. A. Yushkanov, Nonuniform Kinetic Problems: Method of Singular Integral Equation (Pomorsk. Gos. Univ., Arkhangel’sk, 2004) [in Russian].

    Google Scholar 

  10. C. Cercignani, Mathematical Methods in Kinetic Theory (Plenum, New York, 1969; Mir, Moscow, 1973).

    MATH  Google Scholar 

  11. S. K. Loyalka, Transp. Theory Stat. Phys. 4, 55 (1975).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Arkhangel’sk State Technical University, nab. Severnoi Dviny 17, Arkhangel’sk, 163002, Russia

    V. N. Popov, I. V. Testova & A. A. Yushkanov

Authors
  1. V. N. Popov
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  2. I. V. Testova
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  3. A. A. Yushkanov
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Correspondence to V. N. Popov.

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Original Russian Text © V.N. Popov, I.V. Testova, A.A. Yushkanov, 2011, published in Zhurnal Tekhnicheskoĭ Fiziki, 2011, Vol. 81, No. 1, pp. 53–58.

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Popov, V.N., Testova, I.V. & Yushkanov, A.A. Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls. Tech. Phys. 56, 49–54 (2011). https://doi.org/10.1134/S1063784211010208

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  • DOI: https://doi.org/10.1134/S1063784211010208

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