Skip to main content
Log in

Couette flow and heat transfer between parallel plates in a rarefied gas

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

The effectiveness of the self-similar interpolation method in its simplest form is demonstrated by solving the problem of a planar Couette flow in a rarefied gas between plates with different temperatures. An analytic representation of the solution is compared with the results obtained by the DSMC method. The most interesting result is the nonmonotonicity of the heat flow and the change in its sign accompanying the modification in the gas rarefaction, i.e., in the Knudsen number Kn.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Gluzman and V. I. Yukalov, “Unified approach to crossover phenomena,” Phys. Rev. 58, 4197 (1998).

    Google Scholar 

  2. S. L. Gorelov, “Application of the self-similar interpolation method to problems of rarefied gas dynamics,” J. Appl. Math. Mech. 69, 398 (2005).

    Article  MathSciNet  Google Scholar 

  3. S. L. Gorelov, “Self-similar interpolation in rarefied gas dynamics,” in Proceedings of the 25th International Symposium on Rarefied Gas Dynamics (St.-Petersburg, 2007), pp. 871–876.

    Google Scholar 

  4. S. L. Gorelov and So. Zeiyar, “Self-similar interpolation in problems of rarefied gas dynamics,” Uch. Zap. TsAGI, No. 5 (2010).

  5. M. N. Kogan, Dynamics of a Rarefied Gas: Kinetic Theory (Nauka, Moscow, 1967) [in Russian].

    Google Scholar 

  6. Yu. A. Koshmarov and Yu. A. Ryzhov, Applied Dynamics of Rarefied Gas (Mashinostroenie, Moscow, 1977) [in Russian].

    Google Scholar 

  7. A. A. Abramov and A. V. Butkovskii, “Effects of nonmonotonicity and change in sign of the energy flux in the transient regime for the Couette problem with heat transfer,” Fluid Dyn. 45, 147 (2010).

    Article  MATH  Google Scholar 

  8. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1974).

    Google Scholar 

  9. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, 1994).

    Google Scholar 

  10. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Mir, Moscow, 1981).

    Google Scholar 

  11. S. L. Gorelov and S. V. Rusakov, “Physicochemical model of hypersonic rarefied gas flow past bodies,” Fluid Dyn. 37, 624 (2002).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to S. L. Gorelov or Vuong Van Tien.

Additional information

Original Russian Text © S.L. Gorelov, Vuong Van Tien, 2014, published in Matematicheskoe Modelirovanie, 2014, Vol. 26, No. 10, pp. 33–46.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gorelov, S.L., Van Tien, V. Couette flow and heat transfer between parallel plates in a rarefied gas. Math Models Comput Simul 7, 294–302 (2015). https://doi.org/10.1134/S2070048215030060

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048215030060

Keywords

Navigation