Doklady Physics

, Volume 60, Issue 8, pp 372–376 | Cite as

Exact solutions of unsteady boundary layer equations for power-law non-Newtonian fluids

Mechanics

Abstract

A number of new exact solutions (with the generalized and functional separation of variables) of unsteady equations of a planar and asymmetric boundary layer of power-law non-Newtonian fluids are described. To find the solutions, the Crocco transformation reducing the order of the equations considered and simpler point transformations are used. Two theorems allowing one to generalize exact solutions of the unsteady axisymmetric boundary layer equations including additional arbitrary functions into them are proven.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Schlichting, Boundary Layer Theory (McGrawHill, New York, 1974).Google Scholar
  2. 2.
    L. G. Loitsyanskiy, Mechanics of Liquids and Gases (Begell House, New York, 1995).Google Scholar
  3. 3.
    L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978) [in Russian].MATHGoogle Scholar
  4. 4.
    G. I. Burde, Quart. J. Mech. Appl. Mat. 48 (4), 611 (1995).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    D. K. Ludlow, P. A. Clarkson, and A. P. Bassom, Quart. J. Mech. Appl. Mat. 53, 175 (2000).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    A. D. Polyanin, Doklady Phys. 46 (7), 526 (2001).MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    A. D. Polyanin and V. F. Zaitsev, Theor. Found. Chem. Eng. 35 (6), 529 (2001).CrossRefGoogle Scholar
  8. 8.
    A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations (Chapman & Hall/CRC Press, Boca Raton–London, 2012).Google Scholar
  9. 9.
    A. V. Aksenov and A. A. Kozyrev, Vestn. NIYaU MIFI 2 (4), 415 (2013).Google Scholar
  10. 10.
    A. D. Polyanin and V. F. Zaitsev, Fluid Dynamics 24 (5), 686 (1989).MathSciNetMATHGoogle Scholar
  11. 11.
    V. F. Zaitsev and A. D. Polyanin, Discrete-Group Methods for Integrating Equations of Nonlinear Mechanics (CRC Press, Boca Raton, 1994).MATHGoogle Scholar
  12. 12.
    G. Saccomandi, J. Phys. A: Math. Gen. 37, 7005 (2004).MathSciNetCrossRefADSMATHGoogle Scholar
  13. 13.
    A. D. Polyanin and A. I. Zhurov, Int. J. Non-Linear Mech. 47 (5), 413 (2012).CrossRefGoogle Scholar
  14. 14.
    A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations (Chapman & Hall/CRC Press, Boca Raton–London, 2003), 2nd ed.MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Ishlinskii Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia
  2. 2.National Research Nuclear University (MEPHI)MoscowRussia

Personalised recommendations