Skip to main content
SpringerLink
Log in

Exact solution for the unsteady flow of a semi-infinite micropolar fluid

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The unsteady motion of an incompressible micropolar fluid filling a half-space bounded by a horizontal infinite plate that started to move suddenly is considered. Laplace transform techniques are used. The solution in the Laplace transform domain is obtained by using a direct approach. The inverse Laplace transforms are obtained in an exact manner using the complex inversion formula of the transform together with contour integration techniques. The solution in the case of classical viscous fluids is recovered as a special case of this work when the micropolarity coefficient is assumed to be zero. Numerical computations are carried out and represented graphically.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Eringen, A.C.: Simple microfluids. Int. J. Eng. Sci. 2, 205–218 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  3. Eringen, A.C.: Microcontinuum Field Theories II, Fluent Media. Springer-Verlag Press, New York (1998)

    Google Scholar 

  4. Sherief, H.H., Faltas, M.S., Ashmawy, E.A.: Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow. J. Fluid Mech. 619, 277–293 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Eringen, A.C.: Microcontinuum Field Theories I, Foundations and Solids. Springer-Verlag Press, New York (1998)

    Google Scholar 

  6. Ariman, T., Turk, M.A., Sylvester, N.D.: Microcontinuum fluid mechanics. Int. J. Eng. Sci. 11, 905–930 (1973)

    Article  MATH  Google Scholar 

  7. Ariman, T., Turk, M.A., Sylvester, N.D.: Applications of microcontinuum fluid mechanics. Int. J. Eng. Sci. 12, 273–293 (1974)

    Article  MATH  Google Scholar 

  8. Lukaszewicz, G.: Micropolar Fluids, Theory and Application. Birkhäuser Press, Basel (1999)

    Google Scholar 

  9. Ariman, T., Cakmak, A.: Some basic viscous flows in micropolar fluids. Rheologica Acta 7, 236–242 (1968)

    Article  MATH  Google Scholar 

  10. Cvetkovié, P.: On the problem of micropolar fluid flow. Sci. J. Facta. Universitatis 2, 669–674 (1998)

    Google Scholar 

  11. Kim, Y., Lee, J.: Analytical studies on MHD oscillatory flow of a micropolar fluid over a vertical porous plate. Surf. Coat Tech. 171, 187–193 (2003)

    Article  Google Scholar 

  12. El-Arabawy, H.: Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation. Int. J. Heat Mass Tarns. 46, 1471–1477 (2003)

    Article  MATH  Google Scholar 

  13. Mizukami, A.: Non-steady shear flow of micropolar fluids. Int. J. Eng. Sci. 19, 75–82 (1981)

    Article  MATH  Google Scholar 

  14. Lukaszewicz, G.: Long time behavior of 2D micropolar fluid flows. Math. Comput. Model 34, 487–509 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ye, S.J., Zhu, K.Q., Wang, W.: Laminar flow of micropolar fluid in rectangle microchannel. Acta Mech. Sin. 22, 403–408 (2006)

    Article  MATH  Google Scholar 

  16. Wang, X.L., Zhu, K.Q.: Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects. Tribol. Int. 39, 227–237 (2006)

    Article  Google Scholar 

  17. Ashraf, M., Kamal, M.A., Syed, K.S.: Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks. Acta Mech. Sin. 25, 787–794 (2009)

    Article  MathSciNet  Google Scholar 

  18. Sherief, H.H., Faltas, M.S., Ashmawy, E.A.: Slow motion of a sphere moving normal to two infinite parallel plane walls in a micropolar fluid. Math. Comput. Model 53, 376–386 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  19. Churchill, R.V.: Operational Mathematics. 3rd edn. McGraw-Hill, New York (1972)

    MATH  Google Scholar 

  20. Spiegel, M.: Theory and Problems of Laplace Transforms. McGraw-Hill, New York (1965)

    Google Scholar 

  21. Lamb, S.H.: Hydrodynamics. 6th edn. Cambridge Univ. Press, New York (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

    H. H. Sherief, M. S. Faltas & E. A. Ashmawy

Authors
  1. H. H. Sherief
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Faltas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. A. Ashmawy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Ashmawy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sherief, H.H., Faltas, M.S. & Ashmawy, E.A. Exact solution for the unsteady flow of a semi-infinite micropolar fluid. Acta Mech Sin 27, 354–359 (2011). https://doi.org/10.1007/s10409-011-0452-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-011-0452-4

Keywords

Search

Navigation