Skip to main content
SpringerLink
Log in

Effects of Hall current on unsteady MHD flows of a second grade fluid

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

The aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B 0 → 0 and for a Newtonian fluid when α 1 → 0.

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. R. S. Rivlin, J. L. Ericksen, J. Ration. Mech. Anal. 4, 323 (1955)

    MathSciNet  Google Scholar 

  2. K. R. Rajagopal, Int. J. Nonlinear Mech. 17, 369 (1982)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. K. R. Rajagopal, Acta Mech. 49, 281 (1983)

    Article  MATH  Google Scholar 

  4. K. R. Rajagopal, R. K. Bhatnagar, Acta Mech. 113, 233 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Corina Fetecau, C. Fectecau, Int. J. Eng. Sci. 43, 781 (2005)

    Article  Google Scholar 

  6. C. Fectecau, Int. J. Nonlinear Mech. 39, 225 (2004)

    Article  ADS  Google Scholar 

  7. M. E. Erdogan, C. E. Imrak, Appl. Math. Model. 31, 170 (2007)

    Article  MATH  Google Scholar 

  8. T. Hayat, S. Asghar, A. M. Siddiqui, J. Eng. Sci. 38, 337 (2000)

    Article  Google Scholar 

  9. T. Hayat, M. Khan, A. M. Siddiqui, S. Asghar, Int. J. Nonlinear Mech. 39, 1621 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. T. Hayat, M. Khan, M. Ayub, A. M. Siddiqui, Arch. Mech. 57, 403 (2005)

    MathSciNet  Google Scholar 

  11. R. L. Fosdick, K. R. Rajagopal, Arch. Ration. Mech. An. 70, 145 (1979)

    MATH  MathSciNet  Google Scholar 

  12. J. E. Dunn, K. R. Rajagopal, Int. J. Eng. Sci. 33, 689 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. V. J. Rossow, NASA, Report No. 1358, 489 (1958)

  14. A. M. Siddiqui, T. Hayat, S. Asghar, Int J. Nonlinear Mech. 34, 895 (1999)

    Article  Google Scholar 

  15. R. Cortell, Chem. Eng. Process. 46, 982 (2007)

    Article  Google Scholar 

  16. R. Cortell, Phys. Lett. A 357, 298 (2006)

    Article  MATH  ADS  Google Scholar 

  17. R. Cortell, Phys. Lett. A 372, 2431 (2008)

    Article  Google Scholar 

  18. R. Cortell, Int. J. Heat Mass Tran. 49, 1851 (2006)

    Article  Google Scholar 

  19. Z. Abbas, Y. Wang, T. Hayat, M. Oberlack, Int J. Nonlinear Mech. 43, 783 (2008)

    Article  ADS  Google Scholar 

  20. A. K. Ghosh, P. Sana, Acta Astronaut. 64, 272 (2009)

    Article  ADS  Google Scholar 

  21. M. Khan, Nonlinear Anal.-Real 10, 745 (2009)

    Article  Google Scholar 

  22. K. R. Rajagopal, In: A. Sequiera (Ed.), On boundary conditions for fluids of the differential type (Plenum press, New York, 1995) 273

    Google Scholar 

  23. R. Bandelli, K. R. Rajagopal, G. P. Galdi, Arch. Mech. 47, 661 (1995)

    MATH  MathSciNet  Google Scholar 

  24. I. N. Sneddon, Fourier Transforms (McGraw Hill Book Company, New York, Toronto, London, 1951)

    Google Scholar 

  25. I. N. Sneddon, Functional analysis, Encyclopedia of physics, Vol. II (Springer, Berlin, Gottingen, Heidelberg, 1955)

    Google Scholar 

  26. I. S. Grandshteyn, I. M. Ryzhik, In: A. Jeffrey (Ed.), Tables of integrals, series and products, 5th edition (Academic Press, San Diego, New york, Bostan, London, Sydney, Toronto, 2000) (translated from Russian)

    Google Scholar 

  27. K. Cramer, S. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists (McGraw — Hill, New York, 1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Sargodha, Sargodha, Pakistan

    Masud Ahmad

  2. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    Haider Zaman & Naila Rehman

Authors
  1. Masud Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haider Zaman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naila Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haider Zaman.

About this article

Cite this article

Ahmad, M., Zaman, H. & Rehman, N. Effects of Hall current on unsteady MHD flows of a second grade fluid. centr.eur.j.phys. 8, 422–431 (2010). https://doi.org/10.2478/s11534-009-0083-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-009-0083-z

Keywords

Search

Navigation