Unsteady magneto-hydrodynamics flow between two orthogonal moving porous plates

  • Kashif Ali KhanEmail author
  • Asma Rashid Butt
  • Nauman Raza
  • K. Maqbool
Regular Article


An investigation has been performed to describe the unsteady MHD, laminar, incompressible and two-dimensional motion of viscous fluid between two orthogonal moving porous plates. The similarity transformation is adopted to amend the governing model into a non-linear problem of the ordinary differential equation. The homotopy analysis method (HAM) is then invoked to get the approximate solution. The influence of different substantial parameters such as wall permeable ratio, Reynold's number and Hartmann number are explained in detail. A further HAM's comparison is shown with an efficient numerical technique.


  1. 1.
    D.D. Joseph, L.N. Tao, J. Appl. Mech. Trans. ASME, Ser. E 88, 753 (1966)CrossRefGoogle Scholar
  2. 2.
    J.J. Connor, J. Boyd, E.A. Avallone, Standard Handbook of Lubrication Engineering (McGraw-Hill, New York, USA, 1968)Google Scholar
  3. 3.
    S.A.T. Rizvi, Appl. Sci. Res. 10, 662 (1962)CrossRefGoogle Scholar
  4. 4.
    M.R. Mohyuddin, Turk. J. Phys. 31, 123 (2007)Google Scholar
  5. 5.
    G.N. Purohit, P. Bansal, Ganita Sandesh 9, 55 (1995)Google Scholar
  6. 6.
    D.D. Ganji, M. Abbasi, J. Rahimi, M. Gholami, I. Rahimipetroudi, Front. Mech. Eng. 9, 270 (2014)CrossRefGoogle Scholar
  7. 7.
    T. Hayat, M. Khan, Non-Linear Dyn. 42, 395 (2005)CrossRefGoogle Scholar
  8. 8.
    G. Domairry, A. Aziz, Math. Prob. Eng. 2009, 603916 (2009)CrossRefGoogle Scholar
  9. 9.
    N. Atif, M. Tahir, Appl. Math. Modell. 35, 3154 (2011)CrossRefGoogle Scholar
  10. 10.
    S. Uchida, H. Aoki, J. Fluid Mech. 82, 371 (1977)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Ohki, Bull. JSME 23, 679 (1980)CrossRefGoogle Scholar
  12. 12.
    J. Barron, J. Majdalani, W.K. Van Moorhem, J. Sound Vib. 235, 281 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    J. Majdalani, C. Zhou, C.A. Dawson, J. Biomech. 35, 1399 (2002)CrossRefGoogle Scholar
  14. 14.
    J. Majdalani, C. Zhou, Z. Angew. Math. Mech. 83, 181 (2003)CrossRefGoogle Scholar
  15. 15.
    C.E. Dauenhauer, J. Majdalani, Phys. Fluids 15, 1485 (2003)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    S. Asghar, M. Mushtaq, T. Hayat, Nonlinear Anal.: Real World Appl. 11, 555 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    S. Dinarvand, M.M. Rashidi, Nonlinear Anal.: Real World Appl. 11, 1502 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    X.H. Si, L.C. Zheng, X.X. Zhang, Y. Chao, Cent. Eur. J. Phys. 9, 825 (2011)Google Scholar
  19. 19.
    X.H. Si, L.C. Zheng, X.X. Zhang, X.Y. Si, J.H. Yang, Chin. Phys. Lett. 28, 963 (2011)CrossRefGoogle Scholar
  20. 20.
    H. Xu, Z.L. Lin, S.J. Liao, J.Z. Wu, J. Majdalani, Phys. Fluids 22, 053601 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    M. Ghaffar, K. Ali, A. Yasmin, M. Ashraf, J. Mech. 31, 147 (2015)CrossRefGoogle Scholar
  22. 22.
    S.J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, 1st ed. (Chapman and Hall/CRC Press, Boca Raton, 2004)Google Scholar
  23. 23.
    K.A. Khan, A.R. Butt, N. Raza, Results Phys. 8, 610 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    S. Abbasbandy, Phys. Lett. A 360, 109 (2006)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    S.J. Liao, High-order deformation equations, in Advances in the homotopy analysis method (World Scientific Publishing, 2014)

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© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Engineering and TechnologyLahorePakistan
  2. 2.Department of MathematicsUniversity of the PunjabLahorePakistan
  3. 3.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

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