Journal of Applied Science and Engineering

Published by Tamkang University Press


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G. S. Seth This email address is being protected from spambots. You need JavaScript enabled to view it.1, Md. S. Ansari1 and R. Nandkeolyar1

1Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India


Received: November 27, 2009
Accepted: May 6, 2010
Publication Date: March 1, 2011

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Unsteady MHD Couette Flow of a viscous incompressible electrically conducting fluid, in the presence of a transverse magnetic field, between two parallel porous plates is studied. The fluid flow within the channel is induced due to the impulsive and uniformly accelerated motion of the lower plate of the channel. The magnetic lines of force are assumed to be fixed relative to the moving plate. Laplace transform technique is applied to obtain the solution for the velocity field. The expression for the non-dimensional shear stress at the lower plate is also derived. The asymptotic solution valid for large time t is obtained to gain some physical insight into the flow pattern. The numerical results for the velocity is depicted graphically for various values of magnetic parameter M2 , suction/injection parameter S and time t whereas numerical values of the shear stress at the lower plate are presented in tabular form for different values of M2 , S and t.

Keywords: MHD Couette Flow, Suction/Injection, Hartmann Boundary Layer


  1. [1] Pai, S. I., Magnetogasdynamics and Plasma Dynamics, New Jersey: Springer-Verlag (1962).
  2. [2] Yen, J. T. and Chang, C. C., “Magnetohydrodynamic Couette Flow as Affected by Wall Electrical Conductances,” ZAMP, Vol. 13, p. 266 (1962).
  3. [3] Hayat, T., Khan, M. and Asghar, S., “Homotopy Analysis of MHD Flows of an Oldroyd 8-Constant Fluid,” Acta Mech., Vol. 168, p. 213 (2004).
  4. [4] Katagiri, M., “Flow Formation in Couette Motion in Magnetohydrodynamics,” J. Phys. Soc. Jpn., Vol. 17, p. 393 (1962).
  5. [5] Muhuri, P. K., “Flow Formation in Couette Motion in Magnetohydrodynamics with Suction,” J. Phys. Soc. Jpn., Vol. 18, p. 1671 (1963).
  6. [6] Singh, A. K. and Kumar, N., “Unsteady Magnetohydrodynamic Couette Flow,” Wear, Vol. 89, p. 125 (1983).
  7. [7] Khan, M., Maqbool, K. and Hayat, T., “Influence of Hall Current on the Flows of a Generalized Oldroyd-B Fluid in a Porous Space,” Acta Mech., Vol. 184, p. 1 (2006).
  8. [8] Khan, M., Fetecau, C. and Hayat, T., “MHD Transient Flows in a Channel of Rectangular Cross-Section with Porous Medium,” Physics Letters A, Vol. 369, p. 44 (2007).
  9. [9] Hayat, T., Maqbool, K. and Khan, M., “Hall and Heat Transfer Effects on the Steady Flow of a Generalized Burgers’ Fluid Induced by a Sudden Pull of Eccentric Rotating Disks,” Nonlinear Dyn., Vol. 51, p. 267 (2008).
  10. [10] Khan, M., Rahman, S. and Hayat, T., “Heat Transfer Analysis and Magnetohydrodynamic Flow of a NonNewtonian Fluid through a Porous Medium with Slip at the Wall,” J. Porous Media, Vol. 12, p. 277 (2009).
  11. [11] Khan, M., Hyder Ali, S. and Fetecau, C., “Exact Solutions of Accelerated Flows for a Burgers’ Fluid. I. The Case y < 2 /4,” Appl. Maths. Comput., Vol. 203, p. 881 (2008).
  12. [12] Khan, M., Hyder Ali, S. and Haitao, Qi, “Some Accelerated Flows for a Generalized Oldroyd-B Fluid,” Nonlinear Analysis: Real World Applications, Vol. 10, p. 980 (2009).
  13. [13] Khan, M., Saleem, M., Fetecau, C. and Hayat, T., “Transient Oscillatory and Constantly Accelerated Non-Newtonian Flow in a Porous Medium,” Int. J. Non-Linear Mech., Vol. 42, p. 1224 (2007).
  14. [14] Bhaskara Reddy, N. and Bathaiah, D., “Hall Effects on MHD Flow through a Porous Straight Channel,” Def. Sci. J., Vol. 32, p. 313 (1982).
  15. [15] Prasad Rao, D. R. V., Krishna, D. V. and Debnath, L., “Combined Effect of Free and Forced Convection on MHD Flow in a Rotating Porous Channel,” Int. J. Math. & Math. Sci., Vol. 5, p. 165 (1982).
  16. [16] Abbas, Z., Sajid, M. and Hayat, T., “MHD Boundary Layer Flow of an Upper Convected Maxwell Fluid in a Porous Channel,” Theor. Comp. Fluid Dyn., Vol. 20, p. 229 (2006).
  17. [17] Hayat, T., Ahmed, N., Sajid, M. and Asghar, S., “On the MHD Flow of Second Grade Fluid in a Porous Channel,” Comp. Math. Applic., Vol. 54, p. 407 (2007).
  18. [18] Hayat, T., Ahmed, N. and Sajid, M., “Analytic Solution for MHD Flow of a Third Order Fluid in a Porous Channel,” J. Comput. Appl. Maths., Vol. 214, p. 572 (2008).
  19. [19] Meyer, R. C., “On Reducing Aerodynamic HeatTransfer Rates by Magnetohydrodynamic Techniques,” J. Aero. Sci., Vol. 25, p. 561 (1958).
  20. [20] Cramer, K. R. and Pai, S. I., Magnetofluiddynamics for Engineers and Applied Plysicists, New York: McGraw Hill Book Company (1973).
  21. [21] Rossow, V. J., “On Flow of Electrically Conducting Fluids over a Flat Plate in the Presence of a Transverse Magnetic Field,” NACA Rept. 1358 (1958).
  22. [22] McLachlan, N. W., Complex Variable and Operational Calculus with Technical Applications, New York: Cambridge Univ. Press (1947).
  23. [23] Schlichting, H., Boundary Layer Theory, New York: McGraw Hill (1979).