Journal of Applied Science and Engineering

Published by Tamkang University Press


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H.A. Attia This email address is being protected from spambots. You need JavaScript enabled to view it.1, A.M.A. Al-kaisy1 and K.M. Ewis1

1Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University, 63514 Fayuom, Egypt


Received: June 19, 2007
Accepted: October 13, 2010
Publication Date: June 1, 2011

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In the present study, the unsteady Couette flow with heat transfer of a viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.

Keywords: Couettee Flow, Magnetohydrodynamics, Heat Transfer, Dusty Fluid, Numerical Solution


  1. [1] Lohrabi, J., “Investigation of Magnetohydrodynamic Heat Transfer in Two-Phase Flow,” Ph.D. Thesis, Tennessee Technological University, P.I. (1980).
  2. [2] Chamkha, A. J., “Unsteady Laminar Hydromagnetic Fluid-Particle Flow and Heat Transfer in Channels and Circular Pipes,” International J. of Heat and Fluid Flow, Vol. 21, pp. 740746 (2000).
  3. [3] Saffman, P. G., “On the Stability of a Laminar Flow of a Dusty Gas,” Journal of Fluid Mechanics, Vol. 13, p. 120 (1962).
  4. [4] Gupta, R. K. and Gupta, S. C., “Flow of a Dusty Gas through a Channel with Arbitrary Time Varying Pressure Gradient,” Journal of Applied Mathematics and Physics, Vol. 27, p. 119 (1976).
  5. [5] Prasad, V. R. and Ramacharyulu, N. C. P., “Unsteady Flow of a Dusty Incompressible Fluid between Two Parallel Plates under an Impulsive Pressure Gradient,” Def. Sci . Journal, Vol. 30, p. 125 (1979).
  6. [6] Dixit, L. A., “Unsteady Flow of a Dusty Viscous Fluid through Rectangular Ducts,” Indian Journal of Theoretical Physics, Vol. 28, p. 129 (1980).
  7. [7] Ghosh, A. K. and Mitra, D. K., “Flow of a Dusty Fluid through Horizontal Pipes,” Rev. Roum. Phys., Vol. 29, (1984).
  8. [8] Singh, K. K., “Unsteady Flow of a Conducting Dusty Fluid through a Rectangular Channel with Time Dependent Pressure Gradient,” Indian Journal of Pure and Applied Mathematics, Vol. 8, p. 1124 (1976).
  9. [9] Mitra, P. and Bhattacharyya, P., “Unsteady Hydromagnetic Laminar Flow of a Conducting Dusty Fluid between Two Parallel Plates Started Impulsively from Rest,” Acta Mechanica, Vol. 39, p. 171 (1981).
  10. [10] Borkakotia, K. and Bharali, A., “Hydromagnetic Flow and Heat Transfer between Two Horizontal Plates, the Lower Plate being a Stretching Sheet,” Quarterly of Applied Mathematics, p. 461 (1983).
  11. [11] Megahed, A. A., Aboul-Hassan, A. L. and Sharaf El-Din, H., “Effect of Joule and Viscous Dissipation on Temperature Distributions through Electrically Conducting Dusty Fluid,” Fifth Miami International Symposium on Multi-Phase Transport and Particulate Phenomena, Miami Beach, Florida, USA, Vol. 3, p. 111 (1988).
  12. [12] Aboul-Hassan, A. L., Sharaf El-Din, H. and Megahed, A. A., “Temperature Due to the Motion of One of Them,” First International Conference of Engineering Mathematics and Physics, Cairo, p. 723 (1991).
  13. [13] Crammer and Pai, Magnetofluid Dynamics for Engineer and Scientists, McGraw-Hill (1973).
  14. [14] Sutton, G. W. and Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill (1965).
  15. [15] Schlichting, H., Boundary Layer Theory, McGrawHill (1968).
  16. [16] Ames, W. F., Numerical Solutions of Partial Differential Equations, Second Ed., Academic Press, New York (1977).