Unsteady MHD Couette Flow with Heat Transfer of a Viscoelastic Fluid under Exponential Decaying Pressure Gradient

Hazem Ali Attia; Karem Mahmoud  Ewis

doi:10.6180/jase.2010.13.4.01

Unsteady MHD Couette Flow with Heat Transfer of a Viscoelastic Fluid under Exponential Decaying Pressure Gradient

Hazem Ali Attia This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Karem Mahmoud Ewis¹

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

Received: October 9, 2008
Accepted: October 21, 2010
Publication Date: December 1, 2010

Download Citation: ||https://doi.org/10.6180/jase.2010.13.4.01

ABSTRACT

The unsteady magnetohydromagnetic Couette flow of an electrically conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer. A sudden uniform and an exponential decaying pressure gradient, an external uniform magnetic field that is perpendicular to the plates and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained using finite difference approximations. The effect of the magnetic field, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is examined.

Keywords: MHD Flow, Heat Transfer, Non-Newtonian, Viscoelastic, Electrically Conducting Fluids

REFERENCES

[1] Tao, I. N., "Magnetohydrodynamic effects on the formation of Couette flow", J. of Aerospace Sci., Vol. 27, pp. 334, 1960.
[2] Alpher, R.A., "Heat transfer in magnetohydrodynamic flow between parallel plates", Int. J. Heat and Mass Transfer, Vol. 3, pp. 108, 1961.
[3] Tani, I., "Steady motion of conducting fluids in channels under transverse magnetic fields with consideration of Hall effect", J. of Aerospace Sci., Vol. 29, pp. 287, 1962.
[4] Sutton, G.W. and Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill, New York, 1965.
[5] Soundalgekar, V.M., "Hall and Ion-slip effects in MHD Couettee flow with heat transfer", IEEE Transactions on Plasma Science, PS-7, No. 3, pp.178, 1979.
[6] Soundalgekar, V.M. and Uplekar, A.G., "Hall effects in MHD Couette flow with heat transfer", IEEE Transactions on Plasma Science Vol. PS-14, No. 5, No. 5, pp. 579, 1986.
[7] Attia, H.A. and Kotb, N.A., "MHD flow between two parallel plates with heat transfer", ACTA Mechanica, Vol. 117, pp. 215, 1996.
[8] Attia, H.A., "Hall current effects on the velocity and temperature fields of an unsteady Hartmann flow", Can. J. Phys., Vol. 76, No. 9, pp. 739, 1998.
[9] Attia, H.A., "Transient MHD flow and heat transfer between two parallel plates with temperature dependent viscosity" Mech. Res. Comm., Vol. 26, No. 1, pp. 115, 1999.
[10] Skelland, A.H.P., Non-Newtonian flow and Heat Transfer, John Wiley, Sons, New York, 1976.
[11] Cho, Y.I. and Hartnett, J.P., Non Newtonian Fluids, McGraw-Hill, New York, 1985.
[12] Hartnett, J.P., "Viscoelastic fluids: A new challenge in heat transfer", ASME Transactions, Vol. 114, No. 296, 1992.
[13] Abel, M.S. and Adress, K.M., "Dusty viscoelastic fluid under the influence of time dependent tangential stress applied at the surface", Indian J. of Theoretical Phys., Vol. 41, No. 1, 1993.
[14] Attia, H.A., “Transient Hartmann flow with heat transfer considering the ion slip”, Physica Scripta, Vol. 66, No. 6, pp. 470, 2002.
[15] Attia, H.A., “Unsteady Hartmann flow of a viscoelastic fluid considering the Hall effect”, Canadian Journal of Physics, Vol. 82, No. 2, pp. 127, 2004.
[16] Schlichting, H., Boundary layer theory, McGraw-Hill, New York, 1986.
[17] Mitchell, A.R. and Griffiths, D.F., The Finite Difference Method in Partial Differential Equations, John Wiley, New York, 1980.