Ion Slip Effect on Unsteady Couette Flow with Heat Transfer under Exponential Decaying Pressure Gradient

Hazem A.  Attia

doi:10.6180/jase.2009.12.2.13

Ion Slip Effect on Unsteady Couette Flow with Heat Transfer under Exponential Decaying Pressure Gradient

Mathematics / Statistics

Hazem A. Attia This email address is being protected from spambots. You need JavaScript enabled to view it.¹

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

Received: December 6, 2005
Accepted: May 10, 2006
Publication Date: June 1, 2009

Download Citation: ||https://doi.org/10.6180/jase.2009.12.2.13

ABSTRACT

The unsteady Couette flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer taking the ion slip into consideration. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying with time pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the ion slip and the uniform suction and injection on both the velocity and temperature distributions is examined.

Keywords: Unsteady Flow, Couette Flow, Conducting Fluid, Heat Transfer

REFERENCES

[1] Hartmann, J. and Lazarus, F., Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. Vol. 15 (1937).
[2] Tao, I. N., J. of Aerospace Sci., Vol. 27, p. 334 (1960).
[3] Alpher, R. A., Int. J. Heat and Mass Transfer., Vol. 3, p. 108 (1961).
[4] Sutton, G. W. and Sherman, A., Engineering Magnetohydrodynamics. McGraw-Hill Book Co. (1965).
[5] Cramer, K. and Pai, S.-I., Magnetofluid dynamics for engineers and applied physicists. McGraw-Hill Book Co. (1973).
[6] Nigam, S. D. and Singh, S. N., Quart. J. Mech. Appl. Math., Vol. 13, p. 85 (1960).
[7] Tani, I., J. of Aerospace Sci., Vol. 29, p. 287 (1962).
[8] Soundalgekar, V. M., Vighnesam, N. V. and Takhar, H. S. IEEE Trans. Plasma Sci., Vol. PS-7, p. 178 (1979).
[9] Soundalgekar, V. M. and Uplekar, A. G., IEEE Trans. Plasma Sci., Vol. PS-14, p. 579 (1986).
[10] Abo-El-Dahab, E. M. H., M.Sc. thesis. Helwan University, Egypt (1993).
[11] Attia, H. A., Can. J. Phys., Vol. 76(9), p. 739 (1998).
[12] Schlichting, H., Boundary layer theory. McGraw-Hill Book Co. (1968).
[13] Ames, W. F., Numerical solutions of partial differential equations. 2nd ed., Academic Press, New York (1977).