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Research Papers: Natural and Mixed Convection

# Magnetohydrodynamic Free Convective Couette Flow With Suction and Injection

[+] Author and Article Information
Basant K. Jha

Department of Mathematics,  Ahmadu Bello University, Zaria, Nigeriabasant777@yahoo.co.uk

Clement A. Apere1

Department of Mathematics,  Ahmadu Bello University, Zaria, Nigeriabasant777@yahoo.co.uk

1

Corresponding author.

J. Heat Transfer 133(9), 092501 (Jul 27, 2011) (12 pages) doi:10.1115/1.4003902 History: Received August 13, 2010; Revised March 28, 2011; Accepted March 30, 2011; Published July 27, 2011; Online July 27, 2011

## Abstract

This paper considers the unsteady MHD free convective Couette flow of a viscous incompressible electrically conducting fluid between two parallel vertical porous plates. Both cases of the applied magnetic field being fixed either to the fluid or to the moving porous plate are considered. The solution of the governing equations has been obtained by using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The unified solution obtained for the velocity have been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as Prandtl number, Grashof number, and the suction/injection parameter are discussed with the aid of line graphs. The skin friction have been seen to decrease with both suction and injection on the surface of the moving plate when the channel is being cooled, while on the stationary plate, the magnitude of the skin friction increases with injection.

###### FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
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## Figures

Figure 1

Temperature profile T showing the effect of t(Pr=0.71 and s=0.5)

Figure 10

Skin friction on the plate at y=0 showing the effect of Gr and s with K=0 and K=1 represented by (a) and (b), respectively Pr=0.71t=0.1, and M=2)

Figure 11

Skin friction on the plate at y=1 showing the effect of Gr and s with K=0 and K=1 represented by (a) and (b), respectively Pr=0.71, t=0.1, and M=2)

Figure 2

Temperature profile T showing the effect of Pr and s at t=0.1

Figure 3

Velocity profile u for the cooling of the plate showing the effect of t with K=0 and K=1 represented by (a) and (b),respectively Pr=0.71, s=0.5, Gr=10, and M=2

Figure 4

Velocity profile u for the heating of the plate showing the effect of time t with K=0 and K=1 represented by (a) and (b), respectively Pr=0.71, s=0.5, Gr =−10, and M=2

Figure 5

Velocity profile u for the cooling of the plate showing the effect of M and s with K=0 and K=1 represented by (a) and (b), respectively (Gr=10, Pr=0.71, y=0.5, and t=0.1

Figure 6

Velocity profile u for the heating of the plate showing the effect of M ands with K=0 and K=1 represented by (a) and (b), respectively (Gr=−10, Pr=0.71, y=0.5, and t=0.1)

Figure 7

Velocity profile u showing the effect of Gr and s with K=0 and K=1 represented by (a) and (b), respectively (y=0.5, Pr=0.71, t=0.1, and M=2)

Figure 8

Rate of heat transfer at y=0 showing the effect of Pr and s at t=0.1

Figure 9

Rate of heat transfer at y=1 showing the effect of Pr and s at t=0.1

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