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Research Papers: Natural and Mixed Convection

Magnetohydrodynamic Transient Free-Convective Flow in a Vertical Annulus With Thermal Boundary Condition of the Second Kind

[+] Author and Article Information
Basant K. Jha

Clement A. Apere1

 Department of Mathematics, Ahmadu Bello University, Zaria, Nigeriaadeapere@gmail.com

1

Corresponding author.

J. Heat Transfer 134(4), 042502 (Feb 15, 2012) (8 pages) doi:10.1115/1.4005109 History: Received February 20, 2011; Revised August 19, 2011; Published February 15, 2012; Online February 15, 2012

A theoretical analysis of an unsteady magnetohydrodynamic free-convective flow of a viscous incompressible and electrically conducting fluid between two concentric vertical cylinders is carried out considering thermal boundary condition of the second kind at the outer surface of the inner cylinder. The governing equations of motion and energy are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. A parametric study depicting the effect of the various parameters on the temperature, velocity, and their related quantities is conducted. On the outer surface of the inner cylinder, the skin friction is seen to decrease with the Hartmann number and increase with time. An opposite behavior is seen on the inner surface of the outer cylinder.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 5

Velocity profile u showing the effect of Pr with t = 0.2 and M = 2

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Figure 6

Velocity profile u showing the effect of M with Pr = 0.71 and t = 0.2

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Figure 7

Contour graph of the rate of heat transfer at the inner surface of the outer cylinder (r = 2) showing the effect of Pr and t

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Figure 8

The skin friction at the outer surface of the inner cylinder (r = 1) showing the effect of Pr and M

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Figure 9

The skin friction at inner surface of the outer cylinder (r = 2) showing the effect of Pr and M

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Figure 4

Velocity profile u showing the effect of t with Pr = 0.71 and M = 2.0

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Figure 3

Temperature profile T showing the effect of Pr with t = 0.2 and M = 2

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Figure 2

Temperature profile T showing the effect of t with Pr = 0.71 and M = 2

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Figure 1

Schematic of the problem

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