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Analytic Approximations for the Flow Near the Equator of a Steady Magnetohydrodynamic Boundary Layer Over a Rotating Sphere

[+] Author and Article Information
A. El-Nahhas

Helwan Faculty of Science, Mathematics Department,  Helwan University, Helbawy Street, Cairo 11795, Egyptaasayed35@yahoo.com

J. Appl. Mech 79(6), 064505 (Sep 17, 2012) (7 pages) doi:10.1115/1.4006773 History: Received October 27, 2011; Revised March 23, 2012; Posted May 03, 2012; Published September 17, 2012; Online September 17, 2012

The strongly nonlinear problem for the steady, laminar, viscous incompressible ,and electrically conducting fluid near the equator of the boundary layer flow due to a rotating sphere and in the presence of a uniform radial magnetic field is considered. Analytic approximations for this problem are obtained through the application of the homotopy analysis method and via a fractional basis. Variations for velocity and temperature profiles with the change of the suction/blowing, rotational, and magnetic parameters are studied.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 6

The variation of the meridional velocity profile F(η ) for s=  1, m=  1, and different values of λ

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Figure 7

The variation of the rotational velocity profile G(η ) for s=  1, m=  1, and different values of λ

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Figure 8

The variation of the radial velocity profile H(η ) for s=  1, m=  1, and different values of λ

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Figure 5

A comparison of the homotopy analytic solution of Θ(η ) (solid) with the numerical solution (dashed) and the initial approximation (thin) at s=  0.5, λ =  0, m=  1, Pr =  1, Ec=  0

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Figure 4

A comparison of the homotopy analytic solution of H(η ) (solid) with the numerical solution (dashed) and the initial approximation (thin) at s=  0.5, λ =  0, m=  1, Pr =  1, Ec=  0

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Figure 9

The variation of the meridional velocity profile F(η ) for s=  1, λ =  − 0.5, and different values of m

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Figure 10

The variation of the rotational velocity profile G(η ) for s=  1, λ =  − 0.5, and different values of m

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Figure 11

The variation of the radial velocity profile H(η ) for s=  1, λ =  − 0.5, and different values of m

Grahic Jump Location
Figure 3

A comparison of the homotopy analytic solution of G(η ) (solid) with the numerical solution (dashed) and the initial approximation (thin) at s=  0.5, λ =  0, m=  1, Pr =  1, Ec=  0

Grahic Jump Location
Figure 2

A comparison of the homotopy analytic solution of F(η ) (solid) with the numerical solution (dashed) and the initial approximation (thin) at s=  0.5, λ =  0, m=  1, Pr =  1, Ec=  0

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Figure 1

The h-curve of F″"(0), G″"(0), H″"(0) and Θ″"(0) at s=  0.5, λ =  0, m=  1, Pr =  1, Ec=  0

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Figure 18

The variation of the temperature profile Θ(η ) for s=  − 1, m=  1, Pr =  1, Ec=  0, and different values of λ

Grahic Jump Location
Figure 12

The variation of the meridional velocity profile F(η ) for s=  1, λ =  0, and different values of m

Grahic Jump Location
Figure 13

The variation of the rotational velocity profile G(η ) for s=  1, λ =  0, and different values of m

Grahic Jump Location
Figure 14

The variation of the radial velocity profile H(η ) for s=  1, λ =  0, and different values of m

Grahic Jump Location
Figure 15

The variation of the meridional velocity profile F(η ) for s=  1, λ =  0.5, and different values of m

Grahic Jump Location
Figure 16

The variation of the rotational velocity profile G(η ) for s=  1, λ =  0.5, and different values of m

Grahic Jump Location
Figure 17

The variation of the radial velocity profile H(η ) for s=  1, λ =  0.5, and different values of m

Grahic Jump Location
Figure 19

The variation of the temperature profile Θ(η ) for s=  0, m=  1, Pr =  1, Ec=  0, and different values of λ

Grahic Jump Location
Figure 20

The variation of the temperature profile Θ(η ) for s=  1, m=  1, Pr =  1, Ec=  0, and different values of λ

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