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.

References

References
1.
Aldoss
,
T. K.
,
Ali
,
Y. D.
, and
Al-Nimr
,
M. A.
, 1996, “
MHD Mixed Convection From a Horizontal Circular Cylinder
Numer. Heat Transfer
,
30
, pp.
379
396
.
2.
Al-Nimr
,
M. A.
, and
Hader
,
M. A.
, 1999, “
MHD Free Convection Flow in Open-Ended Vertical Porous Channels
,”
Chem. Eng. Sci.
,
54
, pp.
1883
1889
.
3.
Al-Odat
,
M. Q.
,
Damseh
,
R. A.
, and
Al-Nimr
,
M. A.
, 2004, “
Effect of Magnetic Field on Entropy Generation Due to Laminar Forced Convection Past a Horizontal Flat Plate
,”
Entropy
,
6
, pp.
293
303
.
4.
Damseh
,
R. A.
,
Al-Odat
,
M. Q.
, and
Al-Nimr
,
M. A.
, 2008, “
Entropy Generation During Fluid Flow in a Channel Under the Effect of Transverse Magnetic Field
,”
Heat Mass Transf.
,
44
, pp.
897
904
.
5.
Howarth
,
L.
, 1951, “
Note on the Boundary Layer on a Rotating Sphere
,”
Phil. Mag.
,
42
, pp.
1308
1315
.
6.
Banks
,
W. H. H.
, 1965, “
The Boundary Layer on a Rotating Sphere
,”
Q. J. Mech. Appl. Math.
,
18
, pp.
443
454
.
7.
Monahar
,
R.
, 1967, “
The Boundary Layer on a Rotating Sphere
,”
Z. Angew. Math. Phys.
,
18
, pp.
320
330
.
8.
Kohama
,
Y.
, and
Kobayashi
,
R.
, 1983, “
Boundary-Layer Transition and the Behaviour of Spiral Vortices on Rotating Spheres
,”
J. Fluid Mech.
,
137
, pp.
153
164
.
9.
Dennis
,
S. C. R.
, and
Duck
,
P. W.
, 1988, “
Unsteady Flow Due to an Impulsively Started Rotating Sphere
,”
Comput. Fluids
,
16
, pp.
291
310
.
10.
Hollerbach
,
R.
,
Wiener
,
R. J.
,
Sullivan
,
I. S.
,
Donnelly
,
R. J.
, and
Barenghi
,
C. F.
, 2002, “
The Flow Around a Torsionally Oscillating Sphere
,”
Phys. Fluids
,
14
, pp.
4192
4205
.
11.
Liao
,
S. J.
, 2003,
Beyond Perturbation: Introduction to Homotopy Analysis Method
,
Chapman and Hall/CRC Press
,
Boca Raton, FL.
12.
Cole
,
J. D.
, 1968,
Perturbation Methods in Applied Mathematics
,
Blaisdell Publishing Company
,
Waltham, MA.
13.
Adomian
,
G.
, 1988, “
A Review of the Decomposition Method in Applied Mathematics
,”
J. Math. Anal. Appl.
,
135
, pp.
501
544
.
14.
Liao
,
S. J.
, 2003, “
An Explicit Analytic Solution to the Thomas-Fermi Equation
,”
Appl. Math. Comput.
,
144
, pp.
495
506
.
15.
Liao
,
S. J.
, 2003, “
On the Analytic Solution of Magnetohydrodynamic Flows of Non-Newtonian Fluids Over a Stretching Sheet
,”
J. Fluid Mech.
,
488
, pp.
189
212
.
16.
Liao
,
S. J.
, and
Pop
,
I.
, 2004, “
Explicit Analytic Solution for Similarity Boundary Layer Equations
,”
Int. J. Heat Mass Transfer
,
47
, pp.
75
85
.
17.
Liao
,
S. J.
, 2005, “
Comparison Between the Homotopy Analysis Method and Homotopy Perturbation Method
,”
Appl. Math. Comput.
,
169
, pp.
1186
1194
.
18.
Liao
,
S. J.
,
Su
,
J.
, and
Chwang
,
A. T.
, 2006, “
Series Solutions for a Nonlinear Model of Combined Convective and Radiative Cooling of a Spherical Body
,”
Int. J. Heat Mass Transfer
,
49
, pp.
2437
2445
.
19.
Liao
,
S. J.
, and
Tan
,
Y.
, 2007, “
A General Approach to Obtain Series Solutions of Nonlinear Differential Equations
,”
Studies Appl. Math.
,
119
, pp.
297
355
.
20.
Cheng
,
J.
,
Liao
,
S. J.
,
Mohapatra
,
R. N.
, and
Vajravelu
,
K.
, 2008, “
Series Solutions of Nano Boundary Layer Flows by Means of the Homotopy Analysis Method
,”
J. Math. Anal. Appl.
,
343
, pp.
233
245
.
21.
Liao
,
S. J.
, 2010, “
An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
15
, pp.
2003
2016
.
22.
Kousar
,
N.
, and
Liao
,
S. J.
, 2011, “
Unsteady Non-Similarity Boundary-Layer Flows Caused by an Impulsively Stretching Flat Sheet
,”
Nonlinear Anal. Real Appl.
,
12
, pp.
333
342
.
23.
Turkyilmazoglu
,
M.
, 2011, “
Numerical and Analytical Solutions for the Flow and Heat Transfer Near the Equator of an MHD Boundary Layer Over a Porous Rotating Sphere
,”
Int. J. Therm. Sci.
,
50
, pp.
831
842
.
24.
Chamkha
,
A. J.
,
Takhar
,
H. S.
, and
Nath
,
G.
, 2003, “
Unsteady MHD Rotating Flow Over a Rotating Sphere Near the Equator
,”
Acta Mech.
,
164
, pp.
31
46
.
25.
Kumari
,
M.
, and
Nath
,
G.
, 2004, “
Transient MHD Rotating Flow Over a Rotating Sphere in the Vicinity of the Equator
,”
Int. J. Eng. Sci.
,
42
, pp.
1817
1829
.
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