In this study, the magnetohydrodynamics (MHD) stagnation-point boundary layer flow of a Carreau fluid towards a permeable stretching/shrinking surface (sheet) is considered. The governing boundary layer equations in the form of nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformations, so that they can be solved numerically by the bvp4c function (programme) in Matlab software. The variations of the numerical solutions for the skin friction coefficients as well as the velocity profiles are obtained for several values of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis show that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

1.
C. Y.
Wang
,
Int J Non-Linear Mech.
43
,
377
382
(
2008
).
2.
K.
Hiemenz
,
Ding Polym J.
321
(
1911
).
3.
B. C.
Sakiadis
,
AIChE Journal
7
,
221
225
(
1961
).
4.
L. J.
Crane
,
Journal of Applied Mathematics and Physics (ZAMP)
21
,
645
647
(
1970
).
5.
M.
Miklavcic
and
C. Y.
Wang
,
Quarterly of Applied Mathematics
64
,
283
290
(
2006
).
6.
F. M.
Ali
,
R.
Nazar
,
N. M.
Arifin
and
I.
Pop
,
Appl. Math. Mech. -Engl. Ed.
32
(
4
),
409
418
(
2011
).
7.
A.
Zaheer
,
M.
Tahmina
and
O. P.
Oladapo
,
J. Cent. South Univ.
22
,
2376
2384
(
2015
).
8.
T.
Hayat
,
Sadia
Asad
,
M.
Mustafa
and
A.
Alsaedi
,
Applied Mathematics and Computation
246
,
12
22
(
2014
).
9.
J. P.
Hsu
,
S. H.
Hung
and
H. Y.
Yu
,
Journal of Colloid and Interface Science
280
,
256
263
(
2004
).
10.
M. S.
Tshehla
,
International Journal of the Physical Sciences
6
(
16
),
3896
3910
(
2011
).
11.
B. I.
Olajuwon
,
Thermal Science
15
(
2
),
S241
S252
(
2011
).
12.
N.
Ali
and
T.
Hayat
,
Applied Mathematics and Computation
193
,
535
552
(
2007
).
13.
R.
Ellahi
,
Arshad
Riaz
,
S.
Nadeem
and
M.
Ali
,
Mathematical Problems in Engineering
2012
,
1
12
(
2012
).
14.
A.
Pantokratoras
,
Journal of the Taiwan Institute of Chemical Engineers
000
,
1
5
(
2015
).
15.
N. S.
Akbar
,
S.
Nadeem
,
U. H.
Rizwan
and
S.
Ye
,
Ain Shams Engineering Journal
5
,
1233
1239
(
2014
).
16.
A. E. H. A. E.
Naby
,
A. E. M. El.
Misery
and
M. F. A. E.
Kareem
,
Physica A
343
,
1
14
(
2004
).
17.
J. H.
Merkin
,
J. Eng. Mathematics
20
,
171
179
(
1985
).
18.
P. D.
Weidman
,
D. G.
Kubittschek
and
A. M. J.
Davis
,
Int J Eng. Sci.
44
,
730
737
(
2006
).
19.
S. D.
Harris
,
D. B.
Ingham
and
I.
Pop
,
Transport in Porous Media
77
,
267
285
(
2009
).
20.
T. R.
Mahapatra
and
Nandy
,
Meccanica
48
,
23
32
(
2013
).
21.
Y. Y.
Lok
,
N.
Amin
and
I.
Pop
,
Int. J. Non-Linear Mech.
41
(
4
),
622
627
(
2006
).
22.
R.
Hermann
,
Association of German Engineers Research Bulletin
379
,
1
24
(
1936
).
This content is only available via PDF.