The squeezing flow of an incompressible micropolar fluid between two parallel infinite disks is investigated in the presence of a magnetic flied. An analysis of strong and weak interactions has been carried out. Similarity solutions are derived by homotopy analysis method. The variation of dimensionless velocities are sketched in order to see the influence of pertinent parameters. Skin friction coefficient and wall couple stress coefficient have been tabulated. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid.

References

References
1.
Rajagopal
,
K. R.
, 1982, “
Boundedness and Uniqueness of Fluids of Differential Type
,”
Acta Sin. Indica
,
18
, pp.
1
11
.
2.
Rajagopal
,
K. R.
, 1995, “
On the Boundary Conditions for Fluids of the Differential Type
,”
Navier-Stokes Equation and Related Nonlinear Problems
,
A.
Sequira
, ed.,
Plenum Press
,
New York
, pp.
273
278
.
3.
Rajagopal
,
K. R.
,
Szeri
,
A. Z.
, and
Troy
,
W.
, 1986, “
An Existence Theorem for the Flow of Non-Newtonian Fluid Past an Infinite Porous Plate
,”
Int. J. Non-Linear Mech.
,
21
(
4
), pp.
279
289
.
4.
Fetecau
,
C.
, and
Fetecau
,
C.
, 2006, “
Starting Solutions of the Motion of a Second Grade Fluid due to Longitudinal and Torsional Oscillations of a Circular Cylinder
,”
Int. J. Eng. Sci.
,
44
(
11–12
), pp.
788
796
.
5.
Fetecau
,
C.
,
Fetecau
,
C.
, and
Vieru
,
D.
, 2007, “
On Some Helical Flows of Oldroyd-B Fluids
,”
Acta Mech.
,
189
(
1–2
), pp.
53
63
.
6.
Fetecau
,
C.
,
Vieru
,
D.
, and
Fetecau
,
C.
, 2008, “
A Note on the Second Problem of Stokes for Newtonian Fluid
,”
Int. J. Non-Linear Mech.
,
43
(
5
), pp.
451
457
.
7.
Zhang
,
Z. Y.
,
Fu
,
C. J.
, and
Tan
,
W. C.
, 2008, “
Linear and Non-Linear Stability Analysis of Thermal Convection for Oldroyd-B Fluids in Porous Media Heated From Below
,”
Phys. Fluids
,
20
(
8
), p.
084103
.
8.
Xue
,
C. F.
,
Nie
,
J. X.
, and
Tan
,
W. C.
, 2008, “
An Exact Solution of Start Up Flow for Fractional Generalized Burgers Fluid in a Porous Half Space
,”
Nonlinear Anal. Theory, Methods Appl.
,
69
(
7
), pp.
2086
2094
.
9.
Wang
,
S. W.
, and
Tan
,
W. C.
, 2008, “
Stability Analysis of Double-Diffusive Convection of Maxwell Fluid in a Porous Medium Heated From Below
,”
Phys. Lett. A
,
372
(
17
), pp.
3046
3050
.
10.
Chen
,
C. I.
,
Chen
,
C. K.
, and
Yang
,
Y. T.
, 2004, “
Unsteady Unidirectional Flow of an Oldroyd-B Fluid in a Circular Duct With Different Given Volume Flow Rate Conditions
,”
Heat Mass Transfer
,
40
(
3–4
), pp.
203
209
.
11.
Hayat
,
T.
,
Abbas
,
Z.
, and
Ali
,
N.
, 2008, “
MHD Flow and Mass Transfer of a Upper-Convected Maxewell Fluid Past a Porous Shrinking Sheet With Chemical Reaction Species
,”
Phys. Lett. A
,
372
(
26
), pp.
4698
4704
.
12.
Ayub
,
M.
,
Rasheed
,
A.
, and
Hayat
,
T.
, 2003, “
Exact Flow of a Third Grade Fluid Past a Porous Plate Using Homotopy Analysis Method
,”
Int. J. Eng. Sci.
,
41
(
18
), pp.
2091
-
2103
.
13.
Hayat
,
T.
,
Ellahi
,
R.
, and
Asghar
,
S.
, 2008, “
Hall Effects on Unsteady Flow due to Non-Coaxially Rotating Disk and a Fluid at Infinity
,”
Chem. Commun.
,
193
(
10
), pp.
1
19
.
14.
Hayat
,
T.
,
Abbas
,
Z.
, and
Javed
,
T.
, 2008, “
Mixed Convection Flow of a Micropolar Fluid over Non-Linearly Stretching Sheet
,”
Phys. Lett. A
,
372
(
5
), pp.
637
647
.
15.
Sajid
,
M.
,
Hayat
,
T.
,
Asghar
,
S.
, and
Vajravelu
,
K.
, 2008, “
Analytic Solution for Axisymmetric Flow Over a Nonlinearly Stretching Sheet
,”
Arch. Appl. Mech.
,
78
(
2
), pp.
127
134
.
16.
Eringen
,
A. C.
, 1966, “
Theory of Micropolar Fluids
,”
J. Math.
,
16
, pp.
1
18
.
17.
Ariman
,
T.
,
Turk
,
M. A.
, and
Sylvester
,
N. D.
, 1974, “
Applications of Micro-Continum Fluid Mechanics
,”
Int. J. Eng. Sci.
,
12
, pp.
273
293
.
18.
Ezzat
,
M. A.
,
Othman
,
M. I.
and
Helmy
,
K. A.
, 1999,
“A Problem of Micropolar Magnetohydrodynamic Boundary Layer Flow,”
Can. J. Phys.
77
(
10
), pp.
813
827
.
19.
Helmy
,
K. A.
,
Idriss
,
H. F.
, and
Kassem
,
S. E.
, 2002, “
MHD Free Convection Flow of a Micropolar Fluid Past a Vertical Porous Plate
,”
Can. J. Phys.
,
80
(
12
), pp.
166
1673
.
20.
Rees
,
D. A. S.
, and
Pop
,
I.
, 1998, “
Free Convection Boundary Layer Flow of a Micropolar Fluid From a Vertical Flat Plate
,”
IMA. J. Appl. Math.
,
61
(
2
), pp.
179
197
.
21.
Jena
,
S. K.
, and
Mathur
,
M. N.
, 1981, “
Similarity Solution for Laminar Free Convection Flow of Thermo-Micropolar Fluid Past a Nonisothermal Flat Plate
,”
Int. J. Eng.
,
19
(
11
), pp.
1431
1439
.
22.
Guram
,
G. S.
, and
Smith
,
A. C.
, 1980, “
Stagnation Flows of Micropolar Fluids With Strong and Weak Interactions
,”
Comput. Math. Appl.
,
6
(
2
), pp.
213
233
.
23.
Ahmadi
,
G.
, 1976, “
Self Similar Solution of Incompressible Micropolar Boundary Layer Flow Over Semi-Infinite Flat Plate
,”
Int. J. Eng. Sci.
,
14
(
7
), pp.
639
646
.
24.
Nazar
,
R.
,
Amin
,
N.
,
Filip
,
D.
, and
Pop
,
I.
, 2004, “
Stagnation Point Flow of Micropolar Fluid Towards a Stretching Sheet
,”
Int. J. Non-Linear Mech.
,
39
(
7
), pp.
1227
1235
.
25.
Takhar
,
H. S.
,
Bhargava
,
R.
,
Agrawal
,
R. S.
, and
Balaji
,
A.V. S.
, 2000, “
Finite Element Solution of a Micropolar Fluid Flow and Heat Transfer Between Two Porous Discs
,”
Int. J. Eng. Sci.
,
38
(
17
), pp.
1907
1922
.
26.
Ishizawa
,
S.
, 1966, “
The Unsteady Flow Between Two Parallel Discs With Arbitrary Varying Gap Width
,”
Bull. Jpn. Soc. Mech. Eng.
,
9
, pp.
533
550
.
27.
Grimm
,
R. J.
, 1976, “
Squeezing Flows of Newtonian Liquid Films an Analysis Include the Fluid Inertia
,”
App. Sci. Res.
,
32
(
2
), pp.
149
166
.
28.
Wang
,
C. Y.
, and
Watson
,
L. T.
, 1979, “
Squeezing of a Viscous Fluid Between Elliptic Plates
,”
App. Sci. Res.
,
35
(
2–3
),
195
207
.
29.
Usha
,
R.
, and
Sridharan
,
R.
, 1999, “
Arbitrary Squeezing of a Viscous Fluid Between Elliptic Plates
,”
Fluid Dyn. Res.
,
18
(
1
), pp.
35
51
.
30.
Laun
,
H. M.
,
Rady
,
M.
, and
Hassager
,
O.
, 1999, “
Analytical Solutions for Squeeze Flow With Partial Wall Slip
,”
J. Non-Newtonian Fluid Mech.
,
81
(
1–2
), pp.
1
15
.
31.
Debaut
,
B.
, 2001,
“Non-Isothermal and Viscoelastic Effects in the Squeeze Flow Between Infinite Plates,”
,
J. Non-Newtonian Fluid Mech.
,
98
(
1
), pp.
15
31
.
32.
Rashidi
,
M. M.
,
Shahmohamadi
,
H.
, and
Dinarvand
,
S.
, 2008, “
Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates
,”
Math. Probl. Eng.
,
2008
(
2
), p.
935095
.
33.
Domairy
,
G.
, and
Aziz
,
A.
, 2009, “
Approximate Analysis of MHD Squeezing Flow Between Two Parallel Disks With Suction or Injection by Homotopy Perturbation Method
,”
Math. Probl. Eng.
,
2009
, p.
603916
.
34.
Liao
,
S. J.
, 2003,
Beyond Perturbation: Introduction to Homotopy Analysis Method
,
Chapman and Hall, CRC Press
,
Boca Raton
.
35.
Xu
,
H.
, and
Liao
,
S. J.
, 2005, “
Dual Solutions of Boundary Layer Flow Over Upstream Moving Plate
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
(
2
), pp.
350
358
.
36.
Liao
,
S. J.
, 2005, “
A New Branch of Solutions of Unsteady Boundary Layer Flows Over an Impermeable Stretched Plate
,”
Int. J. Heat Mass Transfer
,
48
(
12
), pp.
2529
2539
.
37.
Chen
,
J.
, and
Liao
,
S. J.
, 2008, “
Series Solutions of Nano-Boundary Layer Flows by Means of the Homotopy Analysis Method
,”
J. Math. Anal. Appl.
,
343
(
1
), pp.
233
245
.
38.
Abbasbandy
,
S.
, and
Parkes
,
E. J.
, 2008, “
Solitary Smooth Hump Solutions of the Camassa-Holm Equation by Means of Homotopy Analysis Method
,”
Chaos, Solitons Fractals
,
36
(
3
), pp.
581
591
.
39.
Abbasbandy
,
S.
, 2008, “
Approximate Solution of the Nonlinear Model of Diffusion and Reaction Catalysts by Means of the Homotopy Analysis Method
,”
Chem. Eng. J.
,
136
(
2–3
), pp.
144
150
.
40.
Abbasbandy
,
S.
, and
Zakaria
,
F. S.
, 2008, “
Soliton Solution for the Fifth-Order Kdv Equation With the Homotopy Analysis Method
,”
Nonlinear Dyn.
,
51
(
1–2
), pp.
83
87
.
41.
Hayat
,
T.
,
Mustafa
,
M.
, and
Pop
,
I.
, 2010, “
Heat and Mass Transfer for Soret and Dufour’s Effect on Mixed Convection Boundary Layer Flow Over a Stretching Vertical Surface in a Porous Medium Filled With a Viscoelastic Fluid
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
5
), pp.
1183
1196
.
42.
Liao
,
S. J.
, 2010, “
An Optimal Homotopy Analysis Approach for Strongly Nonlinear Differential Equations
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
8
), pp.
2003
2016
.
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