In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

1.
Sakiadis
,
B. C.
, 1961, “
Boundary Layer Behavior on Continuous Solid Surface. I Boundary Layer Equations for Two-Dimensional and Axisymmetric Flow
,”
AIChE J.
0001-1541,
7
, pp.
26
28
.
2.
Crane
,
L. J.
,1970, “
Flow Past a Stretching Plate
,”
Z. Angew. Math. Phys.
0044-2275,
21
, pp.
645
647
.
3.
Andersson
,
H. I.
, 1992, “
MHD Flow of a Viscoelastic Fluid Past a Stretching Surface
,”
Acta Mech.
0001-5970,
95
, pp.
227
230
.
4.
Troy
,
W. C.
,
Overman
, II,
E. A.
,
Eremont-Rout
,
G. B.
, and
Keener
,
J. P.
, 1987, “
Uniqueness of Flow of Second Order Fluid Past a Stretching Sheet
,”
Q. Appl. Math.
0033-569X,
44
, pp.
753
755
.
5.
Ariel
,
P. D.
,1994, “
MHD Flow of a Viscoelastic Fluid Past a Stretching Sheet With Suction
,”
Acta Mech.
0001-5970,
105
, pp.
49
56
.
6.
Jacobi
,
A. M.
,1993, “
A Scale Analysis Approach to the Correlation of Continuous Moving Sheet, (Backward Boundary Layer) Forced Convective Heat Transfer
,”
ASME J. Heat Transfer
0022-1481,
115
, pp.
1058
1061
.
7.
Banks
,
W. H. H.
, 1983, “
Similarity Solutions of the Boundary-Layer Equations for a Stretching Wall
,”
J. Mec. Theor. Appl.
0750-7240,
2
, pp.
375
392
.
8.
Banks
,
W. H. H.
, and
Zaturska
,
M. B.
, 1986, “
Eigensolutions in Boundary Layer Flow Adjacent to a Stretching Wall
,”
IMA J. Appl. Math.
0272-4960,
36
, pp.
263
273
.
9.
Rajagopal
,
K. R.
, 1987, “
A Non Similar Boundary Layer on a Stretching Sheet in a Non-Newtonian Fluid With Uniform Stream
,”
J. Mathematical and Physical Sciences
,
21
, pp.
189
200
.
10.
Chakrabarti
,
A.
, and
Gupta
,
A. S.
, 1979, “
Hydromagnetic Flow and Heat Transfer Over a Stretching Sheet
,”
Q. Appl. Math.
0033-569X,
37
, pp.
756
755
.
11.
Chaudhary
,
M. A.
,
Merkin
,
J. H.
, and
Pop
,
I.
, 1995, “
Similarity Solutions in the Free Convection Boundary-Layer Flows Adjacent to Vertical Permeable Surface in Porous Media
,”
Eur. J. Mech. B/Fluids
0997-7546,
14
, pp.
217
237
.
12.
Chamkha
,
A. J.
, 1999, “
Hydromagnetic Three-Dimensional Free Convection on a Vertical Stretching Surface With Heat Generation or Absorption
,”
Int. J. Heat Fluid Flow
0142-727X,
20
, pp.
84
92
.
13.
Xu
,
H.
, and
Liao
,
S. J.
, 2005, “
Series Solution of Unsteady Magnetohydrodynamic Flows of Non-Newtonian Fluids Cause by an Impulsively Stretching Plate
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
129
, pp.
46
55
.
14.
Vajravelu
,
K.
, 1986, “
Hydromagnetic Flow and Heat Transfer Over a Continuous, Moving Porous Flat Surface
,”
Acta Mech.
0001-5970,
64
, pp.
179
185
.
15.
Zakaria
,
M.
, 2004, “
Magnetohydrodynamic Viscoelastic Boundary Layer Flow Past a Stretching Plate and Heat Transfer
,”
Appl. Math. Comput.
0096-3003,
155
, pp.
165
177
.
16.
Dutta
,
B. K.
,
Roy
,
P.
, and
Gupta
,
A. S.
, 1985, “
Temperature Field in Flow Over a Stretching Surface With Uniform Heat Flux
,”
Int. Commun. Heat Mass Transfer
0735-1933,
12
, pp.
89
94
.
17.
Andersson
,
H. I.
,
Aarseth
,
J. B.
,
Braud
,
N.
, and
Dandapat
,
B. S.
, 1996, “
Flow of a Power-Law Fluid Film on an Unsteady Stretching Surface
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
62
(
1
), pp.
1
8
.
18.
Bujurke
,
N. M.
,
Biradar
,
S. N.
, and
Hiremath
,
P. S.
, 1987, “
2nd-Order Fluid-Flow Past a Stretching Sheet With Heat-Transfer
,”
ZAMP
0044-2275,
38
(
4
), pp.
653
657
.
19.
Dandapat
,
B. S.
, and
Gupta
,
A. S.
, 1989, “
Flow and Heat Transfer in a Viscoelastic Fluid Over a Stretching Sheet
,”
Int. J. Non-Linear Mech.
0020-7462,
24
pp.
215
219
.
20.
Mehmood
,
A.
, and
Ali
,
A.
, “
An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Towards a Heated Plate
,”
ASME J. Appl. Mech.
, to be published.
21.
Mehmood
,
A.
, and
Ali
,
A.
, 2006, “
Analytic Solution of Generalized Three-Dimensional Flow and Heat Transfer Over a Stretching Plane Wall
,”
Int. Commun. Heat Mass Transfer
0735-1933,
33
, pp.
1243
1252
.
22.
Chen
,
C. K.
, and
Chen
,
M. I.
, 1988, “
Heat and Mass Transfer of a Continuous Stretching Surface With Suction or Blowing
,”
J. Math. Anal. Appl.
0022-247X,
135
, pp.
568
580
.
23.
Gupta
,
P. S.
, and
Gupta
,
A. S.
, 1977, “
Heat and Mass Transfer on a Stretching Sheet With Suction or Blowing
,”
Can. J. Chem. Eng.
0008-4034,
55
, pp.
744
746
.
24.
Ali
,
M. E.
, 1994, “
Heat Transfer Characteristics of a Continuous Stretching Surface
,”
Waerme- Stoffuebertrag.
0042-9929,
29
, pp.
227
234
.
25.
Mehmood
,
A.
,
Ali
,
A.
, and
Shah
,
T.
, 2008, “
Heat Transfer Analysis of Unsteady Boundary Layer Flow by Homotopy Analysis Method
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
(
5
), pp.
902
912
.
26.
Borkakoti
,
A. K.
, and
Bharali
,
A.
, 1983, “
Hydromagnetic Flow and Heat Transfer Between Two Horizontal Plates, the Lower Plate Being a Stretching Sheet
,”
Q. Appl. Math.
0033-569X,
41
, pp.
461
467
.
27.
Vajravelu
,
K.
, and
Kumar
,
B. V. R.
, 2004, “
Analytic and Numerical Solutions of Coupled Nonlinear System Arising in Three-Dimensional Rotating Flow
,”
Int. J. Non-Linear Mech.
0020-7462,
39
, pp.
13
24
28.
Liao
,
S. J.
, 2003,
Beyond Perturbation: Introduction to Homotopy Analysis Method
,
CRC
,
Boca Raton, FL
.
29.
Liao
,
S. J.
, and
Cheung
,
K. F.
, 2003, “
Homotopy Analysis of Nonlinear Progressive Waves in Deep Water
,”
J. Eng. Math.
0022-0833,
45
, pp.
105
116
.
30.
Liao
,
S. J.
, and
Pop
,
I.
, 2004, “
Explicit Analytic Solution for Similarity Boundary Layer Equations
,”
Int. J. Heat Mass Transfer
0017-9310,
47
(1), pp.
75
85
.
31.
Wang
,
C.
,
Zhu
,
J. M.
,
Liao
,
S. J.
, and
Pop
,
I.
, 2003, “
On the Explicit Analytic Solutions of Cheng-Chang Equations
,”
Int. J. Heat Mass Transfer
0017-9310,
46
(
10
), pp.
1855
1860
.
32.
Liao
,
S. J.
, 2006, “
An Analytic Solution of Unsteady Boundary Layer Flows Caused by Impulsively Stretching Plate
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
11
, pp.
326
339
.
33.
Ali
,
A.
, and
Mehmood
,
A.
, 2008, “
Homotopy Analysis of Unsteady Boundary Layer Flow Adjacent to Permeable Stretching Surface in a Porous Medium
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
, pp.
340
349
.
34.
Allan
,
F. M.
, and
Syam
,
M. I.
, 2005, “
On Analytic Solution of the Non-Homogeneous Blasius Problem
,”
J. Comput. Appl. Math.
0377-0427,
182
, pp.
355
365
.
35.
Liao
,
S. J.
, 2005, “
A New Branch of Solution of Boundary Layer Flows Over an Impermeable Stretched Plate
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
2529
2539
.
36.
Liao
,
S. J.
, 1999, “
A Uniformly Valid Analytical Solution of 2D Viscous Flow Past a Semi Infinite Flat Plate
,”
J. Fluid Mech.
0022-1120,
385
, pp.
101
128
.
37.
Liao
,
S. J.
, 1999, “
An Explicit, Totally Analytic Approximate Solution for Blasius Viscous Flow Problems
,”
Int. J. Non-Linear Mech.
0020-7462,
34
, pp.
759
778
.
38.
Mehmood
,
A.
, and
Ali
,
A.
, 2007, “
Unsteady Boundary Layer Flow Due to an Impulsively Started Moving Plate
,”
Proc. Inst. Mech. Eng., Part G: J. Aero. Engr.
,
221
, pp.
385
390
.
39.
Liao
,
S. J.
, and
Campo
,
A.
, 2002, “
Analytic Solutions of the Temperature Distribution in Blasius Viscous Flow Problems
,”
J. Fluid Mech.
0022-1120,
453
, pp.
411
425
.
40.
Yang
,
C.
, and
Liao
,
S. J.
, 2006, “
On the Explicit, Purely Analytic Solution of Von Karman Swirling Viscous Flow
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
11
(
1
), pp.
83
93
.
41.
Liao
,
S. J.
, 2003, “
On the Analytic Solution of Magnetohydrodynamic Flows of Non-Newtonian Fluids Over a Stretching Sheet
,”
J. Fluid Mech.
0022-1120,
488
, pp.
189
212
.
42.
Liao
,
S. J.
, 2004, “
On Homotopy Analysis Method for Nonlinear Problems
,”
Appl. Math. Comput.
0096-3003,
147
, pp.
499
513
.
You do not currently have access to this content.