In this study, the effect of magnetic field, viscous dissipation, nonuniform heat source, and/or sink and thermal radiation on flow and heat transfer in a hydromagnetic liquid film over an unsteady stretching sheet with prescribed heat flux condition is investigated. The governing equations are transformed into a set of ordinary differential equations with six free parameters by using a similarity transformation before being solved numerically. The temperature profiles depending on the governing parameters are displayed in graphical form and the relevant thermal characteristics are depicted in tabular representation. It is found that the dimensionless temperature profile, sheet temperature, and free surface temperature, with a specific unsteadiness parameter, are enhanced as the increase in magnetic parameter, Eckert number, space- and temperature-dependent parameters, and they are reduced for increasing effective Prandtl number.

References

References
1.
Andersson
,
H. I.
,
Aarseth
,
J. B.
, and
Dandapat
,
B. S.
,
2000
, “
Heat Transfer in a Liquid Film on an Unsteady Stretching Surface
,”
Int. J. Heat Mass Transfer
,
43
, pp.
69
74
.10.1016/S0017-9310(99)00123-4
2.
Dandapat
,
B. S.
,
Santra
,
B.
, and
Vajravelu
,
K.
,
2007
, “
The Effects of Variable Fluid Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
50
, pp.
991
996
.10.1016/j.ijheatmasstransfer.2006.08.007
3.
Crane
,
L. J.
,
1970
, “
Flow Past a Stretching Plate
,”
ZAMP
,
21
, pp.
645
647
.10.1007/BF01587695
4.
Gupta
,
P. S.
, and
Gupta
,
A. S.
,
1977
, “
Heat and Mass Transfer on a Stretching Sheet With Suction or Blowing
,”
Can. J. Chem. Eng.
,
55
, pp.
744
746
.10.1002/cjce.5450550619
5.
Chakrabarti
,
A.
, and
Gupta
,
A. S.
,
1979
, “
Hydromagnetic Flow and Heat Transfer Over a Stretching Sheet
,”
Q. Appl. Math.
,
37
, pp.
73
78
.
6.
Grubka
,
L. G.
, and
Bobba
,
K. M.
,
1985
, “
Heat Transfer Characteristics of a Continuous, Stretching Surface With Variable Temperature
,”
ASME J. Heat Transfer
,
107
, pp.
248
250
.10.1115/1.3247387
7.
Jeng
,
D. R.
,
Chang
,
T. C. A.
, and
De Witt
,
K. J.
,
1986
, “
Momentum and Heat Transfer on a Continuous Surface
,”
ASME J. Heat Transfer
,
108
, pp.
532
539
.10.1115/1.3246967
8.
Chen
,
C. K.
, and
Char
,
M. I.
,
1988
, “
Heat Transfer of a Continuous, Stretching Surface With Suction or Blowing
,”
J. Math. Anal. Appl.
,
135
(
2
), pp.
568
580
.10.1016/0022-247X(88)90172-2
9.
Laha
,
M. K.
,
Gupta
,
P. S.
, and
Gupta
,
A. S.
,
1989
, “
Heat Transfer Characteristics of the Flow of an Incompressible Viscous Fluid Over a Stretching Sheet
,”
Warme Stoffubertrag.
,
24
, pp.
151
153
.10.1007/BF01590013
10.
Afzal
,
N.
,
1993
, “
Heat Transfer From a Stretching Surface
,”
Int. J. Heat Mass Transfer
,
36
, pp.
1128
1131
.10.1016/S0017-9310(05)80296-0
11.
Wang
,
C. Y.
,
1990
, “
Liquid Film on an Unsteady Stretching Surface
,”
Q. Appl. Math.
,
48
, pp.
601
610
.
12.
Andersson
,
H. I.
,
Aarseth
,
J. B.
,
Braud
,
N.
, and
Dandapat
,
B. S.
,
1996
, “
Flow of a Power-Law Fluid on an Unsteady Stretching Surface
,”
J. Non-Newtonian Fluid Mech.
,
62
, pp.
1
8
.10.1016/0377-0257(95)01392-X
13.
Wang
,
C.
, and
Pop
,
I.
,
2006
, “
Analysis of the Flow of a Power-Law Fluid Film on an Unsteady Stretching Surface by Means of Homotopy Analysis Method
,”
J. Non-Newtonian Fluid Mech.
,
138
, pp.
161
172
.10.1016/j.jnnfm.2006.05.011
14.
Abbas
,
Z.
,
Hayat
,
T.
,
Sajid
,
M.
, and
Asghar
,
S.
,
2008
, “
Unsteady Flow of a Second Grade Fluid Film Over an Unsteady Stretching Sheet
,”
Math. Comput. Modell.
,
48
, pp.
518
526
.10.1016/j.mcm.2007.09.015
15.
Hayat
,
T.
,
Saif
,
S.
, and
Abbas
,
Z.
,
2008
, “
The Influence of Heat Transfer in an MHD Second Grade Fluid Film Over an Unsteady Stretching Sheet
,”
Phys. Lett. A
,
372
, pp.
5037
5045
.10.1016/j.physleta.2008.03.066
16.
Chen
,
C. H.
,
2003
, “
Heat Transfer in a Power-Law Fluid Film Over a Unsteady Stretching Sheet
,”
Heat Mass Transfer
,
39
, pp.
791
796
.10.1007/s00231-002-0363-2
17.
Dandapat
,
B. S.
,
Santra
,
B.
, and
Andersson
,
H. I.
,
2003
, “
Thermocapillarity in a Liquid Film on an Unsteady Stretching Surface
,”
Int. J. Heat Mass Transfer
,
46
, pp.
3009
3015
.10.1016/S0017-9310(03)00078-4
18.
Chen
,
C. H.
,
2007
, “
Marangoni Effects on Forced Convection of Power-Law Liquids in a Thin Film Over a Stretching Surface
,”
Phys. Lett. A
,
370
, pp.
51
57
.10.1016/j.physleta.2007.05.024
19.
Chen
,
C. H.
,
2006
, “
Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet
,”
J. Non-Newtonian Fluid Mech.
,
135
, pp.
128
135
.10.1016/j.jnnfm.2006.01.009
20.
Elgazery
,
N. S.
, and
Hassan
,
M. A.
,
2008
, “
The Effects of Variable Fluid Properties and Magnetic Field on the Flow of Non-Newtonian Fluid Film on an Unsteady Stretching Sheet Through a Porous Medium
,”
Commun. Numer. Methods Eng.
,
24
, pp.
2113
2129
.10.1002/cnm.1099
21.
Mahmoud
,
M. A. A.
, and
Megahed
,
A. M.
,
2009
, “
MHD Flow and Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet With Variable Fluid Properties
,”
Can. J. Phys.
,
87
, pp.
1065
1071
.10.1139/P09-066
22.
Abel
,
M. S.
,
Mahesha
,
M.
, and
Tawade
,
J.
,
2009
, “
Heat Transfer in a Liquid Film Over an Unsteady Stretching Surface With Viscous Dissipation in the Presence of External Magnetic Field
,”
Appl. Math. Model.
,
33
, pp.
3430
3441
.10.1016/j.apm.2008.11.021
23.
Abel
,
M. S.
,
Tawade
,
J.
, and
Nandeppanavar
,
M. M.
,
2009
, “
Effect of Non-Uniform Heat Source on MHD Heat Transfer in a Liquid Film Over an Unsteady Stretching Sheet
,”
Int. J. Non-Linear Mech.
,
44
, pp.
990
998
.10.1016/j.ijnonlinmec.2009.07.004
24.
Noor
,
N. F. M.
, and
Hashim
,
I.
,
2010
, “
Thermocapillarity and Magnetic Field Effects in a Thin Liquid Film on an Unsteady Stretching Surface
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2044
2051
.10.1016/j.ijheatmasstransfer.2009.12.052
25.
Noor
,
N. F. M.
,
Abdulaziz
,
O.
, and
Hashim
,
I.
,
2010
, “
MHD Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet by the Homotopy Analysis Method
,”
Int. J. Numer. Methods Fluids
,
63
, pp.
357
373
.10.1002/fld.2078
26.
Aziz
,
R. C.
, and
Hashim
,
I.
,
2010
, “
Liquid Film on Unsteady Stretching Sheet With General Surface Temperature and Viscous Dissipation
,”
Chin. Phys. Lett.
,
27
, p.
110202
.10.1088/0256-307X/27/11/110202
27.
Aziz
,
R. C.
,
Hashim
,
I.
, and
Alomari
,
A. K.
,
2011
, “
Thin Film Flow and Heat Transfer on an Unsteady Stretching Sheet With Internal Heating
,”
Meccanica
,
46
, pp.
349
357
.10.1007/s11012-010-9313-0
28.
Aziz
,
R. C.
,
Hashim
,
I.
, and
Abbasbandy
,
S.
,
2012
, “
Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet
,”
Math. Probl. Eng.
,
2012
, p.
127320
.10.1155/2012/127320
29.
Mukhopadhyay
,
S.
,
2009
, “
Effect of Thermal Radiation on Unsteady Mixed Convection Flow and Heat Transfer Over a Porous Stretching Surface in Porous Medium
,”
Int. J. Heat Mass Transfer
,
52
, pp.
3261
3265
.10.1016/j.ijheatmasstransfer.2008.12.029
30.
Abd El-Aziz
,
M.
,
2009
, “
Radiation Effect on the Flow and Heat Transfer Over an Unsteady Stretching Sheet
,”
Int. Commun. Heat Mass Transfer
,
36
, pp.
521
524
.10.1016/j.icheatmasstransfer.2009.01.016
31.
Pal
,
D.
,
2011
, “
Combined Effects of Non-Uniform Heat Source/Sink and Thermal Radiation on Heat Transfer Over an Unsteady Stretching Permeable Surface
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
16
, pp.
1890
1904
.10.1016/j.cnsns.2010.08.023
32.
Attia
,
H. A.
,
Ewis
,
K. M.
, and
Abdeen
,
M. A. M.
,
2012
, “
Stagnation Point Flow Through a Porous Medium Towards a Radially Stretching Sheet in the Presence of Uniform Suction or Injection and Heat Generation
,”
ASME J. Fluids Eng.
,
134
, p.
081202
.10.1115/1.4006246
33.
Khan
,
W. A.
, and
Pop
,
I. M.
,
2012
, “
Effects of Homogeneous-Heterogeneous Reactions on the Viscoelastic Fluid Towards a Stretching Sheet
,”
ASME J. Heat Transfer
,
134
, p.
064506
.10.1115/1.4006016
34.
Liu
,
I.-C.
,
Megahed
,
A. M.
, and
Wang
,
H.-H.
,
2012
, “
Heat Transfer in a Liquid Film Due to an Unsteady Stretching Surface With Variable Heat Flux
,”
ASME J. Appl. Mech.
(in press).10.1115/1.4007966
35.
Magyari
,
E.
, and
Pantokratoras
,
A.
,
2011
, “
Note on the Effect of Thermal Radiation in the Linearized Rosseland Approximation on the Heat Transfer Characteristics of Various Boundary Layer Flows
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
554
556
.10.1016/j.icheatmasstransfer.2011.03.006
36.
Abo-Eldahab
,
E. M.
, and
El Aziz
,
M. A.
,
2004
, “
Blowing/Suction Effect on Hydromagnetic Heat Transfer by Mixed Convection From an Inclined Continuously Stretching Surface With Internal Heat Generation/Absorption
,”
Int. J. Therm. Sci.
,
43
, pp.
709
719
.10.1016/j.ijthermalsci.2004.01.005
37.
Liu
,
I.-C.
,
2005
, “
Flow and Heat Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium Over a Stretching Sheet Subject to a Transverse Magnetic Field
,”
Int. J. Non-Linear Mech.
,
40
, pp.
465
474
.10.1016/j.ijnonlinmec.2004.07.008
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