The two-dimensional flow of a thin nanoliquid film over an unsteady stretching sheet is studied under the assumption of planar film thickness when the sheet is heated/cooled along the stretching direction. The governing equations of momentum, energy are solved numerically by using finite difference method. The rate of film thinning decreases with the increase in the nanoparticle volume fraction. On the other hand, thermocapillary parameter influences the film thinning. A boundary within the film is delineated such that the sign of Tz changes depending on the stretching distance from the origin. Further the boundary for Tz > 0 enlarges when the volume fraction of the nanoparticle increases.

References

References
1.
Crane
,
L. J.
,
1970
, “
Flow Past a Stretching Plate
,”
Z. Angew. Math. Phys.
,
21
, pp.
645
647
.
2.
Grubka
,
L. G.
, and
Bobba
,
K. M.
,
1985
, “
Heat Transfer Characteristics of a Continuous Stretching Surface With Variable Temperature
,”
ASME J. Heat Transfer
,
107
(
1
), pp.
248
250
.
3.
Pavlov
,
K. B.
,
1974
, “
Magnetohydrodynamic Flow of an Incompressible Viscous Fluid Caused by Deformation of a Plane Surface
,”
Magn. Gidrodin.
,
10
(
4
), pp.
43
46
.
4.
Andersson
,
H. I.
,
Bech
,
K. H.
, and
Dandapat
,
B. S.
,
1992
, “
Magnetohydrodynamic Flow of a Power-Law Fluid Over a Stretching Sheet
,”
Int. J. Nonlinear Mech.
,
27
(
6
), pp.
929
936
.
5.
Wang
,
C. Y.
,
1990
, “
Liquid Film on an Unsteady Stretching Surface
,”
Q. Appl. Math.
,
48
, pp.
601
610
.
6.
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
(
1
), pp.
1
8
.
7.
Dandapat
,
B. S.
,
Santra
,
B.
, and
Andersson
,
H. I.
,
2003
, “
Thermocapillarity in a Liquid Film on an Unsteady Stretching Surface
,”
Int. J. Heat and Mass Transfer.
,
46
(
16
), pp.
3009
3015
.
8.
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
(
9–10
), pp.
2044
2051
.
9.
Able
,
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. Nonlinear Mech.
,
44
(
9
), pp.
990
998
.
10.
Dandapat
,
B. S.
,
Kitamura
,
A.
, and
Santra
,
B.
,
2006
, “
Transient Film Profile of Thin Liquid Film Flow on a Stretching Surface
,”
Z. Angew. Math. Phys.
,
57
(
4
), pp.
623
635
.
11.
Dandapat
,
B. S.
, and
Maity
,
S.
,
2006
, “
Flow of a Thin Liquid Film on an Unsteady Stretching Sheet
,”
Phys. Fluids
,
18
(
10
), p.
102101
.
12.
Dandapat
,
B. S.
,
Maity
,
S.
, and
Kitamura
,
A.
,
2008
, “
Liquid Film Flow Due to an Unsteady Stretching Sheet
,”
Int. J. Nonlinear Mech.
,
43
(
9
), pp.
880
886
.
13.
Maity
,
S.
,
2014
, “
Thermocapillary Flow of Thin Liquid Film Over a Porous Stretching Sheet in Presence of Suction/Injection
,”
Int. J. Heat Mass Transfer
,
70
, pp.
819
826
.
14.
Choi
,
S. U. S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” Proceedings of the 1995
ASME
International Mechanical Engineering Congress and Exposition
, San Francisco, CA, FED231/MD66, pp.
99
105
.
15.
Choi
,
S. U. S.
,
Zhang
,
Z. G.
,
Yu
,
W.
,
Lockwood
,
F. E.
, and
Grulke
,
E. A.
,
2001
, “
Anomalously Thermal Conductivity Enhancement in Nanotube Suspension
,”
Appl. Phys. Lett.
,
79
(
14
), pp.
2252
2254
.
16.
Xuan
,
Y.
, and
Li
,
Q.
,
2000
, “
Heat Transfer Enhancement of Nanofluids
,”
Int. J. Heat Fluid Flow
,
21
(
1
), pp.
58
64
.
17.
Eastman
,
J. A.
,
Choi
,
S. U. S.
,
Li
,
S.
,
Thompson
,
L. J.
, and
Lee
,
S.
,
1997
, “
Enhanced Thermal Conductivity Through the Development of Nanofluids
,”
1996, Fall Meeting of the Materials Research Society
(
MRS
), Boston, MA, Vol. 457, pp. 3–11.
18.
Das
,
S. K.
,
Choi
,
S. U. S.
,
Yu
,
W.
, and
Pradeep
,
T.
,
2007
,
Nanofluids; Sciences and Technology
,
Wiley
,
Hoboken, NJ
.
19.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
20.
Wang
,
X. Q.
, and
Majumdar
,
A. S.
,
2007
, “
Heat Transfer Characteristic of Nanofluids: A Review
,”
Int. J. Therm. Sci.
,
46
(
1
), pp.
1
19
.
21.
Kakac
,
S.
, and
Pramuanjaroenkij
,
A.
,
2009
, “
Review of Convective Heat Transfer Enhancement With Nanofluids
,”
Int. J. Heat Mass Transfer
,
52
(13–14), pp.
3187
3196
.
22.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2009
, “
The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by Nanofluid
,”
Int. J. Heat Mass Transfer
,
52
(25–26), pp.
5792
5795
.
23.
Khan
,
W. A.
, and
Pop
,
I.
,
2010
, “
Boundary Layer Flow of a Nanofluid Past a Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
53
(11–12), pp.
2477
2483
.
24.
Rana
,
P.
, and
Bhargava
,
R.
,
2012
, “
Flow and Heat Transfer of a Nanofluid Over a Nonlinearly Stretching Sheet: A Numerical Study
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
, pp.
212
226
.
25.
Vajravelu
,
K.
,
Prasad
,
K. V.
,
Lee
,
J.
,
Lee
,
C.
,
Pop
,
I.
, and
Van Gorder
,
R. A.
,
2011
, “
Convective Heat Transfer in the Flow of Viscous Ag–Water and Cu–Water Nanofluid Over a Stretching Surface
,”
Int. J. Therm. Sci.
,
50
(
5
), pp.
843
851
.
26.
Bochok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2012
, “
Unsteady Boundary Layer Flow and Heat Transfer of a Nanofluid Over a Permeable Stretching/Shrinking Sheet
,”
Int. J. Heat Mass Transfer
,
55
(7–8), pp.
2102
2109
.
27.
Das
,
K.
,
Durai
,
P. R.
, and
Kundu
,
P. K.
,
2014
, “
Nanofluid Flow Over an Unsteady Stretching Surface in Presence of Thermal Radiation
,”
Alexandria Eng. J.
,
53
(
3
), pp.
737
745
.
28.
Narayana
,
M.
, and
Sibanda
,
P.
,
2012
, “
Laminar Flow of Nanoliquid Film Over an Unsteady Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
55
(25–26), pp.
7552
7560
.
29.
Xu
,
H.
,
Pop
,
I.
, and
You
,
X. C.
,
2013
, “
Flow and Heat Transfer in a Nano-Liquid Film Over an Unsteady Stretching Surface
,”
Int. J. Heat Mass Transfer
,
60
(
1
), pp.
646
652
.
30.
Zeytounian
,
R. Kh.
,
2009
,
Convection in Fluids: A Rational Analysis and Asymptotic Modelling
,
Heidelberg
.
31.
Hamad
,
M. A. A.
,
2011
, “
Analytical Solution of Natural Convection Flow of Nanofluid Over a Linearly Stretching Sheet in the Presence of Magnetic Field
,”
Int. Commun. Heat Mass Transfer
,
38
(
4
), pp.
487
492
.
32.
Oztop
,
H. F.
, and
Abu-Nada
,
E.
,
2008
, “
Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled With Nanofluids
,”
Int. J. Heat Fluid Flow
,
29
(
5
), pp.
1326
1336
.
33.
Dandapat
,
B. S.
, and
Ray
,
P. C.
,
1994
, “
The Effects of Thermocapillarity on the Flow of a Thin Liquid Film on a Rotating Disc
,”
J. Phys. D: Appl. Phys.
,
27
(
10
), pp.
2041
2045
.
34.
Robert
,
G. O.
,
1971
,
Lecture Notes in Physics
,
Springer-Verlag
,
New York
.
35.
Fletcher
,
C. A. J.
,
1988
,
Computational Technique for Fluid Dynamics
, Vol.
II
,
Springer-Verlag
,
New York
.
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