An analysis is carried out to study the steady two-dimensional stagnation-point flow of a nanofluid over a stretching/shrinking sheet in its own plane. The stretching/shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and thermophoresis parameter Nt. It is found that the local Nusselt number is a decreasing function, while the local Sherwood number is an increasing function of each parameters Pr, Le, Nb, and Nt. Different from a stretching sheet, the solutions for a shrinking sheet are nonunique.

References

1.
Ding
,
Y.
,
Chen
,
H.
,
Wang
,
L.
,
Yang
,
C-Y.
,
He
,
Y.
,
Yang
,
W.
,
Lee
,
W. P.
,
Zhang
,
L.
, and
Huo
,
R.
,
2007
, “
Heat Transfer Intensification Using Nanofluids
,”
KONA
,
25
, pp.
23
38
. Available at http://kona.or.jp/search/25_023.pdf
2.
Kinloch
,
I. A.
,
Roberts
,
S. A.
, and
Windle
,
A. H.
,
2002
, “
A Rheological Study of Concentrated Aqueous Nanotube Dispersions
,”
Polymer
,
43
, pp.
7483
7491
.10.1016/S0032-3861(02)00664-X
3.
Tohver
,
V.
,
Chan
,
A.
,
Sakurada
,
O.
, and
Lewis
,
J. A.
,
2001
, “
Nanoparticle Engineering of Complex Fluid Behaviour
,”
Langmuir
,
17
, pp.
8414
8421
.10.1021/la011252w
4.
Wasan
,
D. T.
, and
Nikolov
,
A. D.
,
2003
, “
Spreading of Nanofluids on Solids
,”
Nature
,
423
, pp.
156
159
.10.1038/nature01591
5.
Celata
,
G. P.
,
Annibale
,
F. D.
, and
Mariani
,
A.
,
2011
, “
Nanofluid Flow Effects on Metal Surfaces
,”
Energia Ambiente e Innovazione
,
4-5
, pp.
94
98
. Available at http://www.enea.it/it/produzione-scientifica/energia-ambiente-e-innovazione-1/anno-2011/n.%204-5%202011%20Luglio-ottobre2011/nanofluid-flow-effects-on-metal-surfaces
6.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Trans.
,
128
(3), pp.
240
250
.10.1115/1.2150834
7.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2009
, “
The Cheng-Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
52
, pp.
3187
3196
.10.1016/j.ijheatmasstransfer.2009.02.006
8.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2011
, “
The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
54
, pp.
374
378
.10.1016/j.ijheatmasstransfer.2010.09.034
9.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
Natural Convective Boundary Layer Flow of a Nanofluid Past a Vertical Plate
,”
Int. J. Therm. Sci.
,
49
, pp.
243
247
.10.1016/j.ijthermalsci.2009.07.015
10.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2011
, “
Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,”
Int. J. Therm. Sci.
,
50
, pp.
712
717
.10.1016/j.ijthermalsci.2011.01.003
11.
Khan
,
A. V.
, and
Pop
,
I.
,
2010
, “
Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2477
2483
.10.1016/j.ijheatmasstransfer.2010.01.032
12.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2010
, “
Boundary Layer Flow of Nanofluids Over a Moving Surface in a Flowing Fluid
,”
Int. J. Therm. Sci.
,
49
, pp.
1663
1668
.10.1016/j.ijthermalsci.2010.01.026
13.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2012
, “
Unsteady Boundary-Layer Flow of a Nanofluid Over a Permeable Stretching/Shrinking Sheet
,”
Int. J. Heat Mass Transfer
,
55
, pp.
2102
2109
.10.1016/j.ijheatmasstransfer.2011.12.013
14.
Grosan
,
T.
, and
Pop
,
I.
,
2012
, “
Fully Developed Mixed Convection in a Vertical Channel Filled by a Nanofluid
,”
ASME J. Heat Trans.
,
134
(8), p.
082501
.10.1115/1.4006159
15.
Tiwari
,
R. K.
, and
Das
,
M. K.
,
2007
, “
Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer
,
50
, pp.
2002
2018
10.1016/j.ijheatmasstransfer.2006.09.034.
16.
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
(8), p.
081202
.10.1115/1.4006246
17.
Mustafa
,
M.
,
Hayat
,
T.
, and
Hendi
,
A. A.
,
2012
, “
Influence of Melting Heat Transfer in the Stagnation-Point Flow of a Jeffrey Fluid in the Presence of Viscous Dissipation
,”
ASME J. Appl. Mech.
,
79
(2), p.
024501
.10.1115/1.4005560
18.
Ishak
,
A.
,
Nazar
,
R.
, and
Pop
,
I.
,
2009
, “
Boundary Layer Flow and Heat Transfer Over an Unsteady Stretching Vertical Surface
,”
Meccanica
,
44
, pp.
369
375
.10.1007/s11012-008-9176-9
19.
Liu
,
I.-C.
,
Megahed
,
A.
, 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.
(accepted).10.1115/1.4007966
20.
Goldstein
,
S.
,
1965
, “
On Backward Boundary Layers and Flow in Converging Passages
,”
J. Fluid Mech.
,
21
, pp.
33
45
.10.1017/S0022112065000034
21.
Fang
,
T.-G.
,
Zhang
,
J.
, and
Yao
,
S.-S.
,
2009
, “
Viscous Fover an Unsteady Shrinking Sheet With Mass Transfer
,”
Chin. Phys. Lett.
,
26
, p.
014703
.10.1088/0256-307X/26/1/014703
22.
Hiemenz
,
K.
,
1911
, “
Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder
,”
Dinglers Polytechn. J.
,
326
, pp.
321
324
.
23.
Wang
,
C. Y.
,
2008
, “
Stagnation Flow Towards a Shrinking Sheet
,”
Int. J. Non-Linear Mech.
,
43
, pp.
377
382
.10.1016/j.ijnonlinmec.2007.12.021
24.
Ishak
,
A.
,
Lok
,
Y. Y.
, and
Pop
,
I.
,
2010
, “
Stagnation-Point Flow Over a Shrinking Sheet in a Micropolar Fluid
,”
Chem. Eng. Comm.
,
197
, pp.
1417
1427
.10.1080/00986441003626169
25.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2010
, “
Melting Heat Transfer in Boundary Layer Stagnation-Point Flow Towards a Stretching/Shrinking Sheet
,”
Phys. Lett. A
,
374
, pp.
4075
4079
.10.1016/j.physleta.2010.08.032
26.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2011
, “
On the Stagnation-Point Flow Towards a Stretching Sheet With Homogeneous-Heterogeneous Reactions Effects
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
, pp.
4296
4302
.10.1016/j.cnsns.2011.01.008
27.
Weidman
,
P. D.
,
Kubitschek
,
D. G.
, and
Davis
,
A. M. J.
,
2006
, “
The Effect of Transpiration on Self-Similar Boundary Layer Flow Over Moving Surfaces
,”
Int. J. Eng. Sci.
,
44
, pp.
730
737
.10.1016/j.ijengsci.2006.04.005
28.
Merkin
,
J. H.
,
1994
, “
A Note on the Similarity Equations Arising in Free Convection Boundary Layers With Blowing and Suction
,”
J. Appl. Math. Phys. (ZAMP)
,
45
, pp.
258
274
.10.1007/BF00943504
29.
Postelnicu
,
A.
, and
Pop
,
I.
,
2011
, “
Falkner-Skan Boundary Layer Flow of a Power-Law Fluid Past a Stretching Wedge
,”
Appl. Math. Comput.
,
217
, pp.
4359
4368
.10.1016/j.amc.2010.09.037
You do not currently have access to this content.