The paper presents a computational study of steady, laminar, two-dimensional (2D) mixed convection heat transfer from a continuously moving isothermal vertical plate to alumina–water nanofluid as in hot extrusion. The simulation is based on a heterogeneous flow model which takes into account Brownian diffusion and thermophoresis of nanoparticles. The finite difference method is used to discretize the governing equations. The SIMPLE algorithm has been applied to obtain flow, thermal, and nanoparticle concentration fields. The numerical results have been validated satisfactorily with the published results for pure fluids. A detailed parametric study reveals that in the mixed convection regime, the enhancement factor (EF) (defined as the ratio of average heat transfer coefficient in nanofluid to that in base fluid) increases with nanoparticle concentration. The enhancement is more at lower Richardson number (Gr/Re2), that is, closer to forced convection regime. In the regime close to free convection, the EF is found to be very small. Larger plate velocity (that is, higher Reynolds number) has a positive effect on heat transfer enhancement but higher plate-fluid temperature difference results in lower EF. An enhancement in heat transfer coefficient as high as 22% is realized at the plate velocity of 0.4 m/s. The effectiveness (defined as the ratio of average heat transfer coefficient in nanofluid to the power required to pull the plate), in general, falls with higher volume fraction of nanoparticles and plate velocity and escalates with a rise in Richardson number and plate-fluid temperature difference.

References

References
1.
Sakiadis
,
B. C.
,
1961
, “
Boundary-Layer Behavior on Continuous Solid Surfaces—I: Boundary-Layer Equation for Two-Dimensional and Axisymmetric Flow
,”
AIChE J.
,
7
(
1
), pp.
26
28
.
2.
Sakiadis
,
B. C.
,
1961
, “
Boundary-Layer Behavior on Continuous Solid Surfaces—II: Boundary-Layer on Continuous Flat Surface
,”
AIChE J.
,
7
(
2
), pp.
221
225
.
3.
Sakiadis
,
B. C.
,
1961
, “
Boundary-Layer Behavior on Continuous Solid Surfaces: III. The Boundary-Layer on a Continuous Cylindrical Surface
,”
AIChE J.
,
7
(
3
), pp.
467
472
.
4.
Tsou
,
F. K.
,
Sparrow
,
E. M.
, and
Kurtz
,
E. F.
,
1966
, “
Hydrodynamic Stability of the Boundary Layer on a Continuous Moving Surface
,”
J. Fluid Mech.
,
26
(Part
1
), pp.
145
161
.
5.
Tsou
,
F. K.
,
Sparrow
,
E. M.
, and
Goldstein
,
R. J.
,
1967
, “
Flow and Heat Transfer in the Boundary Layer on a Continuous Moving Surface
,”
Int. J. Heat Mass Transfer
,
10
(
2
), pp.
219
235
.
6.
Chinda
,
K.
, and
Katto
,
Y.
,
1976
, “
Conjugate Heat Transfer of Continuously Moving Surfaces
,”
Int. J. Heat Mass Transfer
,
19
(
5
), pp.
461
470
.
7.
Char
,
M.
,
Chen
,
C.
, and
Cleaver
,
W.
,
1990
, “
Conjugate Forced Convection Heat Transfer From a Continuous, Moving Flat Sheet
,”
Int. J. Heat Fluid Flow
,
11
(
3
), pp.
257
261
.
8.
Revankar
,
S. T.
,
1989
, “
Heat Transfer to a Continuous Moving Flat Surface With Variable Wall Temperature
,”
Int. J. Heat Fluid Flow
,
10
(
4
), pp.
357
360
.
9.
Abdelhafez
,
T. A.
,
1985
, “
Skin Friction and Heat Transfer on a Continuous Flat Surface Moving in a Parallel Stream
,”
Int. J. Heat Mass Transfer
,
28
(
6
), pp.
1234
1237
.
10.
Afzal
,
N.
,
Badaruddin
,
A.
, and
Elgarvi
,
A. A.
,
1993
, “
Momentum and Heat Transport on a Continuous Flat Surface Moving in a Parallel Stream
,”
Int. J. Heat Mass Transfer
,
36
(
13
), pp.
3399
3403
.
11.
Hayat
,
T.
,
Iqbal
,
Z.
, and
Mustafa
,
M.
,
2012
, “
Flow and Heat Transfer of Jeffry Fluid Over a Continuously Moving Surface With a Parallel Free Stream
,”
ASME J. Heat Transfer
,
134
(
1
), p.
011701
.
12.
Abdallah
,
A. M.
,
1987
, “
Heat Transfer Between a Stagnant Fluid and a Continuously Moving Surface of Variable Temperature and Velocity
,”
Int. J. Heat Mass Transfer
,
14
(
4
), pp.
457
466
.
13.
Howell
,
T. G.
,
Jeng
,
D. R.
, and
Dewitt
,
K. J.
,
1997
, “
Momentum and Heat Transfer on a Continuous Moving Surface in a Power Law Fluid
,”
Int. J. Heat Mass Transfer
,
40
(
8
), pp.
1853
1861
.
14.
Moutsoglou
,
A.
, and
Bhattacharya
,
A. K.
,
1982
, “
Laminar and Turbulent Boundary Layers on Moving Non-Isothermal Continuous Surfaces
,”
ASME J. Heat Transfer
,
104
(
4
), pp.
707
714
.
15.
Karwe
,
M. V.
, and
Jaluria
,
Y.
,
1988
, “
Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes
,”
ASME J. Heat Transfer
,
110
(
3
), pp.
655
661
.
16.
Karwe
,
M. V.
, and
Jaluria
,
Y.
,
1991
, “
Numerical Simulation of Thermal Transport Associated With a Continuously Moving Flat Sheet in Material Processing
,”
ASME J. Heat Transfer
,
113
(
3
), pp.
612
619
.
17.
Karwe
,
M. V.
, and
Jaluria
,
Y.
,
1992
, “
Experimental Investigation of Thermal Transport From Heated Moving Plate
,”
Int. J. Heat Mass Transfer
,
35
(
2
), pp.
493
511
.
18.
Lee
,
S. L.
, and
Tsai
,
J. S.
,
1990
, “
Cooling of a Continuous Moving Sheet of Finite Thickness in the Presence of Natural Convection
,”
Int. J. Heat Mass Transfer
,
33
(
3
), pp.
457
464
.
19.
Al-Sanea
,
S. A.
,
2003
, “
Convective Regimes and Heat Transfer Characteristics Along a Continuously Moving Heated Vertical Plate
,”
Int. J. Heat Fluid Flow
,
24
(
6
), pp.
888
901
.
20.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
,
1962
, “
Thermal Conductivity of Heterogeneous Two-Component System
,”
Ind. Eng. Chem. Fundam.
,
1
(
3
), pp.
187
191
.
21.
Maxwell
,
J. C.
,
1873
,
A Treatise on Electricity and Magnetism
,
Clarendon Press
,
Oxford, UK
.
22.
Choi
,
S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
Developments and Applications of Non-Newtonian Flows
, FED-Vol. 231/MD-Vol.
66
,
D. A.
Siginer
and
H. P.
Wang
, eds.,
ASME
,
New York
, pp.
99
105
.
23.
Xu
,
H.
, and
Pop
,
I.
,
2012
, “
Fully Developed Mixed Convection Flow in a Vertical Channel Filled With Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
39
(
8
), pp.
1086
1092
.
24.
Shames
,
M.
,
Ahmadi
,
G.
, and
Rahimzadeh
,
H.
,
2000
, “
A Sublayer Model for Deposition of Nano- and Micro-Particles in Turbulent Flows
,”
Chem. Eng. Sci.
,
55
(
24
), pp.
6097
6107
.
25.
Xuan
,
Y.
, and
Roetzel
,
W.
,
2000
, “
Concept of Heat Transfer Correlation of Nanofluids
,”
Int. J. Heat Mass Transfer
,
43
(
19
), pp.
3701
3707
.
26.
Keblinski
,
P.
,
Phillpot
,
S. R.
,
Choi
,
S. U. S.
, and
Eastman
,
J. A.
,
2002
, “
Mechanisms of Heat Flow in Suspension of Nanosized Particles (Nanofluid)
,”
Int. J. Heat Mass Transfer
,
45
(
4
), pp.
855
863
.
27.
Ding
,
Y.
, and
Wen
,
D.
,
2005
, “
Particle Migration in a Flow of Nanoparticle Suspensions
,”
Powder Technol.
,
149
(2–3), pp.
84
92
.
28.
Schwarzer
,
H. C.
, and
Peukert
,
W.
,
2005
, “
Prediction of Aggregation Kinetics Based on Surface Properties of Nanoparticles
,”
Chem. Eng. Sci.
,
60
(
1
), pp.
11
25
.
29.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluid
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
30.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2010
, “
The Effect of Local Thermal Non-Equilibrium on the Onset of Convection in Nanofluid
,”
ASME J. Heat Transfer
,
132
(
5
), p.
052405
.
31.
Grosan
,
T.
, and
Pop
,
I.
,
2012
, “
Fully Developed Mixed Convection in a Vertical Channel Filled by a Nanofluid
,”
ASME J. Heat Transfer
,
134
(
8
), p.
082501
.
32.
Duangthongsuk
,
W.
, and
Wongwises
,
S.
,
2012
, “
A Dispersion Model for Predicting the Heat Transfer Performance of TiO2—Water Nanofluids Under a Laminar Flow Regime
,”
Int. J. Heat Mass Transfer
,
55
(11–12), pp.
3138
3146
.
33.
Jung
,
J. Y.
, and
Yoo
,
J. Y.
,
2009
, “
Thermal Conductivity Enhancement of Nanofluid in Conjunction With Electrical Double Layer (EDL)
,”
Int. J. Heat Mass Transfer
,
52
(1–2), pp.
525
528
.
34.
Eapen
,
J.
,
Rusconi
,
R.
,
Piazza
,
R.
, and
Yip
,
S.
,
2010
, “
The Classical Nature of Thermal Conductivity in Nanofluids
,”
ASME J. Heat Transfer
,
132
(
10
), p.
102402
.
35.
Bai
,
C.
, and
Wang
,
L.
,
2010
, “
Constructal Allocation of Nanoparticles in Nanofluids
,”
ASME J. Heat Transfer
,
132
(
5
), p.
052404
.
36.
Pang
,
C.
,
Jung
,
J.
, and
Kang
,
Y. T.
,
2014
, “
Aggregation Based Model for Heat Conduction Mechanism in Nanofluids
,”
Int. J. Heat Mass Transfer
,
72
, pp.
392
399
.
37.
Bourantas
,
G. C.
, and
Loukopoulos
,
V. C.
, “
Modeling the Natural Convective Flow of Micropolar Nanofluids
,”
Int. J. Heat Mass Transfer
,
68
, pp.
35
61
.
38.
Pak
,
B. C.
, and
Cho
,
I.
,
1998
, “
Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles
,”
Exp. Heat Transfer
,
11
(
2
), pp.
151
170
.
39.
Ghoshdastidar
,
P. S.
,
2012
,
Heat Transfer
,
2nd ed.
,
Oxford University Press
,
New Delhi, India
.
40.
Alvarino
,
P. F.
,
Jabardo
,
J. M. S.
,
Arce
,
A.
, and
Galdo
,
M. I. L.
,
2013
, “
A Numerical Investigation of Laminar Flow of a Water/Alumina Nanofluid
,”
Int. J. Heat Mass Transfer
,
59
, pp.
423
432
.
41.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Taylor and Francis
,
Washington, DC
.
You do not currently have access to this content.