A numerical investigation of mixed convection due to a copper–water nanofluid in an enclosure is presented. The mixed convection is governed by moving the upper lid of the enclosure and imposing a vertical temperature gradient. The transport equations for fluid and heat are modeled by using the Boussinesq approximation. A modified form of the control volume based SIMPLET algorithm is used for the solution of the transport equations. The fluid flow and heat transfer characteristics are studied for a wide range of Reynolds number and Grashof number so as to have the Richardson number greater or less than 1. The nanoparticle volume fraction is considered up to 20%. Heat flow patterns are analyzed through the energy flux vector. The rate of enhancement in heat transfer due to the addition of nanoparticles is analyzed. The entropy generation and Bejan number are evaluated to demonstrate the thermodynamic optimization of the mixed convection. We have obtained the enhancement rate in heat transfer and entropy generation in nanofluid for a wide range of parameter values.

References

References
1.
Eastman
,
J. A.
,
Choi
,
S. U. S.
,
Li
,
S.
,
Yu
,
W.
, and
Thompson
,
L. J.
,
2001
, “
Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,”
Appl. Phys. Lett.
,
78
(6), pp.
718
720
.
2.
Xuan
,
Y.
, and
Li
,
Q.
,
2003
, “
Investigation on Convective Heat Transfer and Flow Features of Nanofluids
,”
ASME J. Heat Transfer
,
125
(
1
), pp.
151
155
.
3.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
4.
Das
,
S. K.
,
Choi
,
S. U. S.
,
Yu
,
W.
, and
Pradet
,
T.
,
2007
,
Nanofluids: Science and Technology
,
Wiley
,
New York
.
5.
Kakaç
,
S.
, and
Pramuanjaroenkij
,
A.
,
2009
, “
Review of Convective Heat Transfer Enhancement With Nanofluids
,”
Int. J. Heat Mass Transfer
,
52
(
13–14
), pp.
3187
3196
.
6.
Wong
,
K. V.
, and
Leon
,
O. D.
,
2010
, “
Applications of Nanofluids: Current and Future
,”
Adv. Mech. Eng.
,
2
, p.
519659
.
7.
Saidur
,
R.
,
Leong
,
K. Y.
, and
Mohammad
,
H. A.
,
2011
, “
A Review on Applications and Challenges of Nanofluids
,”
Renewable Sustainable Energy Rev.
,
15
(
3
), pp.
1646
1668
.
8.
Wen
,
D.
,
Lin
,
G.
,
Vafaei
,
S.
, and
Zhang
,
K.
,
2007
, “
Review of Nanofluids for Heat Transfer Applications
,”
Particuology
,
7
(
2
), pp.
141
150
.
9.
Mahian
,
O.
,
Kianifar
,
A.
,
Kalogirou
,
S. A.
,
Pop
,
I.
, and
Wongwises
,
S.
,
2013
, “
A Review of the Applications of Nanofluids in Solar Energy
,”
Int. J. Heat Mass Transfer
,
57
(
2
), pp.
582
594
.
10.
Celli
,
M.
,
2013
, “
Non-Homogeneous Model for a Side Heated Square Cavity Filled With a Nanofluid
,”
Int. J. Heat Fluid Flow
,
44
, pp.
327
335
.
11.
Mojarrad
,
M. S.
,
Keshavarz
,
A.
, and
Shokouhi
,
A.
,
2013
, “
Nanofluids Thermal Behavior Analysis Using a New Dispersion Model Along With Single-Phase
,”
Heat Mass Transfer
,
49
(
9
), pp.
1333
1343
.
12.
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
(
25–26
), pp.
5792
5795
.
13.
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
(
2
), pp.
243
247
.
14.
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
(
5
), pp.
712
717
.
15.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2011
, “
The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
374
378
.
16.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2013
, “
The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid: A Revised Model
,”
Int. J. Heat Mass Transfer
,
65
, pp.
682
685
.
17.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2014
, “
Forced Convection in a Parallel-Plate Channel Occupied by a Nanofluid or a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
70
, pp.
430
433
.
18.
Ahmad
,
S.
,
Rohni
,
A. M.
, and
Pop
,
I.
,
2011
, “
Blasius and Sakiadis Problems in Nanofluids
,”
Acta Mech.
,
218
(
3–4
), pp.
195
204
.
19.
Magyari
,
E.
,
2011
, “
Comment on the Homogeneous Nanofluid Models Applied to Convective Heat Transfer Problems
,”
Acta Mech.
,
222
(
3–4
), pp.
381
385
.
20.
Khanafer
,
K.
,
Vafai
,
K.
, and
Lightstone
,
M.
,
2003
, “
Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer
,
46
(
19
), pp.
3639
3653
.
21.
Jou
,
R. Y.
, and
Tzeng
,
S. C.
,
2006
, “
Numerical Research of Nature Convective Heat Transfer Enhancement Filled With Nanofluids in Rectangular Enclosures
,”
Int. Commun. Heat Mass Transfer
,
33
(
6
), pp.
727
736
.
22.
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
.
23.
Maïga
,
S. E. B.
,
Palm
,
S. J.
,
Nguyen
,
C. T.
,
Roy
,
G.
, and
Galanis
,
N.
,
2008
, “
Heat Transfer Enhancement by Using Nanofluids in Forced Convection Flows
,”
Int. J. Heat Fluid Flow
,
26
(
4
), pp.
530
546
.
24.
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
(
9–10
), pp.
2002
2018
.
25.
Abu-Nada
,
E.
, and
Chamkha
,
A. J.
,
2010
, “
Mixed Convection Flow in a Lid-Driven Inclined Square Enclosure Filled With a Nanofluid
,”
Eur. J. Mech. B/Fluids
,
29
(
6
), pp.
472
482
.
26.
Talebi
,
F.
,
Mahmoudi
,
A. H.
, and
Shahi
,
M.
,
2010
, “
Numerical Study of Mixed Convection Flows in a Square Lid-Driven Cavity Utilizing Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
37
(
1
), pp.
79
90
.
27.
Mahmoodi
,
M.
,
2011
, “
Mixed Convection Inside Nanofluid Filled Rectangular Enclosures With Moving Bottom Wall
,”
Therm. Sci.
,
15
(3), pp.
889
903
.
28.
Chamkha
,
A. J.
, and
Abu-Nada
,
E.
,
2012
, “
Mixed Convection Flow in Single and Double-Lid Driven Square Cavities Filled With Water–Al2O3 Nanofluid: Effect of Viscosity Models
,”
Eur. J. Mech. B/Fluids
,
36
, pp.
82
96
.
29.
Khorasanizadeh
,
H.
,
Nikfar
,
M.
, and
Amani
,
J.
,
2013
, “
Entropy Generation of Cu–Water Nanofluid Mixed Convection in a Cavity
,”
Eur. J. Mech. B/Fluids
,
37
, pp.
143
152
.
30.
Nayak
,
R. K.
,
Bhattacharyya
,
S.
, and
Pop
,
I.
,
2015
, “
Numerical Study on Mixed Convection and Entropy Generation of Cu–Water Nanofluid in a Differentially Heated Skewed Enclosure
,”
Int. J. Heat Mass Transfer
,
85
, pp.
620
634
.
31.
Kimura
,
S.
, and
Bejan
,
A.
,
1983
, “
The Heatline Visualization of Convective Heat Transfer
,”
ASME J. Heat Transfer
,
105
(
4
), pp.
916
919
.
32.
Bello-Ochende
,
F. L.
,
1988
, “
A Heat Function Formulation for Thermal Convection in a Square Cavity
,”
Comput. Methods Appl. Mech. Eng.
,
68
(
2
), pp.
141
149
.
33.
Costa
,
V. A. F.
,
1999
, “
Unification of the Streamline, Heatline and Massline Methods for the Visualization of Two-Dimensional Transport Phenomena
,”
Int. J. Heat Mass Transfer
,
42
(
1
), pp.
27
33
.
34.
Deng
,
Q. H.
, and
Tang
,
G. F.
,
2002
, “
Numerical Visualization of Mass and Heat Transport for Conjugate Natural Convection/Heat Conduction by Streamline and Heatline
,”
Int. J. Heat Mass Transfer
,
45
(
11
), pp.
2373
2385
.
35.
Basak
,
T.
,
Roy
,
S.
,
Sharma
,
P. K.
, and
Pop
,
I.
,
2009
, “
Analysis of Mixed Convection Flows Within a Square Cavity With Uniform and Non-Uniform Heating of Bottom Wall
,”
Int. J. Therm. Sci.
,
48
(
5
), pp.
891
912
.
36.
Varol
,
Y.
,
Oztop
,
H. F.
,
Mobedi
,
M.
, and
Pop
,
I.
,
2010
, “
Visualization of Heat Flow Using Bejan's Heatline Due to Natural Convection of Water Near 4 °C in Thick Walled Porous Cavity
,”
Int. J. Heat Mass Transfer
,
53
(
9–10
), pp.
1691
1698
.
37.
Guo
,
Z. Y.
,
Li
,
D. Y.
, and
Wang
,
B. X.
,
1998
, “
A Novel Concept for Convective Heat Transfer Enhancement
,”
Int. J. Heat Mass Transfer
,
41
(
14
), pp.
2221
2225
.
38.
Bejan
,
A.
,
2014
, “
Heatlines (1983) Versus Synergy (1998)
,”
Int. J. Heat Mass Transfer
,
81
, pp.
654
658
.
39.
Hooman
,
K.
,
2010
, “
Energy Flux Vector as New Tool for Convection Visualization
,”
Int. J. Numer. Method Heat Fluid Flow
,
20
(
2
), pp.
240
249
.
40.
Bejan
,
A.
,
1996
,
Entropy Generation Minimization
,
CRC Press
,
Boca Raton, FL
.
41.
Bejan
,
A.
,
1979
, “
A Study of Entropy Generation in Fundamental Convective Heat Transfer
,”
ASME J. Heat Transfer
,
101
(
4
), pp.
718
725
.
42.
Baytaş
,
A. C.
,
2000
, “
Entropy Generation for Natural Convection in an inclined Porous cavity
,”
Int. J. Heat Mass Transfer
,
43
(
12
), pp.
2089
2099
.
43.
Magherbi
,
M.
,
Abbassi
,
H.
, and
Brahim
,
B. A.
,
2003
, “
Entropy Generation at the Onset of Natural Convection
,”
Int. J. Heat Mass Transfer
,
46
(
18
), pp.
3441
3450
.
44.
Varol
,
Y.
,
Oztop.
,
H. F.
, and
Koca
,
A.
,
2008
, “
Entropy Generation Due to Conjugate Natural Convection in Enclosures Bounded by Vertical Solid Walls With Different Thicknesses
,”
Int. Commun. Heat Mass Transfer
,
35
(
5
), pp.
648
656
.
45.
Ilis
,
G. G.
,
Mobedi
,
M.
, and
Sunden
,
B.
,
2008
, “
Effect of Aspect Ratio on Entropy Generation in a Rectangular Cavity With Differentially Heated Vertical Walls
,”
Int. Commun. Heat Mass Transfer
,
35
(
6
), pp.
696
703
.
46.
Sheng
,
Y.
,
Shoukri
,
M.
,
Sheng
,
G.
, and
Wood
,
P.
,
1998
, “
A Modification to the Simple Method for Buoyancy-Driven Flows
,”
Numer. Heat Transfer, Part B: Fundam.
,
33
(
1
), pp.
65
78
.
47.
Brinkman
,
H. C.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solution
,”
J. Chem. Phys
,
20
, pp.
571
581
.
48.
Sarkar
,
S.
,
Ganguly
,
S.
, and
Dalal
,
A.
,
2013
, “
Buoyancy Driven Flow and Heat Transfer of Nanofluids Past a Square Cylinder in Vertically Upward Flow
,”
Int. J. Heat Mass Transfer
,
59
, pp.
433
450
.
49.
Abu-Nada
,
E.
,
2010
, “
Effects of Variable Viscosity and Thermal Conductivity of CuO–Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation
,”
ASME J. Heat Transfer
,
132
(
5
), p.
052401
.
50.
Koo
,
J.
, and
Kleinstreuer
,
C.
,
2004
, “
A New Thermal Conductivity Model for Nanofluids
,”
J. Nanopart. Res.
,
6
(
6
), pp.
577
588
.
51.
Prasher
,
R.
,
Bhattacharyya
,
P.
, and
Phelan
,
P. E.
,
2005
, “
Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids)
,”
Phys. Rev. Lett.
,
94
, p.
025901
.
52.
Leonard
,
B. P.
,
1979
, “
A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
,
19
(
1
), pp.
59
98
.
53.
Cheng
,
T. S.
, and
Liu
,
W. H.
,
2010
, “
Effect of Temperature Gradient Orientation on the Characteristics of Mixed Convection Flow in a Lid-Driven Square Cavity
,”
Comput. Fluids
,
39
(
6
), pp.
965
978
.
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