The developing and developed nanofluid Rayleigh–Bénard flows between two parallel plates was simulated using the mesoscopic thermal lattice-Boltzmann method (LBM). The coupled effects of the thermal conductivity and the dynamic viscosity on the evolution of Rayleigh–Bénard flows were examined using different particle volume fractions (1–4%), while the individual effects of the thermal conductivity and the dynamic viscosity were tested using various particle sizes (11 nm, 20 nm, and 30 nm) and nanoparticle types (Al2O3, Cu, and CuO2). Two different heating modes were also considered. The results show that Rayleigh–Bénard cell in nanofluids is significantly different from that in pure fluids. The stable convection cells in nanofluids come from the expansion and shedding of an initial vortex pair, while the flow begins suddenly in pure water when the Rayleigh number reaches a critical value. Therefore, the average Nusselt number increases gradually for nanofluids but sharply for pure liquids. Uniform fully developed flow cells with fewer but larger vortex pairs are generated with the bottom heating with nanofluids than with pure liquid, with extremely tiny vortexes confined near the top heating plate for top heating. The number of vortex pairs decreases with increasing nanoparticle volume fraction and particle diameter due to the increasing of dynamic viscosity. The average Nusselt number increases with the increasing Rayleigh number, while decreases with the increasing nanoparticle diameters. The nanoparticle types have little effect on the Rayleigh–Bénard flow patterns. The Rayleigh–Bénard flows are more sensitive with the dynamic viscosity than the thermal conductivity of nanofluids.

References

References
1.
de Vahl Davis
,
G.
, and
Jones
, I
. P.
,
1983
, “
Natural Convection in a Square Cavity: A Bench Mark Numerical Solution
,”
Int. J. Numer. Methods Fluids
,
3
, pp.
227
248
.10.1002/fld.1650030304
2.
Guenter
,
A.
,
Siegfried
,
G.
, and
Detlef
,
L.
,
2009
, “
Heat Transfer and Large Scale Dynamics in Turbulent Rayleigh–Benard Convection
,”
Rev. Mod. Phys.
,
81
, pp.
503
537
.10.1103/RevModPhys.81.503
3.
Olga
,
S.
, and
Andre
,
T.
,
2009
, “
Mean Temperature Profiles in Turbulent Rayleigh–Benard Convection of Water
,”
J. Fluid Mech.
,
633
, pp.
449
460
.10.1017/S0022112009990528
4.
Stevens
,
R. J.
,
Lohse
,
D.
, and
Verzicco
,
R.
,
2011
, “
Prandtl and Rayleigh Number Dependence of Heat Transport in High Rayleigh Number Thermal Convection
,”
J. Fluid Mech.
,
688
, pp.
31
43
.10.1017/jfm.2011.354
5.
Grants
,
I.
, and
Gerbeth
,
G.
,
2012
, “
Transition Between Turbulent Magnetically Driven Flow States in a Rayleigh–Benard Cell
,”
Phys. Fluids
,
24
, p.
024103
.10.1063/1.3682374
6.
He
,
X. Z.
,
Funfschilling
,
D.
, and
Nobach
,
H.
,
2012
, “
Transition to the Ultimate State of Turbulent Rayleigh–Benard Convection
,”
Phys. Rev. Lett.
,
108
, p.
024502
.10.1103/PhysRevLett.108.024502
7.
Prosperetti
,
A.
,
2011
, “
A Simple Analytic Approximation to the Rayleigh–Benard Stability Threshold
,”
Phys. Fluids
,
23
, p.
124101
.10.1063/1.3662466
8.
Haddad
,
Z.
,
Abu-Nada
,
E.
,
Oztop
,
H. F.
, and
Mataoui
,
A.
,
2012
, “
Natural Convection in Nanofluids: Are the Thermophoresis and Brownian Motion Effects Significant in Nanofluid Heat Transfer Enhancement?
,”
Int. J. Therm. Sci.
,
57
, pp.
152
162
.10.1016/j.ijthermalsci.2012.01.016
9.
Corcione
,
M.
,
2011
, “
Rayleigh–Benard Convection Heat Transfer in Nanoparticle Suspensions
,”
Int. J. Heat Fluid Flow
,
32
, pp.
65
77
.10.1016/j.ijheatfluidflow.2010.08.004
10.
Saidur
,
R.
,
Leong
,
K. Y.
, and
Mohammad
,
A.
,
2011
, “
A Review on Applications and Challenges of Nanofluids
,”
Renewable Sustainable Energy Rev.
,
15
, pp.
1646
1668
.10.1016/j.rser.2010.11.035
11.
Fan
,
J.
, and
Wang
,
L. Q.
,
2011
, “
Review of Heat Conduction in Nanofluids
,”
ASME J. Heat Transfer
,
133
, p.
040801
.10.1115/1.4002633
12.
Lee
,
S.
,
Choi
,
S. U.
, and
Li
,
S.
,
1999
, “
Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles
,”
ASME J. Heat Transfer
,
121
, pp.
280
289
.10.1115/1.2825978
13.
Paul
,
G.
,
Chopkar
,
M.
, and
Manna
,
I.
,
2010
, “
Techniques for Measuring the Thermal Conductivity of Nanofluids: A Review
,”
Renewable Sustainable Energy Rev.
,
14
, pp.
1913
1924
.10.1016/j.rser.2010.03.017
14.
Wang
,
X. W.
,
Xu
,
F.
, and
Choi
,
S. U.
,
1999
, “
Thermal Conductivity of Nanoparticle–Fluid Mixture
,”
J. Thermophys. Heat Transfer
,
13
, pp.
474
480
.10.2514/2.6486
15.
Sarit
,
K. D.
,
Nandy
,
P.
, and
Peter
,
T.
,
2003
, “
Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids
,”
ASME J. Heat Transfer
,
125
, pp.
567
574
.10.1115/1.1571080
16.
Murshed
,
S. M. S.
,
Leong
,
K. C.
, and
Yang
,
C.
,
2008
, “
Investigations of Thermal Conductivity and Viscosity of Nanofluids
,”
Int. J. Therm. Sci.
,
47
, pp.
560
568
.10.1016/j.ijthermalsci.2007.05.004
17.
Putra
,
N.
,
Roetzel
,
W.
, and
Das
,
S. K.
,
2003
, “
Natural Convection of Nanofluids
,”
Int. J. Therm. Sci.
,
57
, pp.
152
162
.10.1007/s00231-002-0382-z
18.
Ho
,
C. J.
,
Liu
,
W. K.
,
Chang
,
Y. S.
, and
Lin
,
C. C.
,
2010
, “
Natural Convection Heat Transfer of Alumina–Water Nanofluid in Vertical Square Enclosures: An Experimental Study
,”
Int. J. Therm. Sci.
,
49
, pp.
1345
1353
.10.1016/j.ijthermalsci.2010.02.013
19.
Wen
,
D.
, and
Ding
,
Y.
,
2005
, “
Formulation of Nanofluids for Natural Convective Heat Transfer Applications
,”
Int. J. Heat Fluid Flow
,
26
, pp.
855
864
.10.1016/j.ijheatfluidflow.2005.10.005
20.
Nnanna
,
A. G. A.
,
2007
, “
Experimental Model of Temperature-Driven Nanofluid
,”
ASME J. Heat Transfer
,
129
, pp.
697
704
.10.1115/1.2717239
21.
Li
,
C. H.
, and
Peterson
,
G. P.
,
2010
, “
Experimental Studies of Natural Convection Heat Transfer of Al2O3/DI Water Nanoparticle Suspensions (Nanofluids)
,”
Adv. Mech. Eng.
,
2010
, p.
742739
.10.1155/2010/742739
22.
Haddad
,
X.
,
Oztop
,
H. F.
,
Abu-Nada
,
E.
, and
Mataoui
,
A.
,
2012
,”
A Review on Natural Convective Heat Transfer of Nanofluids
,”
Renewable Sustainable Energy Rev.
,
16
, pp.
5363
5378
.10.1016/j.rser.2012.04.003
23.
Abouali
,
O.
, and
Falahatpisheh
,
A.
,
2009
, “
Numerical Investigation of Natural Convection of Al2O3 Nanofluids in Vertical Annuli
,”
J. Heat Mass Transfer
,
49
, pp.
15
23
.10.1007/s00231-009-0540-7
24.
Abu-Nada
,
E.
,
2009
, “
Effects of Variable Viscosity and Thermal Conductivity of Al2O3-Water Nanofluid on Heat Transfer Enhancement in Natural Convection
,”
Int. J. Heat Fluid Flow
,
30
, pp.
679
690
.10.1016/j.ijheatfluidflow.2009.02.003
25.
Abu-Nada
,
E.
,
2011
, “
Rayleigh-Bénard Convection in Nanofluids: Effect of Temperature Dependent Properties
,”
Int. J. Therm. Sci.
,
50
, pp.
1720
1730
.10.1016/j.ijthermalsci.2011.04.003
26.
Li
,
K. C.
, and
Violi
,
A.
,
2010
, “
Natural Convection Heat Transfer of Nanofluids in a Vertical Cavity: Effects of Non-Uniform Particle Diameter and Temperature on Thermal Conductivity
,”
Int. J. Heat Fluid Flow
,
3
, pp.
236
245
.10.1016/j.ijheatfluidflow.2009.11.003
27.
Santra
,
A. K.
,
Sen
,
S.
, and
Chakraborty
,
N.
,
2008
, “
Study of Heat Transfer Augmentation in a Differentially Heated Square Cavity Using Copper-Water Nanofluid
,”
Int. J. Therm. Sci.
,
47
, pp.
1113
1122
.10.1016/j.ijthermalsci.2007.10.005
28.
Rashmi
,
W.
,
Ismail
,
A. F.
, and
Khalid
,
M.
,
2011
, “
CFD Studies on Natural Convection Heat Transfer of Al2O3–Water Nanofluids
,”
Heat Mass Transfer
,
47
, pp.
1301
1310
.10.1007/s00231-011-0792-x
29.
Ho
,
C. J.
,
Chen
,
M. W.
, and
Li
,
Z. W.
,
2008
, “
Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effects Due to Uncertainties of Viscosity and Thermal Conductivity
,”
Int. J. Heat Mass Transfer
,
51
, pp.
4506
4516
.10.1016/j.ijheatmasstransfer.2007.12.019
30.
Cianfrini
,
M.
,
Corcione
,
M.
, and
Quintino
,
A.
,
2011
, “
Natural Convection Heat Transfer of Nanofluids in Annular Spaces Between Horizontal Concentric Cylinders
,”
Appl. Therm. Eng.
,
31
, pp.
4055
4063
.10.1016/j.applthermaleng.2011.08.010
31.
Fattahi
,
E.
,
Farhadi
,
M.
, and
Sedighi
,
K.
,
2011
, “
Lattice Boltzmann Simulation of Natural Convection Heat Transfer in Nanofluids
,”
Int. J. Therm. Sci.
,
52
, pp.
137
144
.10.1016/j.ijthermalsci.2011.09.001
32.
Lai
,
F. H.
, and
Yang
,
Y. T.
,
2011
, “
Lattice Boltzmann Simulation of Natural Convection Heat Transfer of Al2O3/Water Nanofluids in a Square Enclosure
,”
Int. J. Therm. Sci.
,
50
, pp.
1930
1941
.10.1016/j.ijthermalsci.2011.04.015
33.
Yang
,
Y. T.
, and
Lai
,
F. H.
,
2011
, “
Numerical Study of Flow and Heat Transfer Characteristics of Alumina-Water Nanofluids in a Microchannel Using the Lattice Boltzmann Method
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
607
614
.10.1016/j.icheatmasstransfer.2011.03.010
34.
Nabavitabatabayi
,
M.
,
Shirani
,
E.
, and
Rahimian
,
M. H.
,
2011
, “
Investigation of Heat Transfer Enhancement in an Enclosure Filled With Nanofluids Using Multiple Relaxation Time Lattice Boltzmann Modeling
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
128
138
.10.1016/j.icheatmasstransfer.2010.09.008
35.
Bararnia
,
H.
,
Hooman
,
K.
, and
Ganji
,
D. D.
,
2011
, “
Natural Convection in a Nanofluids-Filled Portioned Cavity: The Lattice-Boltzmann Method
,”
Numer. Heat Transfer, Part A
,
59
, pp.
487
502
.10.1080/10407782.2011.541195
36.
Kefayati
,
Gh. R.
,
Hosseinizadeh
,
S. F.
, and
Gorji
,
M.
,
2012
, “
Lattice Boltzmann Simulation of Natural Convection in an Open Enclosure Subjugated to Water/Copper Nanofluid
,”
Int. J. Therm. Sci.
,
52
, pp.
91
101
.10.1016/j.ijthermalsci.2011.09.005
37.
Kefayati
,
Gh. R.
,
Hosseinizadeh
,
S. F.
, and
Gorji
,
M.
,
2011
, “
Lattice Boltzmann Simulation of Natural Convection in Tall Enclosures Using Water/SiO2 Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
798
805
.10.1016/j.icheatmasstransfer.2011.03.005
38.
He
,
Y. R.
,
Qi
,
C.
, and
Hu
,
Y. W.
,
2011
, “
Lattice Boltzmann Simulation of Alumina-Water Nanofluid in a Square Cavity
,”
Nanoscale Res. Lett.
,
6
.10.1186/1556-276X-6-184
39.
Nemati
,
H.
,
Farhadi
,
M.
, and
Sedighi
,
K.
,
2010
, “
Lattice Boltzmann Simulation of Nanofluid in Lid-Driven Cavity
,”
Int. Commun. Heat Mass Transfer
,
37
, pp.
1528
1534
.10.1016/j.icheatmasstransfer.2010.08.004
40.
Xuan
,
Y. M.
,
Yu
,
K.
, and
Li
,
Q.
,
2005
, “
Investigation on Flow and Heat Transfer of Nanofluids by the Thermal Lattice Boltzmann Model
,”
Prog. Comput. Fluid Dyn.
,
5
, pp.
13
19
.10.1504/PCFD.2005.005813
41.
Xuan
,
Y. M.
,
Li
,
Q.
, and
Yao
,
Z. P.
,
2004
, “
Application of Lattice Boltzmann Scheme to Nanofluids
,”
Sci. China, Ser. E
,
47
, pp.
129
140
.10.1360/03ye0163
42.
Xuan
,
Y. M.
, and
Yao
,
Z. P.
,
2005
, “
Lattice Boltzmann Model for Nanofluids
,”
Heat Mass Transfer
,
41
(3), pp.
199
205
.10.1007/s00231-004-0539-z
43.
Zhou
,
L. J.
,
Xuan
,
Y. M.
, and
Li
,
Q.
,
2010
, “
Multiscale Simulation of Flow and Heat Transfer of Nanofluid With Lattice Boltzmann Method
,”
Int. J. Multiphase Flow
,
36
, pp.
364
374
.10.1016/j.ijmultiphaseflow.2010.01.005
44.
Zou
,
Q.
,
Hou
,
S.
, and
Chen
,
S.
,
1995
, “
An Improved Incompressible Lattice Boltzmann Model for Time-Independent Flows
,”
J. Stat. Phys.
,
81
, pp.
35
48
.10.1007/BF02179966
45.
Pak
,
B. C.
, and
Cho
,
Y.
,
1998
, “
Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particle
,”
Exp. Heat Transfer
,
11
, pp.
151
170
.10.1080/08916159808946559
46.
Xuan
,
Y.
, and
Roetzel
,
W.
,
2004
, “
Conceptions for Heat Transfer Correlation of Nanofluids
,”
Int. J. Heat Mass Transfer
,
43
, pp.
3701
3707
.10.1016/S0017-9310(99)00369-5
47.
Chon
,
C. H.
,
Kihm
,
K. D.
,
Lee
,
S. P.
, and
Choi
,
S. U.
,
2005
, “
Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement
,”
Appl. Phys. Lett.
,
87
, p.
153107
.10.1063/1.2093936
48.
Saha
,
L. K.
,
Hossain
,
M. A.
, and
Gorla
,
R. S. R.
,
2007
, “
Effect of Hall Current on the MHD Laminar Natural Convection Flow From a Vertical Permeable Flat Plate With Uniform Surface Temperature
,”
Int. J. Therm. Sci.
,
46
, pp.
790
801
.10.1016/j.ijthermalsci.2006.10.009
49.
Corcione
,
M.
,
2011
, “
Empirical Correlating Equations for Predicting the Effective Thermal Conductivity and Dynamic Viscosity of Nanofluids
,”
Energy Convers. Manage.
,
52
, pp.
789
793
.10.1016/j.enconman.2010.06.072
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