Abstract

Nanofluids have drawn increasing attention in heat transfer applications due to their anomalous enhancement of the thermophysical properties in contemporary literature. Various studies have shown that the addition of minute concentration of the nanoparticles to a base solvent can yield dramatic enhancement of the effective thermal conductivity. A number of parameters have been reported to affect the level of such enhancement such as size, shape, morphology, concentration, and material properties of the nanoparticles. Many different theoretical models have also been proposed in the past literature for predicting the thermal conductivity of nanofluids under different conditions. In general, these models are based on either simplified static composite model or nanoconvection effect considering the Brownian motion of the nanoparticles. However, a few studies have explored the impact of nanoparticle aggregation on the nanofluid thermal conductivity. In particular, the formation of porous percolation structure by the nanoparticles can alter the effective thermal conductivity of nanofluid substantially. In this study, a two-stage numerical simulation is performed to analyze the thermal transport behavior inside nanofluid considering different levels of percolation network formed by the nanoparticles. Based on the simulation results, an empirical model is developed to predict the effective thermal conductivity of nanofluid as a function of nanoparticle size, concentration, and the permeability of nano-aggregation. The results demonstrated a strong dependence of nanofluid thermal conductivity on the nanocluster density, where a looser nanonetwork can yield a significantly higher level of thermal conductivity enhancement under the same particle size and concentration conditions.

References

1.
Masuda
,
H.
,
Ebata
,
A.
, and
Teramae
,
K.
,
1993
, “Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles. Dispersion of Al2O3, SiO2 and TiO2 Ultra-Fine Particles,” Netsu Bussei, 7(4), pp. 227–233.
2.
Eastman
,
J. A.
, Choi, U. S., Li, S., Thompson, L. J., and Lee, S.,
1996
, “
Enhanced Thermal Conductivity Through the Development of Nanofluids
,”
MRS Online Proc.
, 457, p. 3.10.1557/PROC-457-3
3.
Xuan
,
Y.
, and
Li
,
Q.
,
2000
, “
Heat Transfer Enhancement of Nanofluids
,”
Int. J. Heat Fluid Flow
,
21
(
1
), pp.
58
64
.10.1016/S0142-727X(99)00067-3
4.
Xie
,
H.
,
Wang
,
J.
,
Xi
,
T.
,
Liu
,
Y.
,
Ai
,
F.
, and
Wu
,
Q.
,
2002
, “
Thermal Conductivity Enhancement of Suspensions Containing Nanosized Alumina Particles
,”
J. Appl. Phys.
,
91
(
7
), pp.
4568
4572
.10.1063/1.1454184
5.
Assael
,
M. J.
,
Metaxa
,
I. N.
,
Kakosimos
,
K.
, and
Constantinou
,
D.
,
2006
, “
Thermal Conductivity of Nanofluids–Experimental and Theoretical
,”
Int. J. Thermophys.
,
27
(
4
), pp.
999
1017
.10.1007/s10765-006-0078-6
6.
Jha
,
N.
, and
Ramaprabhu
,
S.
,
2009
, “
Thermal Conductivity Studies of Metal Dispersed Multiwalled Carbon Nanotubes in Water and Ethylene Glycol Based Nanofluids
,”
J. Appl. Phys.
,
106
(
8
), p.
084317
.10.1063/1.3240307
7.
Beck
,
M. P.
,
Yuan
,
Y.
,
Warrier
,
P.
, and
Teja
,
A. S.
,
2009
, “
The Effect of Particle Size on the Thermal Conductivity of Alumina Nanofluids
,”
J. Nanopart. Res.
,
11
(
5
), pp.
1129
1136
.10.1007/s11051-008-9500-2
8.
Shima
,
P.
, and
Philip
,
J.
,
2011
, “
Tuning of Thermal Conductivity and Rheology of Nanofluids Using an External Stimulus
,”
J. Phys. Chem. C
,
115
(
41
), pp.
20097
20104
.10.1021/jp204827q
9.
Teng
,
T.-P.
,
Hung
,
Y.-H.
,
Teng
,
T.-C.
,
Mo
,
H.-E.
, and
Hsu
,
H.-G.
,
2010
, “
The Effect of Alumina/Water Nanofluid Particle Size on Thermal Conductivity
,”
Appl. Therm. Eng.
,
30
(
14–15
), pp.
2213
2218
.10.1016/j.applthermaleng.2010.05.036
10.
Kim
,
S. H.
,
Choi
,
S. R.
, and
Kim
,
D.
,
2007
, “
Thermal Conductivity of Metal-Oxide Nanofluids: Particle Size Dependence and Effect of Laser Irradiation
,”
ASME J. Heat Transfer
,
129
(
3
), pp.
298
307
.10.1115/1.2427071
11.
Maxwell
,
J. C.
,
1881
,
A Treatise on Electricity and Magnetism
, Vol.
1
,
Clarendon Press, Oxford, UK
.
12.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
,
1962
, “
Thermal Conductivity of Heterogeneous Two-Component Systems
,”
Ind. Eng. Chem. Fundam.
,
1
(
3
), pp.
187
191
.10.1021/i160003a005
13.
Fricke
,
H.
,
1953
, “
The Maxwell-Wagner Dispersion in a Suspension of Ellipsoids
,”
J. Phys. Chem.
,
57
(
9
), pp.
934
937
.10.1021/j150510a018
14.
Polder
,
D.
, and
Van Santeen
,
J.
,
1946
, “
The Effective Permeability of Mixtures of Solids
,”
Physica
,
12
(
5
), pp.
257
271
.10.1016/S0031-8914(46)80066-1
15.
Granqvist
,
C.
, and
Hunderi
,
O.
,
1978
, “
Conductivity of Inhomogeneous Materials: Effective-Medium Theory With Dipole-Dipole Interaction
,”
Phys. Rev. B
,
18
(
4
), p.
1554
.10.1103/PhysRevB.18.1554
16.
Qingzhong
,
X.
,
2000
, “
Effective-Medium Theory for Two-Phase Random Composites With an Interfacial Shell
,”
J. Mater. Sci. Technol. (Shenyang, China)
,
16
, pp.
367
369
.http://www.jmst.org/CN/Y2000/V16/I04/367
17.
Rayleigh
,
L.
,
1892
, “
LVI. On the Influence of Obstacles Arranged in Rectangular Order Upon the Properties of a Medium
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
,
34
(
211
), pp.
481
502
.10.1080/14786449208620364
18.
Cheng
,
S.
, and
Vachon
,
R.
,
1970
, “
A Technique for Predicting the Thermal Conductivity of Suspensions, Emulsions and Porous Materials
,”
Int. J. Heat Mass Transfer
,
13
(
3
), pp.
537
546
.10.1016/0017-9310(70)90149-3
19.
Hasselman
,
D.
, and
Johnson
,
L. F.
,
1987
, “
Effective Thermal Conductivity of Composites With Interfacial Thermal Barrier Resistance
,”
J. Compos. Mater.
,
21
(
6
), pp.
508
515
.10.1177/002199838702100602
20.
Benveniste
,
Y.
,
1987
, “
Effective Thermal Conductivity of Composites With a Thermal Contact Resistance Between the Constituents: Nondilute Case
,”
J. Appl. Phys.
,
61
(
8
), pp.
2840
2843
.10.1063/1.337877
21.
Xuan
,
Y.
,
Li
,
Q.
, and
Hu
,
W.
,
2003
, “
Aggregation Structure and Thermal Conductivity of Nanofluids
,”
AIChE J.
,
49
(
4
), pp.
1038
1043
.10.1002/aic.690490420
22.
Prasher
,
R.
,
Evans
,
W.
,
Meakin
,
P.
,
Fish
,
J.
,
Phelan
,
P.
, and
Keblinski
,
P.
,
2006
, “
Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids
,”
Appl. Phys. Lett.
,
89
(
14
), p.
143119
.10.1063/1.2360229
23.
Feng
,
Y.
,
Yu
,
B.
,
Xu
,
P.
, and
Zou
,
M.
,
2007
, “
The Effective Thermal Conductivity of Nanofluids Based on the Nanolayer and the Aggregation of Nanoparticles
,”
J. Phys. D: Appl. Phys.
,
40
(
10
), p.
3164
.10.1088/0022-3727/40/10/020
24.
Hotze
,
E. M.
,
Phenrat
,
T.
, and
Lowry
,
G. V.
,
2010
, “
Nanoparticle Aggregation: Challenges to Understanding Transport and Reactivity in the Environment
,”
J. Environ. Qual.
,
39
(
6
), pp.
1909
1924
.10.2134/jeq2009.0462
25.
Philip
,
J.
,
Shima
,
P.
, and
Raj
,
B.
,
2008
, “
Evidence for Enhanced Thermal Conduction Through Percolating Structures in Nanofluids
,”
Nanotechnology
,
19
(
30
), p.
305706
.10.1088/0957-4484/19/30/305706
26.
Fan
,
J.
, and
Wang
,
L.
,
2011
, “
Review of Heat Conduction in Nanofluids
,”
ASME J. Heat Transfer
,
133
(
4
), p.
040801
.10.1115/1.4002633
27.
Devpura
,
P. E. P.
,
Ravi
,
S.
, and
Prasher
,
A.
,
2001
, “
Size Effects on the Thermal Conductivity of Polymers Laden With Highly Conductive Filler Particles
,”
Microscale Thermophys. Eng.
,
5
(
3
), pp.
177
189
.10.1080/108939501753222869
28.
Ghadimi
,
A.
,
Saidur
,
R.
, and
Metselaar
,
H.
,
2011
, “
A Review of Nanofluid Stability Properties and Characterization in Stationary Conditions
,”
Int. J. Heat Mass Transfer
,
54
(
17–18
), pp.
4051
4068
.10.1016/j.ijheatmasstransfer.2011.04.014
29.
Gharagozloo
,
P. E.
, and
Goodson
,
K. E.
,
2010
, “
Aggregate Fractal Dimensions and Thermal Conduction in Nanofluids
,”
J. Appl. Phys.
,
108
(
7
), p.
074309
.10.1063/1.3481423
30.
Prasher
,
R.
,
Phelan
,
P. E.
, and
Bhattacharya
,
P.
,
2006
, “
Effect of Aggregation Kinetics on the Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluid)
,”
Nano Lett.
,
6
(
7
), pp.
1529
1534
.10.1021/nl060992s
31.
Liu
,
M.
,
Ding
,
C.
, and
Wang
,
J.
,
2016
, “
Modeling of Thermal Conductivity of Nanofluids Considering Aggregation and Interfacial Thermal Resistance
,”
RSC Adv.
,
6
(
5
), pp.
3571
3577
.10.1039/C5RA16327G
32.
Srivastava
,
S.
,
2012
, “
Effect of Aggregation on Thermal Conductivity and Viscosity of Nanofluids
,”
Appl. Nanosci.
,
2
(
3
), pp.
325
331
.10.1007/s13204-012-0082-z
33.
Zhang
,
S.
,
Ge
,
Z.
,
Wang
,
H.
, and
Wang
,
H.
,
2016
, “
A New Semi-Analytical Model for Effective Thermal Conductivity of Nanofluids
,”
Phys. Chem. Liq.
,
54
(
5
), pp.
647
662
.10.1080/00319104.2016.1139706
34.
Kang
,
H.
,
Zhang
,
Y.
,
Yang
,
M.
, and
Li
,
L.
,
2012
, “
Molecular Dynamics Simulation on Effect of Nanoparticle Aggregation on Transport Properties of a Nanofluid
,”
ASME J. Nanotechnol. Eng. Med.
,
3
(
2
), p.
021001
.10.1115/1.4007044
35.
Lee
,
S. L.
,
Saidur
,
R.
,
Sabri
,
M. F. M.
, and
Min
,
T. K.
,
2015
, “
Molecular Dynamic Simulation on the Thermal Conductivity of Nanofluids in Aggregated and Non-Aggregated States
,”
Numer. Heat Transfer, Part A
,
68
(
4
), pp.
432
453
.10.1080/10407782.2014.986366
36.
Chen
,
Y.-H.
,
2013
,
Investigating the Aggregation Effect in Nanofluids by Molecular Dynamics
,
The Pennsylvania State University, State College, PA
.
37.
Evans
,
W.
,
Prasher
,
R.
,
Fish
,
J.
,
Meakin
,
P.
,
Phelan
,
P.
, and
Keblinski
,
P.
,
2008
, “
Effect of Aggregation and Interfacial Thermal Resistance on Thermal Conductivity of Nanocomposites and Colloidal Nanofluids
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1431
1438
.10.1016/j.ijheatmasstransfer.2007.10.017
38.
Jeng
,
M.-S.
,
Yang
,
R.
,
Song
,
D.
, and
Chen
,
G.
,
2008
, “
Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation
,”
ASME J. Heat Transfer
,
130
(
4
), p.
042410
.10.1115/1.2818765
39.
Ammar
,
A.
,
Chinesta
,
F.
, and
Heyd
,
R.
,
2016
, “
Thermal Conductivity of Suspension of Aggregating Nanometric Rods
,”
Entropy
,
19
(
1
), p.
19
.10.3390/e19010019
40.
Demirel
,
Y.
,
2007
,
Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems
,
Elsevier, Amsterdam, The Netherlands
.
41.
Wang
,
L.
,
Zhou
,
X.
, and
Wei
,
X.
,
2007
,
Heat Conduction: Mathematical Models and Analytical Solutions
,
Springer Science & Business Media, Berlin, Germany
.
42.
Gupta
,
A.
, and
Kumar
,
R.
,
2007
, “
Role of Brownian Motion on the Thermal Conductivity Enhancement of Nanofluids
,”
Appl. Phys. Lett.
,
91
(
22
), p.
223102
.10.1063/1.2816903
43.
Jang
,
S. P.
, and
Choi
,
S. U.
,
2004
, “
Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids
,”
Appl. Phys. Lett.
,
84
(
21
), pp.
4316
4318
.10.1063/1.1756684
44.
Kumar
,
D. H.
,
Patel
,
H. E.
,
Kumar
,
V. R. R.
,
Sundararajan
,
T.
,
Pradeep
,
T.
, and
Das
,
S. K.
,
2004
, “
Model for Heat Conduction in Nanofluids
,”
Phys. Rev. Lett.
,
93
(
14
), p.
144301
.10.1103/PhysRevLett.93.144301
45.
Keblinski
,
P.
, and
Cahill
,
D. G.
,
2005
, “
Comment on Model for Heat Conduction in Nanofluids
,”
Phys. Rev. Lett.
,
95
(
20
), p.
209401
.10.1103/PhysRevLett.95.209401
46.
Prasher
,
R.
,
Bhattacharya
,
P.
, and
Phelan
,
P. E.
,
2005
, “
Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids)
,”
Phys. Rev. Lett.
,
94
(
2
), p.
025901
.10.1103/PhysRevLett.94.025901
47.
Lewis
,
T.
, and
Nielsen
,
L.
,
1970
, “
Dynamic Mechanical Properties of Particulate‐Filled Composites
,”
J. Appl. Polym. Sci.
,
14
(
6
), pp.
1449
1471
.10.1002/app.1970.070140604
You do not currently have access to this content.