Thermal conductivity equations for the suspension of nanoparticles (nanofluids) have been derived from the kinetic theory of particles under relaxation time approximations. These equations, which take into account the microconvection caused by the particle Brownian motion, can be used to evaluate the contribution of particle Brownian motion to thermal transport in nanofluids. The relaxation time of the particle Brownian motion is found to be significantly affected by the long-time tail in Brownian motion, which indicates a surprising persistence of particle velocity. The long-time tail in Brownian motion could play a significant role in the enhanced thermal conductivity in nanofluids, as suggested by the comparison between the theoretical results and the experimental data for the Al2O3-in-water nanofluids.

1.
Masuda
,
H.
,
Ebata
,
A.
,
Teramae
,
K.
, and
Hishinuma
,
N.
, 1993, “
Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles (Dispersion of γ-Al2O3, SiO2 and TiO2 Ultra-Fine Particles)
,”
Netsu Bussei
0913-946X,
4
, pp.
227
233
.
2.
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.
0003-6951,
78
, pp.
718
720
.
3.
Das
,
S. K.
,
Putra
,
N.
,
Thiesen
,
P.
, and
Roetzel
,
W.
, 2003, “
Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
567
574
.
4.
Patel
,
H. E.
,
Das
,
S. K.
,
Sundararajan
,
T.
,
Sreekumaran Nair
,
A.
,
George
,
B.
, and
Pradeep
,
T.
, 2003, “
Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects
,”
Appl. Phys. Lett.
0003-6951,
83
, pp.
2931
2933
.
5.
Chon
,
C. H. K.
,
Khim
,
K. D.
,
Lee
,
S. P.
, and
Choi
,
S. U. S.
, 2005, “
Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement
,”
Appl. Phys. Lett.
0003-6951,
87
, p.
153107
.
6.
Yang
,
B.
, and
Han
,
Z. H.
, 2006, “
Thermal Conductivity Enhancement in Water-in-FC72 Nanoemulsion Fluids
,”
Appl. Phys. Lett.
0003-6951,
88
, p.
261914
;
also selected for the July 11, 2006 issue of the Virtual Journal of Nanoscale Science and Technology, http://www.vjnano.org.http://www.vjnano.org.
7.
Yang
,
B.
, and
Han
,
Z. H.
, 2006, “
Temperature-Dependent Thermal Conductivity of Nanorods-Based Nanofluids
,”
Appl. Phys. Lett.
0003-6951,
89
, p.
083111
;
also selected for the September 4, 2006 issue of the Virtual Journal of Nanoscale Science and Technology, http://www.vjnano.orghttp://www.vjnano.org.
8.
Han
,
Z. H.
,
Yang
,
B.
,
Kim
,
S. H.
, and
Zachariah
,
M. R.
, 2007, “
Application of Hybrid Sphere/Carbon Nanotube Particles in Nanofluids
,”
Nanotechnology
0957-4484,
18
, p.
105701
.
9.
Buongiorno
,
J.
, 2006, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
240
250
.
10.
Vadasz
,
P.
, 2006, “
Heat Conduction in Nanofluid Suspensions
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
465
477
.
11.
Maxwell
,
J. C.
, 1904,
A Treatise on Electricity and Magnetism
,
2nd ed.
,
Oxford University Press
,
Cambridge, UK
.
12.
Nan
,
C. W.
,
Birringer
,
R.
,
Clarke
,
D. R.
, and
Gleiter
,
H.
, 1997, “
Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,”
J. Appl. Phys.
0021-8979,
81
, pp.
6692
6699
.
13.
Keblinski
,
P.
,
Phillpot
,
S. R.
,
Choi
,
S. U. S.
, and
Eastman
,
J. A.
, 2002, “
Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluids)
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
855
863
.
14.
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.
0031-9007,
93
, p.
144301
.
15.
Prasher
,
R.
,
Bhattacharya
,
P.
, and
Phelan
,
P. E.
, 2005, “
Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids)
,”
Phys. Rev. Lett.
0031-9007,
94
, p.
025901
.
16.
Koo
,
J.
, and
Kleinstreuer
,
C.
, 2004, “
A New Thermal Conductivity Model for Nanofluids
,”
J. Nanopart. Res.
1388-0764,
6
, pp.
577
588
.
17.
Bastea
,
S.
, 2005, “
Comment on ‘Model for Heat Conduction in Nanofluids’
,”
Phys. Rev. Lett.
0031-9007,
95
, p.
019401
.
18.
Keblinski
,
P.
, and
Cahill
,
D. G.
, 2005, “
Comment on ‘Model for Heat Conduction in Nanofluids’
,”
Phys. Rev. Lett.
0031-9007,
95
, p.
209401
.
19.
Einstein
,
A.
, 1956,
Investigations on the Theory of the Brownian Movement
,
Dover
,
New York
.
20.
Wilde
,
R. E.
, and
Singh
,
S.
, 1998,
Statistical Mechanics: Fundamentals and Modern Applications
,
Wiley
,
New York
.
21.
Panton
,
R. L.
, 2005, Incompressible Flow,
3rd ed.
,
Wiley
,
New York
.
22.
Bloch
,
E.
, 1930,
The Kinetic Theory of Gases
,
2nd ed.
,
Methuen
,
London
.
23.
Hirschfelder
,
J. O.
,
Curtiss
,
C. F.
, and
Bird
,
R. B.
, 1964,
Molecular Theory of Gases and Liquids
,
Wiley
,
New York
.
24.
Alder
,
B. J.
, and
Wainwright
,
T. E.
, 1970, “
Decay of the Velocity Autocorrelation Function
,”
Phys. Rev. A
1050-2947,
1
, pp.
18
21
.
25.
Paul
,
G. L.
, and
Pusey
,
P. N.
, 1981, “
Observation of a Long-Time Tail in Brownian-Motion
,”
J. Phys. A
0305-4470,
14
, pp.
3301
3327
.
26.
Hauge
,
E. H.
, and
Marin-Lof
,
A.
, 1973, “
Fluctuating Hydrodynamics and Brownian Motion
,”
J. Stat. Phys.
0022-4715,
7
, pp.
259
281
.
27.
Hinch
,
E. J.
, 1975, “
Application of the Langevin Equation to Fluid Suspensions
,”
J. Fluid Mech.
0022-1120,
72
, pp.
499
511
.
You do not currently have access to this content.