The addition of a small amount of nanoparticles in heat transfer fluids results in the new thermal phenomena of nanofluids (nanoparticle-fluid suspensions) reported in many investigations. However, traditional conductivity theories such as the Maxwell or other macroscale approaches cannot explain the thermal behavior of nanofluids. Recently, Jang and Choi proposed and modeled for the first time the Brownian-motion-induced nanoconvection as a key nanoscale mechanism governing the thermal behavior of nanofluids, but did not clearly explain this and other new concepts used in the model. This paper explains in detail the new concepts and simplifying assumptions and reports the effects of various parameters such as the ratio of the thermal conductivity of nanoparticles to that of a base fluid, volume fraction, nanoparticle size, and temperature on the effective thermal conductivity of nanofluids. Comparison of model predictions with published experimental data shows good agreement for nanofluids containing oxide, metallic, and carbon nanotubes.

1.
Bar-Cohen
,
A.
, and
Jelinek
,
M.
, 1986, “
Optimum Arrays of Longitudinal, Rectangular Fins in Convective Heat Transfer
,”
Heat Transfer Eng.
0145-7632,
6
, pp.
596
601
.
2.
Knight
,
R. W.
,
Hall
,
D. J.
,
Gooding
,
J. S.
, and
Jaeger
,
R. C.
, 1992, “
Heat Sink Optimization With Application to Microchannels
,”
IEEE Trans. Compon., Hybrids, Manuf. Technol.
0148-6411,
15
, pp.
832
842
.
3.
Wirtz
,
R. A.
,
Chen
,
W.
, and
Zhou
,
R.
, 1994, “
Effect of Flow Bypass on the Performance of Longitudinal Fin Heat Sinks
,”
ASME J. Electron. Packag.
1043-7398,
116
, pp.
206
211
.
4.
Tuckerman
,
D. B.
, and
Pease
,
R. F. W.
, 1981, “
High-Performance Heat Sinking for VLSI
,”
IEEE Electron Device Lett.
0741-3106,
2
, pp.
126
129
.
5.
Min
,
J. Y.
,
Jang
,
S. P.
, and
Kim
,
S. J.
, 2004, “
Effect of Tip Clearance on the Cooling Performance of a Microchannel Heat Sink
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
2823
2327
.
6.
Jang
,
S. P.
,
Kim
,
S. J.
, and
Paik
,
K. W.
, 2003, “
Experimental Investigation of Thermal Characteristics for a Microchannel Heat Sink Subject to an Impinging Jet, Using a Micro-thermal Sensor Array
,”
Sens. Actuators, A
0924-4247,
A105
, pp.
211
224
.
7.
Lee
,
S.
,
Choi
,
S. U. S.
,
Li
,
S.
, and
Eastman
,
J. A.
, 1999, “
Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
280
289
.
8.
Xuan
,
Y.
, and
Li
,
Q.
, 2000, “
Heat Transfer Enhancement of Nanofluids
,”
Int. J. Heat Fluid Flow
0142-727X,
21
, pp.
58
64
.
9.
Eastman
,
J. A.
,
Choi
,
S. U. S.
,
Li
,
S.
,
Yu
,
W.
, and
Thompson
,
L. J.
, 2001, “
Anomalously Increased Effective Thermal Conductivity of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,”
Appl. Phys. Lett.
0003-6951,
78
, pp.
718
720
.
10.
Choi
,
S. U. S.
,
Zhang
,
Z. G.
,
Yu
,
W.
,
Lockwood
,
F. E.
, and
Grulke
,
E. A.
, 2001, “
Anomalous Thermal Conductivity Enhancement in Nanotube Suspensions
,”
Appl. Phys. Lett.
0003-6951,
79
, pp.
2252
2254
.
11.
Patel
,
H. E.
,
Das
,
S. K.
,
Sundararajan
,
T.
,
Nair
,
A. S.
,
George
,
B.
, and
Pradeep
,
T.
, 2003, “
Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Base Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects
,”
Appl. Phys. Lett.
0003-6951,
83
, pp.
2931
2933
.
12.
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
.
13.
Xie
,
H.
,
Lee
,
H.
,
Youn
,
W.
, and
Choi
,
M.
, 2003, “
Nanofluids Containing Multiwalled Carbon Nanotubes and Their Enhanced Thermal Conductivities
,”
J. Appl. Phys.
0021-8979,
94
, pp.
4967
4971
.
14.
Jang
,
S. P.
, and
Choi
,
S. U. S.
, 2004, “
Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids
,”
Appl. Phys. Lett.
0003-6951,
84
, pp.
4316
4318
.
15.
Chen
,
G.
, 1996, “
Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles
,”
ASME J. Heat Transfer
0022-1481,
118
, pp.
539
545
.
16.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
, 1962, “
Thermal Conductivity of Heterogeneous Two-component Systems
,”
Indust. & Eng. Chem.
,
1
, pp.
187
191
.
17.
Cheng
,
S. C.
, and
Vachon
,
R. I.
, 1969, “
The Prediction of the Thermal Conductivity of Two and Three Phase Solid Heterogeneous Mixtures
,”
Int. J. Heat Mass Transfer
0017-9310,
12
, pp.
249
264
.
18.
Jeffrey
,
D. J.
, 1973, “
Conduction Through a Random Suspension of Spheres
,”
Proc. R. Soc. London, Ser. A
1364-5021,
335
, pp.
355
367
.
19.
Maxwell
,
J. C.
, 1873,
Electricity and Magnetism
,
Clarendon
, Oxford, UK.
20.
Keblinski
,
P.
,
Phillpot
,
S. R.
,
Choi
,
S. U. S.
, and
Eastman
,
J. A.
, 2002, “
Mechanism of Heat Flow in Suspension of Nano-Sized Particles (Nanofluids)
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
855
863
.
21.
Yu
,
W.
, and
Choi
,
S. U. S.
, 2003, “
The Role of Interfacial Layers in the Enhancement Thermal Conductivity of Nanofluids: A Renovated Maxwell Model
,”
J. Nanopart. Res.
1388-0764,
5
, pp.
167
171
.
22.
Yu
,
C.-J.
,
Richter
,
A. G.
,
Datta
,
A.
,
Durbin
,
M. K.
, and
Dutta
,
P.
, 1999, “
Observation of Molecular Layering in Thin Liquid Films Using X-Ray Reflectivity
,”
Phys. Rev. Lett.
0031-9007,
82
, pp.
2326
2329
.
23.
Xuan
,
Y.
,
Li
,
Q.
, and
Hu
,
W.
, 2003, “
Aggregation Structure and Thermal Conductivity of Nanofluids
,”
AIChE J.
0001-1541,
49
, pp.
1038
1043
.
24.
Kumar
,
D. H.
,
Patel
,
H. E.
,
Rajeev Kumar
,
V. R.
,
Sundararajan
,
T.
,
Pradeep
,
T.
, and
Das
,
S. K.
, 2004, “
Model for Heat Conduction in Nanofluids
,”
Phys. Rev. Lett.
0031-9007,
93
, p.
144301
-1-
4
.
25.
Koo
,
J.
, and
Kleinstreuer
,
C.
, 2004, “
A New Thermal Conductivity Model for Nanofluids
,”
J. Nanopart. Res.
1388-0764,
6
, pp.
577
588
.
26.
Prasher
,
R. S.
,
Bhattacharya
,
P.
, and
Phelan
,
P. E.
, 2005, “
Thermal Conductivity of Nanoscale Colloidal Solution
,”
Phys. Rev. Lett.
0031-9007,
94
, pp.
025901
-1-4.
27.
Evans
,
W.
,
Fish
,
J.
, and
Keblinski
,
P.
, 2006, “
Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity
,”
Appl. Phys. Lett.
0003-6951,
88
,
093116
-1-
3
.
28.
Incropera
,
F. P.
, and
Dewitt
,
D. P.
, 1996,
Fundamentals of Heat and Mass Transfer
,
4th ed.
,
Wiley
, New York.
29.
Kittel
,
C.
, and
Kroemer
,
H.
, 1980,
Thermal Physics
,
2nd ed.
,
W.H. Freeman and Company
, San Francisco.
30.
Kapitza
,
P. L.
, 1941, “
The Study of Heat Transfer in Helium II
,”
J. Phys. (Moscow)
0368-3400,
4
, p.
181
-
210
.
31.
Huxtable
,
S. T.
,
et al.
, 2003, “
Interfacial Heat Flow in Carbon Nanotube Suspensions
,”
Nat. Mater.
1476-1122,
2
, pp.
731
734
.
32.
Einstein
,
A.
, 1956,
Investigation on the Theory of Brownian Movement
,
Dover
, New York.
33.
Min
,
J. Y.
,
Jang
,
S. P.
, and
Choi
,
S. U. S.
, “
Motion of Nanoparticles in Nanofluids under an Electric Field
,” in
Proceedings of IMECE 2005, 2005 ASME International Mechanical Engineering Congress and Exhibition
, Orlando, Florida, November 5–11, 2005, Paper No. IMECE2005-80139.
34.
Bejan
,
A.
, 1995,
Convective Heat Transfer
,
2nd ed.
, Chap. 2,
Wiley
, Hoboken, Chap. 2.
35.
Tomitika
,
S.
,
Aoi
,
T.
, and
Yosinabu
,
H.
, 1953, “
On the Force Acting on a Circular Cylinder Set Obliquely in a Uniform Stream at Lower Values of Reynolds Number
,”
Proc. R. Soc. London, Ser. A
1364-5021,
219
, pp.
233
244
.
36.
Masuda
,
H.
,
Ebata
,
A.
,
Teramae
,
K.
, and
Hishinuma
,
N.
, 1993, “
Alternation of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles
,”
Netsu Bussei
0913-946X,
4
, pp.
227
233
.
37.
Schlichting
,
H.
, 1979,
Boundary Layer Theory
,
7th ed.
,
McGraw-Hill
, New York.
38.
Geiger
,
G. H.
, and
Poirier
,
D. R.
, 1973,
Transport Phenomena in Metallurgy
,
Addision-Wesley
, Reading, PA.
39.
Chon
,
C. H.
,
Kihm
,
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
-1-
3
.
40.
Krishnamurthy
,
S.
,
Bhattacharya
,
P.
, and
Phelan
,
P. E.
, 2006, “
Enhanced Mass Transport in Nanofluids
,”
Nano Lett.
1530-6984,
6
, pp.
419
423
.
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