Instability of natural convection in nanofluids is investigated in this work. As a result of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be much lower, by one to two orders of magnitude, as compared to that for regular fluids. The highly promoted turbulence, in the presence of nanoparticles for as little as 1% in volume fraction, significantly enhances heat transfer in nanofluids, which may be much more pronounced than the enhancement of the effective thermal conductivity alone. Seven dominating groups are extracted from the nondimensional analysis. By extending the method of eigenfunction expansions in conjunction with the method of weighted residuals, closed-form solutions are derived for the Rayleigh number to justify such remarkable change by the nanoparticles at the onset of instability.

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.
0003-6951,
78
, pp.
718
720
.
2.
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
.
3.
Xuan
,
Y.
, and
Li
,
Q.
, 2000, “
Heat Transfer Enhancement of Nanofluids
,”
Int. J. Heat Mass Transfer
0017-9310,
21
, pp.
58
64
.
4.
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
.
5.
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
.
6.
Pak
,
B. C.
, and
Cho
,
Y.
, 1998, “
Hydrodynamics and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles
,”
Exp. Heat Transfer
0891-6152,
11
, pp.
151
170
.
7.
Xuan
,
Y.
, and
Li
,
Q.
, 2003, “
Investigation of Convective Heat Transfer and Flow Features of Nanofluids
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
151
155
.
8.
Xuan
,
Y.
, and
Roetzel
,
W.
, 2000, “
Conceptions for Heat Transfer Correlation of Nanofluids
,”
Int. J. Heat Mass Transfer
0017-9310,
43
, pp.
3701
3707
.
9.
Maïga
,
S.
,
Nguyen
,
C. T.
,
Galanis
,
N.
, and
Roy
,
G.
, 2004, “
Heat Transfer Behaviors of Nanofluids Under in a Uniformly Heated Tube
,”
Superlattices Microstruct.
0749-6036,
35
, pp.
543
557
.
10.
Buongiorno
,
J.
, 2006, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
240
250
.
11.
Yu
,
W.
, and
Choi
,
S. U. S.
, 2003, “
The Role of Interfacial Layers in the Enhanced Thermal Conductivity: A Renovated Maxwell Model
,”
J. Nanopart. Res.
1388-0764,
5
, pp.
167
171
.
12.
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
(
21
), pp.
4316
4318
.
13.
Kumar
,
D. H.
,
Patel
,
H. E.
,
Rajeev Kumar
,
V. R.
,
Sundararajan
,
J.
,
Pradeep
,
T.
, and
Das
,
S. K.
, 2004, “
Model for Heat Conduction in Nanofluids
,”
Phys. Rev. Lett.
0031-9007,
93
, p.
144301
.
14.
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
.
15.
Chen
,
G.
, 2001, “
Ballistic-Diffusive Heat-Conduction Equation
,”
Phys. Rev. Lett.
0031-9007,
86
(
11
), pp.
2297
2300
.
16.
Vadasz
,
P.
, 2006, “
Heat Conduction in Nanofluid Suspensions
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
465
477
.
17.
Ma
,
H. B.
,
Wilson
,
C.
,
Yu
,
Q.
,
Choi
,
U. S.
, and
Tirumala
,
M.
, 2006, “
An Experimental Investigation of Heat Transport Capability in a Nanofluid Oscillating Heat Pipe
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
1213
1216
.
18.
McNab
,
G. S.
, and
Meisen
,
A.
, 1973, “
Thermophoresis in Liquids
,”
J. Colloid Interface Sci.
0021-9797,
44
(
2
), p.
339
.
19.
Jang
,
S. P.
, and
Choi
,
U. S. U.
, 2004, “
Free Convection in a Rectangular Cavity (Bénard Convection) With Nanofluids
,”
Proceedings of the 2004 IMECE
, Anaheim, CA, Nov. 13–20.
20.
Incropera
,
F. P.
,
Dewitt
,
D. P.
,
Bergman
,
T. L.
, and
Lavine
,
A. S.
, 2007,
Introduction to Heat Transfer
,
5th ed.
,
Wiley
,
Hoboken, NJ
.
21.
Yih
,
C. S.
, 1977,
Fluid Mechanics: A Concise Introduction to the Theory
,
West River Press
,
Ann Arbor, MI
, Chap. 9.
22.
Chandrasekhar
,
S.
, 1961,
Hydrodynamic and Hydromagnetic Stability
,
Oxford University Press
,
Oxford
.
23.
Finlayson
,
B. A.
, 1972,
The Method of Weighted Residuals and Variational Principles
,
Academic
,
New York
.
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