thermal conductance of nanofluids-is the controversy over
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8/13/2019 Thermal Conductance of Nanofluids-Is the Controversy Over
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F O C U S O N N A N O F L U ID S
Thermal conductance of nanofluids: is the controversy over?
Pawel Keblinski Ravi Prasher Jacob Eapen
Received: 16 December 2007 / Accepted: 22 December 2007 / Published online: 18 January 2008
Springer Science+Business Media B.V. 2008
Abstract Over the last decade nanofluids (colloidal
suspensions of solid nanoparticles) sparked excite-
ment as well as controversy. In particular, a number
of researches reported dramatic increases of thermal
conductivity with small nanoparticle loading, while
others showed moderate increases consistent with the
effective medium theories on well-dispersed conduc-
tive spheres. Accordingly, the mechanism of thermal
conductivity enhancement is a hotly debated topic.
We present a critical analysis of the experimental
data in terms of the potential mechanisms and showthat, by accounting for linear particle aggregation, the
well established effective medium theories for com-
posite materials are capable of explaining the vast
majority of the reported data without resorting to
novel mechanisms such as Brownian motion induced
nanoconvection, liquid layering at the interface, or
near-field radiation. However, particle aggregation
required to significantly enhance thermal conductiv-
ity, also increases fluid viscosity rendering the benefit
of nanofluids to flow based cooling applications
questionable.
Keywords Nanofluids AggregationThermal conductivity Theory Nanoparticles Heat transfer
Introduction
Cooling is one of the most important technical
challenges facing numerous diverse industries, includ-
ing microelectronics, transportation, solid-state
lighting, and manufacturing. Developments driving
the increased thermal loads that require advances in
cooling include faster speeds (in the multi-GHz range)
and smaller features (to\100 nm) for microelectronic
devices, higher power engines, and brighter optical
devices. The conventional method for increasing heat
dissipation is to increase the area available for
exchanging heat with a heat transfer fluid but thisapproach requires an undesirable increase in the size of
thermal management system. There is therefore an
urgent need for new and innovative coolants with
improved performance. About a decade ago a novel
concept of nanofluidsheat transfer fluids contain-
ing suspensions of nanoparticleshas been proposed
as a means of meeting these challenges (Choi1995).
Nanofluids are solid-liquid composite materials
consisting of solid nanoparticles or nanofibers, with
P. Keblinski (&)
Materials Science and Engineering Department,
Rensselaer Polytechnic Institute, Troy, NY 12180, USA
e-mail: keblip@rpi.edu
R. Prasher
Intel Corporation, 5000 W. Chandler Blvd, Chandler, AZ
85226, USA
J. Eapen
Theoretical Division (T-12), Los Alamos National
Laboratory, Los Alamos, NM 87545, USA
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sizes typically on the order of 1100 nm, suspended
in a liquid. Nanofluids have attracted great interest
recently due to reports of greatly enhanced thermal
properties at low volume fractions. For example, a
small amount (less than 1% volume fraction) of
copper nanoparticles and carbon nanotubes dispersed
in ethylene glycol and oil, respectively, was reportedto increase the inherently poor thermal conductivity
of the liquid by 40 and 150%, respectively (Choi
et al. 2001; Eastman et al. 2001). Conventional
suspensions of well-dispersed particles require high
concentrations ([10%) of particles to achieve such
enhancement; problems of rheology and stability,
which are amplified at high concentrations, preclude
the widespread use of conventional slurries as heat
transfer fluids. In several cases, the observed
enhancement in thermal conductivity of nanofluids
is orders-of-magnitude larger than predicted by well-established theories of dispersed particles (Chopkar
et al. 2006; Chopkar et al. 2007; Hong et al. 2006;
Kang et al. 2006; Murshed et al. 2005, 2006; Zhu
et al. 2006; Zhu et al. 2007).
The purported inadequacy of the effective medium
theories
The experimental observations described above led tonumerous statements about inability of well-estab-
lished effective medium theories for explaining the
thermal conductivity enhancements of nanofluids. In
particular, in the limit of low particle volume
fraction,/, and the particle conductivity, KNP, being
much higher than the fluid conductivity, Kfluid, the
effective medium (Maxwell) theory for vanishing
interfacial thermal resistance predicts (Maxwell
1881; Nan et al. 1997)
KNF
Kfluid 1 3/ 1
Maxwells expression (the limiting case of which
is given by Eq. 1) also corresponds to the lower
bound of the well known Hashin and Shtrikman (H
S) bounds for thermal conductivity obtained under
the effective medium theory analysis (Hashin and
Shtrikman 1962) without any restriction on the
volume fraction. The HS bounds for a nanofluid
are given by:
Kfluid 1 3/KNP Kfluid
3Kfluid 1/KNPKfluid
KNF 131/KNP Kfluid
3KNP/KNP Kfluid
KNP
2
In the inequality given by Eq. 2, the lower
(Maxwell) bound physically corresponds to a set of
well-dispersed nanoparticles in a fluid matrix while
the upper limit corresponds to large pockets of fluid
separated by linked, chain-forming or clustered
nanoparticles. From the point of view of circuit
analysis, the lower HS limit lies closer to conductors
connected in a series mode, while the upper limit lies
closer to those in a parallel mode. The HS bounds do
not give a precise mechanism of thermal conductance
but sets the most restrictive limits based on the
knowledge of volume fraction alone. It is relatively
well known that a large number of experimental data
on solid composites, and to a lesser extent the data on
liquid mixtures, fall between the HS bounds (Eapen
et al. 2007c). An unbiased estimation (neither favor-
ing series nor parallel modes) predicts thermal
conductivity values that lie between the upper and
lower HS bounds (Landauer 1952).
Several experimental data show that the enhance-
ment in nanofluids are well-described by Eq. 1
(Keblinski et al. 2005; Putnam et al. 2006; Venerus
et al.2006; Zhang et al.2006a,b). For example at 1%
particle volume fraction, the maximum relative
enhancement is 3%. However, those experimental
reports demonstrating much larger enhancements
deem the classical effective medium theories to be
inadequate, thereby giving credence to the so called
anomalous or unusual thermal conductivity
enhancements. This judgment is solely reached by
comparing the experimental results with the theories
that assume good dispersions of spherical nanoparti-
cles. The evidences from Scanning Electron
Microscopy (SEM) however, point to the existence
of partial clustering and chain-like linear aggregation
(Kim et al. 2007; Murshed et al. 2005; Zhu et al. 2006;
Zhu et al. 2007). This demands a different effective
medium model for nanofluids wherein the effects of
clustering is explicitly taken into account. The upper
HS bound in Eq.2indicates that a linear aggregation
will increase the thermal conductivity beyond the limit
of well-dispersed nanofluids. Viscosity data on nano-
fluids has also shown anomalous increase as compared
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to the Einstein model for well-dispersed particles
(Prasher et al. 2006c). Large increase in the viscosity is
another indication of aggregation in the nanofluids. It
was also recognized that elongated nanoparticles
would lead to larger predictions of the conductivity
enhancements (Keblinski et al.2002), however, in the
most spectacular cases, the required nanoparticleaspect ratio was of the order of 100 or more, which is
rather unrealistic for individual nanoparticles, unless
there is linear particle agglomeration. Interestingly, in
case of carbon nanotube suspension, the effective
medium theory accounting for very high aspect ratio of
nanotubes (Nan et al.1997), predicts thermal conduc-
tivity enhancements which are in fact well above the
reported values. This was attributed to a significant
interfacial resistance to heat flow between carbon
nanotubes and the fluid (Huxtable et al.2003). On the
basis of these observations, there is no sufficient reasonto presume that there is a failure of effective medium
theories in accounting for the thermal conductivity of
nanofluids.
Other interesting observations in this rapidly evolv-
ing field include a temperature dependence on the
thermal conductivity (Das et al. 2003; Patel et al.
2003) and a strong size dependency (Hong et al. 2006;
Kim et al. 2007). There appears to be a fundamental
difference between the conductance behavior of solid
composites and nanofluids where smaller particle sizes
favor an increased conductivity for the latter, and thereverse for the former. As with the nanotubes suspen-
sions, the solid composite behavior is easily explained
through the interfacial thermal resistance for nanome-
ter sized filler particles (Every et al.1992; Nan et al.
1997) while its role in nanofluids is less than transpar-
ent. A few experiments (Hong et al. 2005; Zhu et al.
2006) also have also shown that the nanofluid thermal
conductivity is not correlated in a simple manner to
that of the nanoparticle as predicted by the effective
medium theories, and a saturation behavior at higher
volume fractions which is qualitatively different fromthat in solid composites (Eapen et al.2007c).
New physics
Brownian motion
Motivated by the unusual thermal conductivity
enhancements, a number of researchers promoted
the concept of Brownian motion induced micro or
nanoconvection (Jang and Choi 2004; Koo and
Kleinstreuer2004; Prasher et al.2005). They argued
in different forms that each Brownian particle
generates a long-ranged velocity field in the sur-
rounding fluid, akin to that present around a particle
moving with a constant velocity, which decaysapproximately as the inverse of the distance from
the particle center. The ability of large volumes of
fluid dragged by the nanoparticles to carry substantial
amount of heat was credited for the large thermal
conductivity increases of nanofluids.
A key weakness of this argument is that the
thermal diffusivity, DT, of base fluid, that measures
the rate of the heat flow via thermal conduction is
several orders of magnitude larger than nanoparticle
diffusivity, DNP, that measures the rate of mass
motion due to nanoparticle diffusion, and thus themagnitude of possible nanoconvection effects is
negligible (Evans et al. 2006). These estimates were
supported by the results of molecular dynamics
simulations (Evans et al. 2006; Vladkov and Barrat
2006), and by the results of experimental measure-
ments on well-dispersed spherical nanoparticle fluids
(Putnam et al. 2006; Rusconi et al. 2006; Venerus
et al. 2006; Zhang et al. 2006a, b) all showing
thermal conductivity enhancements (positive and
negative) that agree with the lower HS (Maxwell)
limit. In a direct experimental investigation, thedensity effects associated with the postulated nano-
convection (Prasher et al. 2005) were experimentally
tested with lighter silica and Teflon particles, and
were shown to be incorrect (Eapen et al. 2007d). The
nanoconvection velocities were further shown to be
of the order of thermophoretic velocities, which for
most nanofluids were insignificant [as low as
(10-9 m/s)]. Even for sub-nanometer clusters, as
evidenced from molecular dynamics simulations, the
thermophoretic velocities are exceedingly small
which effectively preclude a discernible contributionto the nanofluid thermal conductivity from any
conceivable nanoconvection mechanism (Eapen et al.
2007c).
Interfacial liquid layer
Considering that the molecular structure of liquid at
the solid interface is more ordered, possibilities of
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observed in solid composites and even liquid mix-
tures (Eapen et al. 2007c). Second, as the filler
particle size approaches the nanometer scales, theeffective thermal conductivity of solid composites
decreases due to increasing interfacial resistance
(Eapen et al. 2007c; Every et al. 1992; Nan et al.
1997). A large body of experimental data in Fig. 1
however, suggests that the interfacial resistance does
not play a significant role in nanofluids even when the
particle sizes are in tens of nanometers. This is easily
verified for well-dispersed nanoparticles where the
thermal conductivity largely follows the classical
Maxwell relationship. The fact that solid composites
are different from nanofluids in this respect is likely
associated with the possibility of having imperfectsolidsolid interfaces, including effects of physical
delamination and voids that can be present near or at
the interface. This can substantially increase the
interface resistance as compared with that originating
solely from acoustic mismatch between the filler and
the matrix. By contrast fluids form void free contacts
with solids. Another important point is that the
Kapitza length which is given by Rbkm, where Rb is
the interface resistance and km is the thermal
21E-3
0.01
0.1
1
10
100
1E-3
0.01
0.1
1
10
100
Water-Al2O3
Enhancementin
(%)
Enhancement
in
(%)
Enhancementin
(%)
Enhancementin
(%)
Enhancementin
(%)
Enhancement(%
)
(Al2O3) %
Eapen et al2007cEastman et al1997
Masuda et al 1993
Das et al 2003Wen et al 2004b
1
10
Water-ZrO2
(ZrO2)%
Eapenet al 2007c
Zhanget al 2006b
1
10
Eapen et al 2007 c
Kang et al 2006
(SiO2) %
Water-SiO2
Eastman et al(1997)Zhu et al(2007)
LiandPeterson(2006)
Lee et al(1999)
Das et al(2003)
(CuO)%
Water-CuO
0.1
1
10
100
Murshed et al 2005Wen and Ding 2006
Zhang et al 2006b
(TiO2) %
Water-TiO2
1
10
Water-Fe3O4(Zhu et al2006)
(Fe3O4)%
0 1 4 53
20 1 4 53
20 1 4 53
20 1 4 653
40 2 8 106
80 4 16 2012102 6 1814
Fig. 1 Lower (dashed) and
upper (solid) Hashin and
Shtrikman (HS) bounds for
nanofluid thermal
conductivity. The thermal
conductivity data are taken
from (Choi et al. 2001; Das
et al. 2003; Eapen et al.2007c; Eastman et al. 1997;
Eastman et al.2001; Hwang
et al. 2007; Kang et al.
2006; Lee et al. 1999; Li
and Peterson2006; Masuda
et al. 1993; Murshed et al.
2005,2006; Patel et al.
2003; Shaikh et al. 2007;
Wen and Ding2004a; Wen
and Ding2004b,2006;
Zhang et al. 2006a,b; Zhu
et al.2006; Zhu et al.2007)
while the properties are
given in (Eapen et al.2007c)
J Nanopart Res (2008) 10:10891097 1093
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conductivity of the matrix is higher in solids than
liquid due to higher value of km. Higher value of
Kapitza length means higher impact of the interfaceresistance.
Increase in the relative thermal conductivity of the
nanofluids with temperature (Das et al. 2003) is
another anomalous behavior that cannot be explained
based on the assumptions of well-dispersed particles.
Similarly increase in the thermal conductivity with
decreasing particle size cannot be explained if the
particles are well dispersed. The probability of
aggregation increases with increasing temperature
and decreasing particle size (Prasher et al. 2006b).
Therefore the apparent contradictions between exper-
iment and theory, such as particle size effects, can beresolved by weighing in the ability of nanoparticles
into forming linear clusters. Furthermore, the tem-
perature dependence is also not as strong as it was
earlier believed with the recent experiments showing
a similar variation for both nanofluids and the base
fluid (Eapen et al. 2007c; Zhang et al. 2006b). This
implies that the mechanism for increase in the
thermal conductivity of water (presumably from the
hydrogen bonded structures) is partly responsible for
0.5 0.60.40.30.20.10.00.01
0.1
1
10
100
1000
With Acid
OldEnhancem
entin
(%)
(Cu) %
EG-Cu (Eastman et al, 2001)
0.004 0.006 0.008 0.010 0.0121E-3
0.01
0.1
1
10
(Au) %
Toulene-Au (Patel et al, 2003)
5
1
10
100
1000
(Al) %
EG-Al (Mursheed et al 2006)
0.0 0.2 0.4 0.6 0.8 1.01E-5
1E-4
1E-3
0.01
0.1
110
100
1000
10000
Shaik et al(2007)
Zhang et al(2006)
Choi et al(2001)
Hwang et al(2007)
Wen and Ding(2007)
Enhancementin
(%)
Enhancementin
(%)
Enhanceme
nt(%)
(Nanotubes)%
Oil/Water-Carbon Nanotubes
1
10
100
1000
10000
Enhancement(%)
(Al) %
Engine Oil-Al (Mursheed et al2006)
0.00 0.25 0.50 1.00 1.25 1.500.750.1
1
10
100
1000
Enhancement(%)
(Diamond) %
EG-Diamond (Kang et al 2006)
1 2 3 4 51 2 3 4
Fig. 1 Continued
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the thermal conductivity increase in nanofluids as
well. Conversely, it is reasonable to expect a decrease
in the nanofluid thermal conductivity for a base fluid
that has a negative change in conductivity with
increasing temperature.
It remains a challenge to accurately identify and
manipulate the cluster configuration to modify thethermal transport properties of a nanofluid. The two
characterization techniques, DLS and SEM have
limitations in assessing the structure of nanoparticles.
DLS measurements are limited to dilute suspensions
(/\ 1%) for most nanofluids while SEM imaging
can be performed only after drying the base fluid.
While the science of making well-dispersed colloids
have reached a fair amount of maturity, the attempts
at generating targeted nanoparticle configurations is
still in an evolving phase.
Conclusions
Our considerations strongly suggest that the apparent
disagreement between the experiment and the effec-
tive medium theory is simply an artifact of focusing
on a particular effective medium theory, namely,
Maxwells theory of well-dispersed particles. Remov-
ing this constraint and allowing chain-forming
morphologies for nanoparticles, we show that the
effective medium theories are capable of predictingthermal conductivity enhancements well beyond the
Maxwell prediction. Indeed, all the published data on
nanofluids, except for a couple of sets, lies between
the well-known Hashin and Shtrikman (HS) effec-
tive medium bounds. Thus, we provide a strong
evidence to show that the thermal conductance
behavior of nanofluids, to a large extent, is no
different from that in binary solid composites or
liquid mixtures (Eapen et al. 2007c).
The fact that significant aggregation is required to
obtain substantial increases in thermal transport hasan important consequence on the potential applica-
tion of such fluids in flow based cooling, which is the
most important benefit from the technological point
of view. It is well know that aggregation into sparse
but large clusters increase fluid viscosity. Such
increases become very dramatic when the aggregates
start to touch each other, which can occur at very low
volume fraction, as low as 0.2% (Kwak and Kim
2005). Therefore, the same aggregate structures that
are most beneficial to the thermal transport are also
the most detrimental to the fluid flow characteristics.
The future research, therefore, should address the
issue of optimization of nanofluid structure with the
best combination of thermal conductivity and
viscosity.
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