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: [email protected]

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

1 3

J Nanopart Res (2008) 10:10891097

DOI 10.1007/s11051-007-9352-1


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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

1090 J Nanopart Res (2008) 10:10891097

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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

J Nanopart Res (2008) 10:10891097 1091

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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

1 3


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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

1094 J Nanopart Res (2008) 10:10891097

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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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