Experimental Investigation of Heat
Conduction Mechanisms in Nanofluids.
Clue on Clustering
J. W. Gao,†,‡R. T. Zheng,‡,§H. Ohtani,|D. S. Zhu,†and G. Chen*,‡
Key Laboratory of Enhanced Heat Transfer and Energy ConserVation, Ministry of
Education, School of Chemistry and Chemical Engineering, South China UniVersity of
Technology, Guangzhou, Guangdong 510641, People’s Republic of China, Department
of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts
AVenue, Cambridge, Massachusetts 02139, Department of Key Laboratory of Radiation
Beam Technology and Materials Modification of Ministry of Education, College of
Nuclear Science and Technology, Beijing Normal UniVersity, Beijing 100875, People’s
Republic of China, and Materials and Nanotechnology Department, Research and
AdVanced Engineering, Ford Motor Company, Dearborn, Michigan 48121
Received July 22, 2009; Revised Manuscript Received October 12, 2009
some experimental observations of their enhanced thermal conductivity beyond the effective medium theory. Although many mechanisms
such as Brownian motion, clustering, ballistic transport, and internanoparticle potential are speculated, experimental proof of any of the
mechanisms has been difficult. Here, we investigate the mechanisms experimentally by thermal conductivity measurements and structural
analysis for the same materials in both liquid and solid states. These studies strongly suggest that clustering holds the key to the thermal
conductivity enhancement of nanofluids.
Over the past decade, nanofluids, suspensions with solid
nanoparticles, have attracted increasing interest due to some
experimental observation of their enhanced thermal conduc-
tivity beyond the predictions of the effective medium theory
and their potential applications in energy technologies.1-5
Mechanisms of the thermal conductivity enhancement in
nanofluids remain unclear and are intensely debated. For
example, the microconvection models attribute the thermal
conductivity enhancement to the Brownian motion,6-9but
other estimations show that Brownian motion effect is
small.10,11Various clustering models have also been pro-
posed, including clustering with microconvection or cluster-
ing with conduction.12-16Ballistic transport model based on
the kinetic theory, and solid-layering around nanoparticles
has also been studied.12Despite that some of experimental
data can be fitted with the models, parameters used in many
cases are way out of range. For example, the kinetic theory
model requires nanoparticle mean free path to be in the order
of centimeters in liquid,17and opposite conclusions have been
drawn on the impact of Brownian motion on the thermal
conductivity enhancement.6-12The lack of understanding in
mechanisms also arises from disparate experimental results,
as different groups report vastly different experimental results
that are contradictory even when similar fluids and nano-
particles are used. As evidence, in a recent round-robin study
of several different nanofluids with 33 groups participating
worldwide, no extraordinary enhancement in thermal con-
ductivity beyond conventional effective medium theory was
observed at all.18A recent review19and its subsequent
comment20further shows that the debate on thermal con-
ductivity enhancement is not settled and new experiments
are needed to understand the mechanisms.
In this letter, we experimentally explored the mechanism
of thermal conductivity enhancement in nanofluids. Our
strategy is to investigate the thermal conductivity in both
the liquid and the solid states. In the solid state, the Brownian
motion is frozen out. We further control the particle
clustering formation through using different host materials.
Our experiments strongly suggest that clustering holds the
key for the thermal conductivity enhancement. When clusters
formed, thermal conductivity even in the solid state can
outperform the prediction of the homogeneous effective
* To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
†South China University of Technology.
‡Massachusetts Institute of Technology.
§Beijing Normal University.
|Ford Motor Company.
Vol. 9, No. 12
Published on Web 11/11/2009
2009 American Chemical Society
medium model. On the basis of the experimental observation,
a two-level effective medium model was developed to
explain the experimental data in both the liquid and the solid
state. Furthermore, the experiment points to the direction of
improving nanofluids thermal conductivity.
We used alumina nanoparticles and two different host
materials, hexadecane and hog fat. The alumina nanoparticles
and n-hexadecane (n-C16H34) used were purchased from
Sigma-Aldrich (99.5% purity). N-hexadecane (denoted as
hexadecane hereafter) is a linear alkane with the melting
temperature of 18 °C. Hog fat was extracted from hog meat
and purified at least three times by filter papers. Hog fat is
a fatty acid mixture consisting of saturated and unsaturated
fatty acids with different melting points,21so it has a
nonuniform melting point within the range of 25-30 °C.
The difference between hot fat and hexadecane is that one
is amorphous and the other is polycrystalline when they are
frozen. As we will show later, the morphologies of the Al2O3
nanoparticles in the solid states in the two hosts are very
different and consequently, the thermal conductivity behavior
is also. The nanofluids were prepared by a two-step method.
First, two droplets of stabilizer (Span-80, Fluka) were fully
mixed with 30 mL of the base fluid (e.g., hog fat or
hexadecane). We have measured the thermal conductivity
of hexadecane with different weight fraction of Span-80. At
3 wt %, the thermal conductivity is reduced only 0.9%. Two
droplets in 30 mL of base fluids (the fraction is less 0.1%)
have no effect on the base fluid thermal conductivity, as
confirmed by our measurement and in agreement with
literature.22Second, alumina nanoparticles were dispersed
into previous base fluids by high-energy ultrasound23to form
a stable suspension.
Thermal conductivity of the suspension with alumina
nanoparticles was measured using the transient hot wire
method developed by Nagasaka and Nagashima.24We have
used this method in the past,23including comparing it with
optical measurement method25and round-robin test.18Mea-
sured thermal conductivity values of pure water and hexa-
decane are within 1% of literature values. We also analyzed
further experimental uncertainties and determined that ran-
dom uncertainties of the experiment are within 0.013%, and
the systematic uncertainties (e.g., due to the hot wire length
inaccuracy) is 1.1%. For the same type of material, the
systematic uncertainty is equal since it is based on the same
wire. We carried out experiments during the heating up and
cooling down processes between 5-52 °C. A thermal bath
with 1 °C accuracy was used to control temperature and the
temperature range of the bath can be changed between 25-80
°C. The cooling process was done in the mixture of water
and ice. Thermal conductivity value for a given temperature
was the same within 0.2% during the heating and cooling
cycle. Average data of the cooling and heating is presented.
Figure 1 shows thermal conductivity enhancement, defined
as (knc- kb)/kb, where kncand kbare the thermal conductivity
of the nanocomposites and the base media (hexadecane and
hog fat), respectively, as a function of temperature along with
the predictions of the Maxwell-Garnet (MG) model based
on the spherical nanoparticles without considering interfacial
thermal resistance.26The thermal conductivity of the two
different media shows different trends in the solid and the
liquid states. For the hog fat, the thermal conductivity
increases slightly with the phase changing from the solid
state to the liquid state with a maximum difference of about
0.5% (in the percent thermal conductivity enhancement) from
the prediction of the MG model. On the contrary, the thermal
conductivity enhancement of the hexadecane-based com-
posites is much larger in the solid state compared to the liquid
state with a maximum difference of about 3.3% from the
predictions of the MG model. The same trend can also be
seen in Figure 2, which shows the thermal conductivity
enhancement as a function of the alumina volume fraction.
Hence, anomalous thermal conductivity enhancement beyond
the MG theory can be observed not only in the liquid state,
but also in the solid state. Clearly, in the solid state, Brownian
motion should not play a major role and the microconvection
mechanism can be excluded.
The different trends of hog fat and hexadecane-based
nanocomposites/nanofluids in the solid and the liquid states
can be explained by the microstructures of the nanoparticle
in their perspective states. Transmission electron microscope
(TEM) images of the nanoparticles are taken based on
samples drawn from both liquid and solid phases. Alumina
nanoparticle has a mean diameter of dp) 70 nm (Figure
3a) by dynamic light scattering method with a polydispersity
of 0.124. The ?-potential of the alumina in water with a pH
value of 7 was determined to be around 51 mV. In hog fat,
the appearance of the nanoparticle aggregation shows no
change before and after frozen as shown in Figure 3b,c due
to hog fat is amorphous in solid state. On the contrary,
Figure 1. Thermal conductivity enhancement as a function of
temperature for composites/nanofluids consisting of alumina in (a)
hog fat and (b) hexadecane. Dots are experimental points, and lines
are based on MG model assuming particles are uniformly distributed
in the host media.
Nano Lett., Vol. 9, No. 12, 20094129
alumina nanoparticles agglomerate in an oriented fashion
within the icelike hexadecane crystal structure upon freezing,
as shown in Figure 3d,e. In taking TEM images of the solid
state, a small hexadecane icicle is placed onto the TEM grid
and the image is taken at room temperature. Icicles should
be molten during the experiment. However, the TEM grids
retained to some degree the clustering configuration of the
nanoparticles in the solid-state. After remelting the solid-
state composites into the liquid state, the continuous clusters
break into the short clusters as shown in Figure 3f, and
thermal conductivity returns to the values very close to these
obtained before freezing as shown in Figure 4. The alumina
nanoparticles aggregate into two kinds of clusters in the
hexadecane crystals; one is a spherical cluster formed by
larger diameter nanoparticles and the other is a “backbone”
structure made of small diameter nanoparticles, forming rod-
type of clusters that play a vital role in the thermal
conductivity of the solid state. The mechanism of the
nanoparticles aggregates in ice molds was detailed in ref 27
previously. The nanoparticles segregate into the grain
boundaries of the ice crystals. The high aspect ratio backbone
of the chainlike aggregates has a higher thermal conductivity,
leading to a thermal conductivity enhancement larger than
the prediction based on the assumption of spherical nano-
particles homogeneously dispersion in the medium. Although
the formation of chainlike aggregation under a magnetic field
was reported28before, the chains formed are along the field
direction, while existing models are all on random three-
dimensional structures likely existing in real nanofluids. Our
experimental approach provides a fresh way to probe heat
conduction mechanisms in nanofluids.
The larger enhancement is observed in the solid state than
the liquid state in hexadecane due to clustering formation,
and an opposite but weaker trend observed in hog fat led
suggests that the effect of nanoparticle Brownian motion on
thermal conductivity enhancement is much less than the
effect of nanoparticle clustering. This is further supported
by the observation that there is no temperature dependence
in thermal conductivity enhancement at both solid and liquid
states for the nanofluids composed by alumina particles and
hog fat. Similarly, no temperature dependence was observed
for alumina in hexadecane in nanofluids in the liquid state.
We could not obtain more data points in the solid state for
hexadecane due to limitations of our experimental system.
The traditional effective medium theory (EMT) model used
for homogenization theories of well-dispersed composites
fails to predict the thermal conductivity in the solid-state.
Several clustering models have been developed in the past
for the liquid state. Prasher et al. first combined clustering
with Brownian motion13and then developed a three-level
clustering model. As shown by TEM images, the spherical
clusters are only a small part compared to the rode-type
clusters (about 1:10 ratio from analysis of more than 10 TEM
images). We evaluated the contribution of the larger spherical
clusters on effective thermal conductivity using the MG
model by assuming all the clusters within are spherical, and
confirmed that the thermal conductivity of nanocomposites/
nanofluids containing spherical clusters is similar to that of
the uniformly dispersed system, even in a extreme case where
all the nanoparticles belong to the spherical clusters. Hence,
spherical clusters cannot explain the experimental data. Our
analysis thus focused on the rod-type clusters. On the basis
of the TEM image, such clusters are not a single-particle
chain, but consist of several particles in the direction
perpendicular to the chain. We can estimate the thermal
conductivity of the rod using the Bruggeman model of
effective thermal conductivity,29which is particularly suited
to the composites with high concentration additives30
where kp, kb, and kc are the thermal conductivity of the
nanoparticle, the base medium and the cluster (or rod, in
this case), respectively, and φc_pdenotes the volume fraction
of the nanoparticle within the clusters.
Assuming the clusters as rods with effective thermal
conductivity calculated from eq 1, we can further calculate
the thermal conductivity of the solid or liquid nanocompos-
ites. We use model by Nan31for random oriented ellipsoidal
inclusions by approximating the rod into ellipsoids
where kncis the thermal conductivity of the solid or liquid
nanocomposite, φcis the volume fraction of the clusters in
the composite. The relationship among φc, φc_p, and φpare
φc) φp/φc_pdue to the particle number conservation, where
φpis volume fraction of nanoparticles in composites. In eq
Figure 2. Thermal conductivity enhancement as a function of
alumina volume fraction for composites/nanofluids consisting of
alumina in (a) hog fat and (b) hexadecane. Dots are experimental
points, and lines are based on MG model for particles uniformly
distributed in the host media.
kp- 2kc)+ (1 - φc_p)(
kb- 2kc)) 0 (1)
3 + φc(2?11(1 - L11) + ?33(1 - L33))
3 - φc(2?11L11+ ?33L33)
Nano Lett., Vol. 9, No. 12, 2009
2, L11) 0.5Q2/(Q2- 1) - 0.5Q cosh-1Q/(Q2- 1)1.5, L33
) 1 - L11, ?11) (kc11- kb)/(kb+ L11(kc11- kb)), and ?33)
(kc33- kb)/(kb+ L33(kc33- kb)), where Q ) L/R denotes
aspect ratio of rod-type clusters (L and R are rod length and
rod radius, respectively). kc11) kc/(1 + rL11kc/kb), and kc33
) kc/(1 + rL33kc/kb), where r ) (2 + 1/Q)RBdkb/dp(Q > 1),
and RBdis the thermal boundary resistance. We do not know
exact values of thermal boundary resistance between Al2O3
and liquids used. However, past experiments of liquid-solid
interfaces gave thermal boundary resistance values in the
range of 2 × 10-9m2·K/W and 2 × 10-8m2·K/W.32,33In
this work, the order of magnitude of 10-9m2·K/W was used.
We found that the thermal boundary resistance does not have
significant impact on the thermal conductivity of the effective
Figure 4 shows the predictions of the above model along
with the experimental value as a function of the volume
fraction of the nanoparticles for hexadecane based nano-
composites. As detailed in ref 27, clusters are formed by
the process of the solidification of the liquid, and the particle
density (φc_p) is dependent on the pressure of grain boundary.
Since our TEM image was taken at room temperature after
the hexadecane icicles melt, the volume fraction of nano-
particles in clusters in the solid state is hard to determine
exactly. According to the model prediction, the thermal
conductivity of the nanocomposites/nanofluids peaks when
the nanoparticle volume fraction within clusters reaches 0.48,
although the maximum packing density (φc_p) can be as large
as 0.74. This is because as more spheres are packed densely
to increase the cluster thermal conductivity, the number of
clusters decreases. We hence plotted in Figure 4 the effective
thermal conductivity at the particle packing density of 0.48
within the clusters. The lower bound shown in the figure is
predicted by the homogeneous MG model. Both the liquid
and the solid-state data are within these bounds. For the solid-
state case, we can fit the experimental results using a
nanoparticle volume fraction of 0.25 within the clusters and
a cluster length to diameter ratio of 5 based on the statistical
analysis of more than 10 TEM images. We should point out
that presently, large uncertainties exist in both the rod length
and the volume fraction, and these are not to be taken as
exact values. The thermal conductivity enhancement of the
composites in the liquid state at room temperature is only
slightly above the MG model. When the solid state composite
was remelted into the liquid state, the measured thermal
conductivity restores the initial value before freezing. The
clusters can still be observed as shown in Figure 3f, but it is
not continuous and broke into short clusters. We can explain
the experimental data on liquid by assuming a rod aspect
ratio about 2.
In conclusions, our results indicate that the Brownian
motion of nanoparticles is not the main cause of the thermal
conductivity enhancement. Rather, nanoparticle clustering
appears to be a key contributor. Our study has provided a
Figure 3. (a) Particles size distribution of alumina in hexadecane by the DLS method. (b) TEM image of alumina in hog fat suspension
before frozen, (c) alumina in hog fat composite after frozen, (d) alumina in hexadecane suspension before frozen, (e) alumina in hexadecane
after frozen, (f) alumina in hexadecane suspension after remelting. The scale bar of (f) is 100 nm, and the others are 500 nm.
Figure 4. Model analysis of thermal conductivity enhancement of
hexadecane based composites/nanofluids. Here, the upper bound
of the thermal conductivity enhancement is calculated with a particle
packing density around 0.48 within nanoparticle clusters; the lower
bound is predicted by the homogeneous MG model. The experi-
mental value is fitted using a volume fraction of 25% and a cluster
length to diameter ratio 5.
Nano Lett., Vol. 9, No. 12, 20094131
strategy for achieving nanofluid systems with high thermal
conductivity. One should look for nanoparticles with high
thermal conductivity and easy to form (nonspherical) cluster-
ing configurations, or nanoparticles with directional high
thermal conductivity values.
Acknowledgment. We would like to thank S. Shen, K.
Collins, Y. Zhang, A. Henry, X. Chen, D. Kraemer, and Q.
Hao for their helpful discussion during the course of this
work. This work is supported by Ford-MIT alliance and NSF
CBET-05-06830. J.W.G. and R.T Z. also gratefully acknowl-
edge partial financial support from China Scholarship Council
(1) Das, S. K.; Choi, S. U.; Yu, W.; Pradeep, T. Nanofluids: Science and
Technology; Wiley-InterScience: Hoboken, NJ, 2007.
(2) Lee, S.; Choi, S. U. S.; Li, S.; Eastman, J. A. ASME J. Heat Transfer
1999, 121, 280.
(3) Choi, S. U. S. ASME J. Heat Transfer 2009, 131, 033106.
(4) Penas, J. R. V.; de Zarate, J. M. O.; Khayet, M. J. Appl. Phys. 2008,
(5) Vladkov, M.; Barrat, J. L. Nano Lett. 2006, 6, 1224.
(6) Jang, S. P.; Choi, S. U. S. Appl. Phys. Lett. 2004, 84, 4316.
(7) Prasher, R.; Bhattacharya, P.; Phelan, P. E. Phys. ReV. Lett. 2005, 94,
(8) Krishnamurthy, S.; Lhattacharya, P.; Phelan, P. E.; Prasher, R. S. Nano
Lett. 2006, 6, 419.
(9) Yang, B. ASME J. Heat Transfer 2008, 130, 042408.
(10) Eapen, J.; Williams, W. C.; Buongiorno, J.; Hu, L. W.; Yip, S.;
Rusconi, R.; Piazza, R. Phys. ReV. Lett. 2007, 99, 095901.
(11) Evans, W.; Fish, J.; Keblinski, P. Appl. Phys. Lett. 2006, 88, 093116.
(12) Keblinski, P.; Phillpot, S. R.; Choi, S. U. S.; Eastman, J. A. Int. J. Heat
Mass Transfer 2002, 45, 855.
(13) Prasher, R.; Evans, W.; Meakin, P.; Fish, J.; Phelan, P.; Keblinski, P.
Appl. Phys. Lett. 2006, 89, 143119.
(14) Xuan, Y. M.; Li, Q.; Hu, W. F. AIChE J. 2003, 49, 1038.
(15) Gharagozloo, P. E.; Eaton, J. K.; Goodson, K. E. Appl. Phys. Lett.
2008, 93, 103110.
(16) Prasher, R.; Phelan, P. E.; Bhattacharya, P. Nano Lett. 2006, 6, 1529.
(17) Kumar, D. H.; Patel, H. E.; Kumar, V. R. R.; Sundararajan, T.; Pradeep,
T.; Das, S. K. Phys. ReV. Lett. 2004, 93, 144301.
(18) Buongiorno, J.; Venerus, D. J. Appl. Phys., in press; see also, the
International Nanofluid Properties Benchmark Exercise (INPBE) Web
site: http://mit.edu/nse/nanofluids/benchmark/index.html. Access date
February 1, 2009.
(19) Keblinski, P.; Prasher, R.; Eapen, J. J. Nanopart. Res. 2008, 10, 1089.
(20) Murshed, S. M. S. J. Nanopart. Res. 2009, 11, 511.
(21) Guille ´n, M.; Cabo, N. J. Am. Oil Chem. Soc. 1997, 74, 1281.
(22) Han, Z. H.; Yang, B.; Kim, S. H.; Zachariah, M. R. Nanotechnology
2007, 18, 105701.
(23) Garg, J.; Poudel, B.; Chiesa, M.; Gordon, J. B.; Ma, J. J.; Wang, J. B.;
Ren, Z. F.; Kang, Y. T.; Ohtani, H.; Nanda, J.; McKinley, G. H.;
Chen, G. J. Appl. Phys. 2008, 103, 074301.
(24) Nagasaka, Y.; Nagashima, A. J. Phys. E 1881, 14, 1435.
(25) Schmidt, A. J.; Chiesa, M.; Torchinsky, D. H.; Johnson, J. A.; Nelson,
K. A.; Chen, G. J. Appl. Phys. 2008, 103, 083529.
(26) Maxwell, C. J. Electricity and Magnetism; Oxford: Clarendon, 1873.
(27) Deville, S.; Saiz, E.; Nalla, R. K.; Tomsia, A. P. Science 2006, 311,
(28) Philip, J.; Shima, P. D.; Raj, B. Appl. Phys. Lett. 2007, 91, 203108.
(29) Bruggeman, D. A. G. Ann. Phys. (Leipzig) 1935, 24, 636.
(30) Wang, B. X.; Zhou, L. P.; Peng, X. F. Int. J. Heat Mass Transfer
2003, 46, 2665.
(31) Nan, C. W.; Birringer, R.; Clarke, D. R.; Gleiter, H. J. Appl. Phys.
1997, 81, 6692.
(32) Ge, Z. B.; Cahill, D. G.; Braun, P. V. Phys. ReV. Lett. 2006, 96,
(33) Schmidt, A. J.; Alper, J. D.; Chiesa, M.; Chen, G.; Das, S. K.; Hamad-
Schifferli, K. J. Phys. Chem. C 2008, 112, 13320.
Nano Lett., Vol. 9, No. 12, 2009