The development of advanced heat transfer fluids with enhanced thermal conductivity is essential to improve the effective heat transfer behavior of conventional coolants. Thermal conductivity enhancement has been reported for colloidal suspensions formulated with different nanoparticles. Reliable thermal conductivity measurement requires that the suspension is stable against sedimentation during the measurement since particle sedimentation may effect the experimental results. The present study proposes a criterion to ensure that thermal conductivity data is independent of the particle sedimentation. A measuring device based on the transient hot-wire method is designed to allow vertical and horizontal thermal conductivity data collection. Our investigation shows that the thermal conductivity measurements in the horizontal and vertical configurations are almost identical when the colloidal suspension is stable while they differ for unstable systems

Chiesa, M.

Simonsen, A. J.

University of Queensland eSpace

16th Australasian Fluid Mechanics Conference
Crown Plaza, Gold Coast, Australia
2-7 December 2007
The Importance of Suspension Stability for the Hot-wire Measurements of Thermal
Conductivity of Colloidal Suspensions.
M. Chiesa1 A. J. Simonsen2
1Department of Mechanical Engineering
Massachussets Institute of Technology, Cambridge, Ma 02139-4307 USA
2Sintef Materials and Chemistry
SINTEF, Trondheim, 7491 Norway
Abstract
The development of advanced heat transfer fluids with enhanced
thermal conductivity is essential to improve the effective heat
transfer behavior of conventional coolants. Thermal conduc-
tivity enhancement has been reported for colloidal suspensions
formulated with different nanoparticles. Reliable thermal con-
ductivity measurement requires that the suspension is stable
against sedimentation during the measurement since particle
sedimentation may effect the experimental results. The present
study proposes a criterion to ensure that thermal conductivity
data is independent of the particle sedimentation. A measur-
ing device based on the transient hot-wire method is designed
to allow vertical and horizontal thermal conductivity data col-
lection. Our investigation shows that the thermal conductivity
measurements in the horizontal and vertical configurations are
almost identical when the colloidal suspension is stable while
they differ for unstable systems.
Introduction
Fluids such as air, water, ethylene glycol and mineral oils are
typically used in applications like power generation, chemical
production, automobiles, computing processes, air conditioning
and refrigeration. However their heat transfer capability is lim-
ited by their very low thermal conductivity. These fluids have
almost two orders of magnitude lower thermal conductivity
compared to metals, resulting in low heat removal efficiencies.
First attempts to improve the thermal conductivity involved dis-
persing micron-sized particles in these liquids. Ahuja and Liu
et al [1] studied the heat transfer augmentation and rheology of
slurries. One of the drawbacks associated with the use of slur-
ries is the abrasive action of the particles causing erosion of the
components. Secondly micron-sized particles tend to rapidly
fall out of the suspension due to their large mass and thus can
cause fouling of the components thereby clogging the flow path
and increasing the pressure drop. Decreasing the particle size
to the nanometer range offers the potential to overcome these
drawbacks. Masuda et al [5] first reported the thermal con-
ductivity and viscosity of liquids containing nanometer sized
particles. Choi [2] also investigated the heat transfer proper-
ties of such colloidal suspensions and coined the term ”nanoflu-
ids”. In addition to overcoming the drawbacks associated with
the use of micron-sized suspensions, nanofluids have often ex-
hibited thermal conductivity enhancement substantially higher
than predicted by the Maxwell-Garnett effective medium the-
ory [4]. Over the past decade, a significant amount of data has
been gathered on the thermal conductivity of nanofluids. Typ-
ical materials used for nanoparticles include metals like cop-
per, silver and gold, metal oxides like alumina, titania and iron
oxide. Carbon nanotubes have also been used to enhance the
thermal conductivity of liquids. Experimental data on the ther-
mal conductivity of nanofluids varies widely and mechanisms
responsible for the thermal conductivity enhancement are un-
der debate, as summarized in recent reviews. There is clearly
a need to resolve the differences and confirm the repeatability
of data obtained. This can be achieved by reporting the ex-
act components of the nanofluid tested like surfactants, particle
material, base fluid, method of synthesis of nanoparticles, and
any possible contamination with other agents. Also the data ob-
tained by different groups need to be verified for repeatability.
Reaching a consensus in regard with the experimental data is
critically important for an accurate physical model to be devel-
oped to explain the anomalous enhancement. Recently, Liu et
al. [3] reported a maximum increase in thermal conductivity of
water of about 23.8% with a volume fraction of 0.1 vol% cop-
per nanoparticles. The reported thermal conductivity increase
was strongly dependent on the time after sonication after which
the measurements were carried out. The thermal conductivity
enhancement decayed to nearly zero after about 10 minutes of
sonication. It was not clear if the measured enhancement was
due to the instability of the nanofluid. In the present study, a
measuring apparatus based on the transient hot-wire method
has been developed. The apparatus is designed to allow mea-
surements in different configurations rotated with respect to a
vertical base configuration. Horizontal and vertical measure-
ments of the thermal conductivity of different systems compris-
ing various colloidal suspensions and their base fluids are car-
ried out. The investigation shows that the thermal conductivity
measurements in the horizontal and vertical configurations is al-
most identical when the colloidal suspension is stable. On the
other hand they differ strongly when the suspension is not sta-
ble. A stability criterion for the colloidal suspension based on
the measurements obtained from two different configurations is
proposed. Such a stability criterion guarantes that the measured
is not effected by particle sedimentation.
Formulation and Thermal Conductivity Measurement of Col-
loidal Suspensions
Formulation of Colloidal Suspensions
Colloidal suspensions were formulated by mixing Al2O3 alu-
mina nanoparticles with a mean particle size of 20nm with dif-
ferent base fluids: a high purity mineral oil made of a single
alkane hydrocarbon, 99.9% C10H22 also referred as decane, and
a highly branched isoparaffinic polyalphaolefin (PAO). The par-
ticles were stabilized by adding a constant amount of surbitan
monolurate 0.25 volume % to both base fluids before adding
the particles. The alumina nanopowder was evenly dispersed
in the base fluid through ultrasonic disruptor. Sonication was
performed in a ice bath to maintain the temperature of the sus-
pension constant. The thermal conductivity variation of the base
fluid due to addition of the surfactants is taken into account.
Thermal Conductivity Measurement set-up
Thermal conductivity measurements of the alumina suspensions
were carried out by means of the transient hot wire method
1154
developed by Nagasaka and Nagashima [6]. Fig. 1 illustrates
the set up used in the present work. It consists of a cylindrical
pipe of internal diameter 19mm and length 190mm. A thin plat-
inum wire (25 µm) coated with an insulation (1.5µm thick isonel
layer) is suspended between two copper electrodes in the center
of the pipe. The length of the wire is 150mm. The leakage of
electrical current from the electrodes to the surrounding fluid is
minimized in order to increase the reliability of our measure-
ments. This is especially important when the based nanofluids
is a conductive medium. The wire is immersed in the nanofluid
and a constant current is passed through it. The temperature rise
of the wire is measured as a function of time. The thermal con-
ductivity of the nanofluid can be calculated from the obtained
data by using the equation,
kn f =
Q
4piL dTd ln t
(1)
Here kn f is the thermal conductivity of the nanofluid, Q is the
total power dissipated in the wire, L is the length of the wire, T
is the wire temperature and t is the time. The constant current
used in the measurement served two purposes, one to act as a
heat source and second to enable the temperature measurement
of the wire. In order to measure the temperature rise, the hot
wire was made part of a Wheatstone bridge. Before starting the
experiment the bridge was balanced. During the experiment,
the change in wire temperature caused a change in wire resis-
tance leading to an imbalance in the bridge. The change in wire
resistance was measured by measuring the voltage imbalance in
the bridge. The temperature coefficient of resistance of the wire
was measured carefully by measuring the resistance as a func-
tion of the temperature of the wire. By knowing the tempera-
ture coefficient of resistance of the wire, the temperature rise
of the wire was calculated from the change in wire resistance
data. By measuring the slope of the temperature rise versus log
of time curve and using Eq. 1, the thermal conductivity of the
nanofluid was measured. Our measurement setup allows mea-
Figure 1: Thermal conductivity measuring apparatus designed
to allow measurements in different configurations rotated with
respect to a vertical base configuration.
surements to be carried out in different configurations rotated
with respect to a vertical base configuration. The experimen-
tal set up was calibrated by comparing the measured value of
thermal conductivity for ethylene glycol against the literature
value. The literature value was reproduced with an uncertainty
of 0.5%. Thermal conductivity measurements in the horizontal
and vertical configuration were performed for different base flu-
ids and for a couple of stable nanofluids systems. Fig. 2 shows
that the measurements in the two configurations provide very
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
 
 
kv
er
tic
al
n
f
khorizontaln f
Pure Decane
Al2O3 in Decane
Ethylene Glycol
H2O
Al2O3 in H2O
khorizontaln f
kverticaln f
≈ 1
Figure 2: Thermal conductivity measurements carried out in the
horizontal and vertical configuration.
Figure 3: TEM image of a stable alumina in decane nanofluid.
similar results as one would expect. On the x-axis of Fig. 2
one reports the thermal conductivity measured in the horizontal
configuration while on y-axis one has the thermal conductivity
measured in the vertical configuration. The thermal conduc-
tivity for each data point was measured 15 times in both the
horizontal and the vertical configuration over a period of about
60mins. The average of the 15 experimental data is reported in
this article. The thermal conductivity measurement did not vary
appreciably over the 60min interval in both the vertical and hor-
izontal configuration. The typical standard deviation involved
was 0.5%.
Thermal Conductivity Measurements
The thermal conductivity of the Al2O3 in decane and PAO
nanofluids was measured in less than a day after dispersing the
nanoparticles in the base fluid as explained earlier. Fig. 3 shows
a TEM image of a stable alumina in decane nanofluid. The
nanoparticles seem to be well distributed. Fig. 4 shows the ther-
mal conductivity enhancement of the Al2O3 in decane and PAO
nanofluid for volume fractions ranging from 0.1% to 1.5%. The
values for the thermal conductivity plotted in Fig. 4 are obtained
in the vertical setup configuration. The thermal conductivity ra-
tio predicted by the Maxwell Garnett theory [4] is given by
kn f
k f
=
kp +2k f −2φ(k f − kp)
kp +2k f +φ(k f − kp) (2)
Here k f , kp and kn f are the thermal conductivity of the base
fluid, particle and nanofluid respectively and φ is the volume
fraction of the nanoparticles. The above expression for effec-
tive thermal conductivity does not take into account the thermal
interface resistance between the particle and the fluid and is ap-
1155
plicable only for spherical particles. The thermal conductivity
ratio prediction based on Eq.2 is plotted in Fig. 4. One can ob-
serve that the measured thermal conductivity ratio was higher
than that predicted by the Maxwell Garnett theory in both PAO
and decane based nanofluids for all the volume fractions stud-
ied.
0 0.5 1 1.5
1
1.05
1.1
1.15
 
 
k n
f/
k f
Al2O3 Volume Fraction [%]
Decane base nanoemulsion
Enhancement prediction by Effective Medium Theory
PAO based nanoemulsion
Figure 4: Thermal conductivity enhancement vs Alumina vol-
ume fraction in a PAO and Decane based nanofluid.
1 1,025 1.1 1,075 1,1 1,125 1,15
1
1.025
1.05
1.075
1.1
1.125
1.15
 
 
(k
n
f/
k f
)v
er
tic
a
l
(kn f /k f )horizontal
Al2O3 in Decane nanofluids
Al2O3 in PAO nanofluids
khorizontal
n f /kverticaln f = 1
Figure 5: Thermal conductivity enhancement
Thermal conductivity measurements are carried out both in the
horizontal and vertical configuration. No significative change
in the thermal conductivity enhancement measured at different
volume fraction is obtained as indicate in Fig. 5. The x-axis
in Fig. 5 represents the thermal conductivity enhancement ob-
tained in the horizontal configuration (kn f /k f )horizontal , while
the y-axis represents the thermal conductivity enhancement ob-
tained in the vertical configuration (kn f /k f )vertical .
Influence of stability issue on hot-wire measurements: a nu-
merical study
The formulated nanofluids have various stability. The PAO
based nanoparticles are extremely stable, no sedimentation has
been observed for more than 3 months, while the decane base
nanofluids have a shorter stability and already after a couple of
days showed signs of sedimentation. Both system can anyway
be considered stable during the time the measurements were
performed so that the data obtained are reliable. In this re-
spect a criterion that can be employed to asses whether the ther-
mal conductivity enhancement measurements are independent
of the stability of the suspension is that the ratio between the
values obtained from the vertical and horizontal setup should
be close to one. On the other side when the ratio is not close
to one the obtained data is most probably effected by stabil-
ity problem and it is therefore not reliable. Figure 6 shows a
schematic representation of the hot-wire experimental set up in
both configurations. Let L and D be the length and the diame-
ter of the hot-wire cell. When the suspension is not stable one
can achieve sedimentation of the particles, illustrated in Fig 6 as
the light blue area, while the dark blue area represents the sus-
pension phase with higher thermal conductivity and hx and hy
represent the extension of the suspension phase in the horizontal
and vertical set up. A numerical study of the thermal conductiv-
ity measurement that one may obtain in case of unstable system
is investigated by varying hx and hy. The time necessary for the
suspension to sediment is the same in the two configuration so
that D−hx = L−hy. One may intuitively understand that in the
horizontal case the hot-wire may eventually not be covered by
the suspension and this affects the thermal conductivity results.
The numerical model is discretized with 222800 elements. The
heat equation is solved to second order accuracy and in double
precision. The wire domain is set to an initial temperature of
293K. A heat flux = 7500W/m2 from the wire is considered.
The effect of time steps on the solution is investigated and the
highest allowable time step that do not influence neither conver-
gence or the numerical result is used.
(a) (b)
Figure 6: schematic representation of the hot wire experimental
set up in both configurations
The nanofluid is described as a fluid with bulk thermal conduc-
tivity kn f 30% higher than its base fluid k f hence kn f = 1.3k f .
The temperature change as a function of time in the vertical
and horizontal configuration is compared at different sedimen-
tation fraction hx/D and hy/L see Fig. 7 and 8. The extreme
cases are hx/D = 0 which represents a case for which the par-
ticles have completely sedimented out of the suspension. In
this case the measurements belong to the base fluid. On the
other end when hx/D = 1 no particle sedimentation has taken
place and the measurements belong to the nanofluid. In the ver-
tical configuration the thermal conductivity is calculated from
the curves obtained in Fig. 7 by means of Eq. 1 in the same way
as we do in our experimental setup. The thermal conductiv-
ity varies linearly with the fraction hy/L. The same is repeated
for the horizontal configuration. The conductivity is calculated
from the curves obtained in Fig. 8 by means of Eq. 1 showng
that it varies in a step-like manner. The calculated conductivity
is very dependent on how close to the wire the conductivities
change between the suspension and the base fluid is. This could
probably be explained by the area effect on the heat flux. The
normalized conductivity for different fractions of sedimentation
is plotted in Fig. 9. From Fig. 9 one can observe how in the case
1156
of unstable system one expects a difference between the hor-
izontal and vertical measurements. On the x-axis we plot the
fraction of sedimentation express as D−hxD =
L−hy
D . The time
necessary for sedimentation to occur is the same and for this
reason the D−hxL−hy. The results shown in Fig. 9 indicates
how the results from the vertical setup are less dependent on
sedimentation issues. Due to this observation one can stress that
the requirement for which one should gather thermal conductiv-
ity enhancements data from both configurations and their ratio
should be close to one, would ensure that experimental data is
not dependent on the stability of the suspension.
10−4 10−3 10−2 10−1 100 101 102
293
293.5
294
294.5
295
295.5
296
296.5
 
 
∆
T
[K
]
t [s]
hy /L=0
hy /L=0.1
hy /L=0.2
hy /L=0.5
hy /L=1
Figure 7: Average wire temperature as a function of time in the
vertical configuration
10−4 10−2 100 102 104
293
293.5
294
294.5
295
295.5
296
296.5
297
297.5
 
 
∆
T
[K
]
t [s]
hx /D=0
hx /D=0.2
hx /D=0.4
hx /D=0.5
hx /D=0.6
hx /D=0.8
hx /D=1
Figure 8: Average wire temperature as a function of time in the
horizontal configuration
Conclusions
Reliable thermal conductivity measurements of colloidal sus-
pensions require that the suspension is stable against sedimen-
tation during the measurement since particle sedimentation may
effect the experimental results. The present study proposes a
criterion to ensure that thermal conductivity data is independent
of the particle sedimentation. A measuring device based on the
transient hot-wire method is designed to allow vertical and hor-
izontal thermal conductivity data collection. Our investigation
shows that the thermal conductivity measurements in the hori-
zontal and vertical configurations are almost identical when the
colloidal suspension is stable while they differ for unstable sys-
0 0.2 0.4 0.6 0.8 1
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
 
 
k n
f/
k f
D−hx
D =
L−hy
D
Horizontal set-up
Vertical set-up
Figure 9: Normalized conductivity for different fractions of sed-
imentation. The thermal conductivity of the suspension is 30%
greater than the thermal conductivity of the base fluid. On the
x-axis we have plotted the fraction of sedimentation.
tems.
Acknowledgements
This work was partially supported by the Norwegian Research
Council. We are also thankful to J. Garg and Professor G. Chen
for their support.
References
[1] A.S. Ahuja, J. Appl. Phys. 46, 3408 (1975).
[2] S.U.S. Choi, Proceedings of the American Society of Me-
chanical Engineers 66, 99 (1995)
[3] M. Liu, M.C. Lin, C.Y. Tsai, and C. Wang, Int. J. Heat Mass
Transfer 49, 3028 (2006).
[4] J.C. Maxwell, A Treatise on Electricity and Magnetism
(Clarendon, Oxford, 1891)
[5] H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma,
Netsu Bussei 4, 227 (1993).
[6] Y. Nagasaka, and A. Nagashima, J. Phys. E 14, 1435
(1981).
1157


The Importance of Suspension Stability for the Hot-wire Measurements of Thermal Conductivity of Colloidal Suspensions.

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The Importance of Suspension Stability for the Hot-wire Measurements of Thermal Conductivity of Colloidal Suspensions.

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