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ENHANCING THERMAL CONDUCTIVITY OF FLUIDS
WITH NANOPARTICLES*
Stephen U. S. Choi* and J. A. Eastman^
1 Energy Technology Division and 2Materials Science Division
Argonne National
Laboratory,
Argonne, IL 60439
October 1995
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Abstract to be submitted to ASME International Mechanical Engineering Congress & Exposition,
November 12-17,1995, San Francisco, CA.
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ENHANCING THERMAL CONDUCTIVITY OF FLUIDS WITH NANOPARTICLES
Stephen U. S. Choi 1and Jeffrey A. Eastman 2
1Energy Technology Division and 2Materials Science Division
Argonne National Laboratory
Argonne, Illinois
ABSTRACT
Low thermal conductivity is a primary limitation in the
development of energy-efficient heat transfer fluids that are
required in many industrial applications. In this paper we
propose that an innovative new class of heat transfer fluids
can be engineered by suspending metallic nanoparticles in
conventional heat transfer fluids. The resulting "nanofluids"
are expected to exhibit high thermal conductivities compared
to those of currently used heat transfer fluids, and they
represent the best hope for enhancement of heat transfer. The
results of a theoretical study of the thermal conductivity of
nanofluids with copper nanophase materials are presented, the
potential benefits of the fluids are estimated, and it is shown
that one of the benefits of nanofluids will be dramatic
reductions in heat exchanger pumping power.
NOMENCLATURE
d Pipe diameter
f Fanning friction factor
h Heat transfer coefficient
k Thermal conductivity
L Length
n Shape factor
Nu Nusselt number
P Pumping power
Pr Prandtl number
Re Reynolds number
V Velocity
a Particle volume fraction
Sp Pressure drop
P Density
¥ Sphericity
Sub scripts
eff Effective
m Metallic particle
nf Nanofluid
o Reference fluid without nanoparticles
INTRODUCTION
Fluids are often used as heat carriers in heat transfer
equipment. Examples of important uses of heat transfer
fluids include vehicular and avionics cooling systems in the
transportation industry, hydronic heating and cooling
systems in buildings, and industrial process heating and
cooling systems in petrochemical, textile, pulp and paper,
chemical, food, and other processing plants. In all of these
applications, the thermal conductivity of heat transfer fluids
plays a vital role in the development of energy-efficient heat
transfer equipment. With an increasing global competition,
industries have a strong need to develop advanced heat transfer
fluids with significantly higher thermal conductivities than
are presently available.
Despite considerable previous research and development
efforts on heat transfer enhancement, major improvements in
cooling capabilities have been constrained because of the low
thermal conductivity of conventional heat transfer fluids.
However, it is well known that at room temperature, metals in
solid form have orders-of-magnitude larger thermal
conductivities than fluids. For example, the thermal
conductivity of copper at room temperature is =700 times
greater than that of water and =3000 times greater than that of
engine oil, as shown in Table 1. The thermal conductivity of
metallic liquids is much greater than that of nonmetallic
liquids. Therefore, the thermal conductivities of fluids that
contain suspended solid metallic particles are expected to be
significantly enhanced when compared with conventional
* To be presented at ASME International Mechanical Engineering Congress & Exposition, November 12-17, 1995, San Francisco,
CA.
Table 1. THERMAL CONDUCTIVITY (W/m-K) OF VARIOUS
MATERIALS AT 300 K UNLESS
OTHERWISE NOTED
Material Thermal
Conductivity
Metallic Solids
Silver 429
Copper 401
Aluminum 237
Nonmetallic Solids
Silicon 148
Metallic Liquids
Sodium® 644 K 72.3
Nonmetallic Liquids
Water 0.613
Engine oil 0.145
heat transfer fluids. In fact, numerous theoretical and
experimental studies of the effective thermal conductivity of
dispersions that contain solid particles have been conducted
since Maxwell's theoretical work was published more than 100
years ago (Maxwell, 1881). However, all of the studies on
thermal conductivity of suspensions have been confined to
millimeter- or micrometer-sized particles. Maxwell's model
shows that the effective thermal conductivity of suspensions
that contain spherical particles increases with the volume
fraction of the solid particles. It is also known that the
thermal conductivity of suspensions increases with the ratio
of the surface area to volume of the particle.
It is proposed that nanometer-sized metallic particles can be
suspended in industrial heat transfer fluids such as water,
ethylene glycol, or engine oil to produce a new class of
engineered fluids with high thermal conductivity. The author
has coined the term nanofluids (NFs) for this new class of
engineered heat transfer fluids, which contain metallic
particles with average particle sizes of about 10 nanometers
and can be produced by current nanophase technology.
Nanofluids are expected to exhibit superior properties when
compared with conventional heat transfer fluids and fluids that
contain micrometer-sized metallic particles. Because heat
transfer takes place at the surface of the particle, it is desirable
to use a particle with a large surface area. Nanoparticles have
extremely large surface areas and therefore have a great
potential for application in heat transfer. The much larger
relative surface areas of nanophase powders, when compared
with conventional micrometer-sized powders, should markedly
improve the heat transfer capabilities and stability of the
suspensions.
Researchers at Argonne National Laboratory (ANL) have
been developing advanced fluids for industrial applications,
including district heating and cooling systems (Choi and Tran,
1991;
Choi et al., 1992a and 1992b). One of the problems
identified in this R&D program was that micrometer-sized
particles cannot be used in practical heat transfer equipment
because of severe clogging problems. However, nanophase
metals are believed to be ideally suited for applications in
which fluids flow through small passages, because the metallic
nanoparticles are small enough that they are expected to
behave like molecules of liquid. Therefore, nanometer-sized
particles will not clog flow passages, but will improve the
thermal conductivity of the fluids. This will open up the
possibility of using nanoparticies even in microchannels for
many envisioned high-heat-load applications. More recently,
a project was begun at ANL to demonstrate the feasibility of
the concept of nanofluids. Successful employment of
nanofluids will result in significant energy and cost savings
and will support the current industrial trend towards
component miniaturization by enabling the design of smaller
and lighter heat exchanger systems.
The purpose of the paper is to demonstrate theoretically the
feasibility of the concept of nanofluids. After briefly
describing the technology for producing nanoparticles and
suspensions, we shall estimate the thermal conductivity of
nanofluids with copper nanophase materials and the
subsequent heat transfer enhancement as a function of thermal
conductivity. We will also explore the potential benefits of
nanofluids in the expectation that the ultra-high-performance
nanofluids may have major implications for many industries.
TECHNOLOGY FOR PRODUCTION OF
NANOPARTICLES AND SUSPENSIONS
Modern fabrication technology provides great
opportunities to actively process materials on micro- and
nanometer scales. Materials with novel properties can be
produced on nanometer scales. Nanostructured or nanophase
materials are nanometer-sized solid substances engineered on
the atomic or molecular scale to produce either new or
enhanced physical properties not exhibited by conventional
bulk solids. All physical mechanisms have a critical length
scale, below which the physical properties of materials are
changed. Therefore, particles < 100 nm in diameter exhibit
properties different from those of conventional solids. The
noble properties of nanophase materials come from the
relatively high surface-area-to-volume ratio that is due to the
high proportion of constituent atoms that reside at the grain
boundaries. The thermal, mechanical, optical, magnetic, and
electrical properties of nanophase materials are superior to
those of conventional materials with coarse grain structures.
Consequently, the exploration in research and development of
nanophase materials has drawn considerable attention from
material scientists and engineers alike (Duncan and Rouvray,
1989;
Siegel, 1991).
Much progress has been made in the production of
nanophase materials, and current nanophase technology can
produce large quantities of powders with average particle sizes
in the 10-nm range. Several "modern" nanophase materials
have been prepared by physical gas-phase condensation or
chemical synthesis techniques (Siegel, 1991). The gas-phase
condensation process involves the evaporation of a source
material and the rapid condensation of vapor into nanometer-
sized crystallites or loosely agglomerated clusters in a cool,
inert, reduced-pressure atmosphere. A chemistry-based
solution-spray conversion process starts with water-soluble
salts of source materials. The solution is then turned into an
aerosol and dried by a spray-drying system. Rapid
vaporization of the solvent and rapid precipitation of the
solute keeps the composition identical to that of the starting
solution. The precursor powder is then placed in a fluidized-
bed reactor to evenly pyrolyze the mixture, drive off volatile
constituents, and yield porous powders with a uniform
homogeneous fine structure (Ashly, 1994). A third technique
is to generate nanophase materials by condensation of metal
vapors during rapid expansion in a supersonic nozzle (Hill, et
al.,
1963; Andres, et al., 1981; Brown, et al., 1992).
If powders are produced by one of these processes, some
agglomeration of individual particles may occur. It is well
known, however, that these agglomerates, which are typically
1 micrometer or so in size, require little energy to fracture into
smaller constituents, and thus it is possible they will not
present a problem in this application. If, however,
agglomeration is a problem, it would prevent realization of
the full potential of high surface areas of nanoparticles in
nanofluids. Under such conditions, these conventional
technologies for production of nanophase materials are not
suitable for nanofluids.
Another promising
•
technique for producing
nonagglomerating nanoparticles involves condensing
nanophase powders from the vapor phase directly into a
flowing low vapor pressure fluid. This technique was
developed in Japan more than 10 years ago by Akoh et al.
(1978),
but has been essentially ignored by the
nanocrystalline-materials community because of difficulties in
subsequently separating the particles that are produced from
the fluids to make dry powders or bulk materials by sintering
individual nanometer-sized particles.
THEORETICAL STUDY OF THERMAL
CONDUCTIVITY OF NANOFLUIDS
Because of the absence of a theory for the thermal
conductivity of nanofluids, two existing models that were
developed for conventional solid-liquid systems with fine
particles are used in this study to estimate the effective thermal
conductivity of nanofluids. Batchelor and O'Brien (1977)
have developed an expression for the effective thermal
conductivity
keff,
which is applicable to two-phase systems
that contain metal powders with particle diameters on the order
of micrometers, i. e.,
keff/ko = 41n(km/k0)-ll. (1)
where km is the thermal conductivity of the metallic particle
and k0 is the thermal conductivity of the reference fluid.
However, it should be noted that the theory of Batchelor and
O'Brien (1977) was originally developed for a point-contact
porous medium. When there is no contact between the
particles, the effective thermal conductivity is independent of
the conductivity ratio. Thus, for values of the conductivity
ratio ranging from 100 to 10,000, the effective thermal
conductivity of noncontacting systems is estimated from the
equation
keff/ko = 4 (2)
If it is assumed that this expression is applicable to
nanofluids, nanoparticles are expected to increase the thermal
conductivity of the base fluids by a factor of 4. However, this
expression seems unfeasible for nanofluids because it does not
involve the particle volume fraction or particle shape.
Hamilton and Crasser (1962) have developed a more
elaborate model for the effective thermal conductivity of two-
component mixtures as a function of the conductivity of the
pure materials, the composition of the mixture, and the shape
of the dispersed particles. For mixtures in which the ratio of
conductivities of two phases is > 100, the effective thermal
conductivity of two-component mixtures can be calculated as
follows:
keff/ko = [km+ (n-1) ko - (n-1) a (ko - km)] / [km+ (n-1) ko
+ a(ko -km)] (3)
where a is the particle volume fraction and n is the empirical
shape factor given by
n =
3
/ y, (4)
where \|/ is the sphericity, defined as the ratio of the surface
area of a sphere with a volume equal to that of the particle to
the surface area of the particle. This model shows that
nonspherical shapes (all other circumstances being the same)
will increase the conductivity above that of spheres.
Applying the Hamilton and Crasser model to copper
nanoparticles in water, the effective thermal conductivity of
the copper-water system has been estimated for three values
for y. The effects of particle volume fraction and sphericity
on the thermal-conductivity ratio for a copper-water system
are plotted in Fig. 1. The results clearly show that the thermal
conductivity of the fluid-particle system depends on both the
particle volume fraction and the shape. Assuming that the
sphericity of copper nanoparticles is 0.3, the thermal
conductivity of water can be enhanced by a factor of 1.5 at the
low volume fraction of 5% and by a factor of almost 3.5 at the
high volume fraction of 20%. This finding demonstrates,
theoretically, the feasibility of the concept of nanofluids, i.e.,
metallic nanoparticles are capable of significantly increasing
the thermal conductivity of conventional heat transfer fluids.
Furthermore, Masuda et al. (1993) have shown experimentally
that y-Al203 particles at a volume fraction of
4.3%
can increase
the effective thermal conductivity of water by =30%. The
agreement between the estimated and measured conductivities
is satisfactory.
POTENTIAL BENEFITS OF NANOFLUIDS
For turbulent convection transfer of heat in smooth pipes,
the heat transfer coefficient can be calculated from the Dittus-
Boelter correlation,
Nu = 0.023 Re08 Pr1/3. (5)
If it is assumed that only the thermal conductivity of the
nanofluid system varies and other properties, such as the
specific heat, density, and dynamic viscosity, are the same as
for the reference fluid, then we obtain from Eq. 5,
which shows that the heat transfer coefficient h may be
increased by increasing the velocity v or the thermal
conductivity of the fluid k.
In heat exchangers that use conventional fluids, the heat
transfer coefficient may only be increased by significantly
increasing the velocity of the fluid in the heat transfer
equipment. However, the pumping power significantly
increases with increasing velocity. The frictional pressure
drop for fully developed turbulent flows in a pipe is given as
8p = 2fpLv2/d, ' (7)
where p is the density of the fluid, L the length of the pipe, d
the pipe diameter, and f the Fanning friction factor given by
f = 0.079 Re"025. (8)
It can be shown that the frictional pressure drop is given by
the relationship
op ~ v175. (9)
Because pumping power P is proportional to the product of the
pressure drop and the flow rate, it can be expressed by the
relationship
P - v2-75. (10)
From Eqs. 6 and 10, enhancement of heat transfer due to
increased pumping power can be estimated from the following
equation:
h/h0 = (P/P0)0'29. (11)
For a nanofluid flowing in the same heat transfer equipment
at a fixed velocity, enhancement of heat transfer due to
increased thermal conductivity can be estimated from the
equation
hnf/h0 = (kn/k0)2/3. (12)
The effects of thermal conductivity and pumping power on
heat transfer are plotted in Fig. 2. In heat exchangers that use
conventional fluids, heat transfer can only be improved by
significantly increasing flow rates. For example, to improve
the heat transfer by a factor of 2, the pumping power should be
increased by a factor of =10. However, if a nanoparticle-based
fluid with a thermal conductivity of =3 times that of a
conventional fluid were used in the same heat transfer
equipment, the rate of heat transfer would be doubled.
Liu et al. (1988) have studied the influence of particle
loading and size on the pressure drop of slurry. Their data
show that solids suspensions in the 20% volume fraction
range incur little or no penalty in pressure drop as compared
with single-phase fluids of comparable flow rate. Therefore, it
is reasonable to assume that the nanofluid pressure drop
behaves like that of a single-phase fluid at volume fractions up
to 20%. Then, the potential savings in pumping power is
particularly significant as the heat transfer enhancement ratio
is increased, as shown in Fig. 3. This could lead to a major
technological breakthrough in the development of energy-
efficient industrial heat transfer fluids. Therefore, the potential
benefits of nanofluids could provide tremendous performance,
size/weight, and cost advantages.
FUTURE RESEARCH PLANS
The research effort to produce and characterize the heat
transfer behavior of nanofluids will consist of five main tasks.
1.
Nanophase metal powders will be produced in existing
state-of-the-art gas-condensation preparation systems at ANL.
The particle size and agglomeration behavior of nanophase
powders in liquids will be studied.
2.
A new technique for producing nonagglomerating
nanoparticles for nanofluids by directly condensing
nanophase powders into a flowing fluid will be developed,
based on the system designed by Akoh et al. (1978). The
properties of nanofluids produced by this technique will be
compared with those produced by inert-gas condensation.
3.
Technology for production of nanoparticle
suspensions will be developed and the stability, dispersion,
and rheological/transport properties of these nanofluids will
be investigated.
4.
The flow characteristics of dilute and concentrated
suspensions of nanoparticles will be studied. Heat transfer
tests with nanoparticles in a range of up to 10 volume fraction
will be conducted to demonstrate the expected dramatic
improvement in energy efficiency from nanofluids.
5.
Practical applications of nanofluids will be
investigated.
CONCLUDING REMARKS
The concept of nanofluids is an innovative idea. The
feasibility of the concept of high-thermal-conductivity
nanofluids has been demonstrated by applying the Hamilton
and Crosser (1962) model to copper nanoparticles in water,
together with some experimental results of Masuda, et al.
(1993) for y-Al203 particles in water. The potential benefits of
nanofluids with copper nanophase materials have been
estimated. One of the benefits of nanofluids will be dramatic
reductions in heat exchanger pumping power. For example, to
improve the heat transfer by a factor of 2, the pumping power
with conventional fluids should be increased by a factor of
=10.
However, if a nanoparticle-based fluid with a thermal
conductivity of =3 times that of a conventional fluid were used
in the same heat transfer equipment, the nanoparticle-based
fluid would double the rate of heat transfer without an increase
in pumping power. The invention of nanofluids presents new
challenges and opportunities for thermal scientists and
engineers.
ACKNOWLEDGMENTS
This work was supported by the U.S. Department of Energy,
under Contract W-31-109-ENG-38. The author would like to
express special thanks to Argonne's Coordinating Council for
Science and Technology for their interest and support of this
work. Thanks are also given to M. W. Wambsganss for
valuable discussions.
REFERENCES
Akoh, H., Tsukasaki, Y., Yatsuya, S., and Tasaki, A., 1978,
"Magnetic Properties of' Ferromagnetic Ultrafine Particles
Prepared by a Vacuum Evaporation on Running Oil Substrate,"
J. Cryst. Growth, 45, pp. 495-500.
Andres, R. P., Bowles, R. S., Kolstad, J. J., and Calo, J. M.,
1981,
"Generation of Molecular Clusters of Controlled Size,"
Surface Sci., 106, pp. 117-124.
Ashly, S., 1994, "Small-scale Structure Yields Big Property
Payoffs," Mechanical Engineering, Vol. 116, No. 2, pp. 52-
57.
Batchelor, G. K. and O'Brien, R. W., 1977, "Thermal or
Electrical Conduction through a Granular Material," Proc. R.
Soc.
Lond.,
A355, pp. 313-333.
Brown, D. P., Chung, J. N., and Crowe, C. T., 1992, "A
Numerical Simulation of Nanocluster Formation in Supersonic
Expansion Flows," Micromechanical Systems, ASME DSC-
Vol. 40, pp. 211-225.
Choi, U. S., Cho Y. I., and Kasza, K. E.. 1992a,
"Degradation Effects of Dilute Polymer Solutions on Turbulent
Friction and Heat Transfer Behavior," J. Non-Newtonian Fluid
Mechanics, 41, pp. 289-307.
Choi, U. S., France, D. M., and Knodel, B. D., 1992b,
"Impact of Advanced Fluids on Costs of District Cooling
Systems," Proc. 83rd Ann. Int. District Heating and Cooling
Assoc.
Conf.,
Danvers, MA, June 13-17., The Int. District
Heating and Cooling Assoc., Washington, D.C., pp. 343-
359.
Choi, U. S. and Tran, T. N., 1991, "Experimental Studies of
the Effects of Non-Newtonian Surfactant Solutions on the
Performance of a Shell-and-Tube Heat Exchanger," Recent
Developments in Non-Newtonian Flows and Industrial
Applications, eds. D. A. Siginer and M. N. Dhaubhadel, The
American Society of Mechanical Engineers, New York, FED-
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Duncan, M. A. and Rouvray, D. H., 1989, "Microclusters,"
Scientific American, Dec., pp. 110-115.
Hamilton, R. L. and Crasser, O. K., 1962, "Thermal
Conductivity of Heterogeneous Two-Component Systems," /
& EC Fundamentals, Vol. 1, No. 3, pp.
187-191.
Hill, P. G., Witting, H., and Demetri, E. P., 1963,
"Condensation of Metal Vapors During Rapid Expansion," J.
Heat Transfer, Nov., pp. 303-317.
Liu, K. V., Choi, U. S., and Kasza, K. E., 1988,
"Measurements of Pressure Drop and Heat Transfer in Turbulent
Pipe Flows of Particulate Slurries," Argonne National
Laboratory Report, ANL-88-15.
Masuda, H., Ebata, A., Teramae K., and Hishinuma, N.,
1993,
"Alteration of Thermal Conductivity and Viscosity of
Liquid by Dispersing Ultra-fine Particles (Dispersion of y-
A1203_
Si02 _ and Ti02 Ultra-fine Particles)," Netsu
Bussei(Japan),.Vol. 4, No. 4, pp. 227-233.
Maxwell, J. C, 1881, A Treatise on Electricity and
Magnetism, 2nd ed., 1, 435, Clarendon Press.
Siegel, R. W., 1991, "Cluster-Assembled Nanophase
Materials," Annual Review of Materials Science, 21, pp. 559-
578.
3.5
2.5 h
2
1.5
1
I i i i | i i i i | i i i i | i i i i 1 i i ! 1
— o Sphericity of 1.0
a Sphericity of 0.5
+ —
— + Sphericity of 0.3 —
I I I
+ -
— • —
— + a
: D
+ o
o -
-a o _
Ej_i_
i i i T i p i i I i i i i 1 i i 1 1 1 1 1 1 1
0.05 0.1 0.15
Particle volume fraction
0.2 0.25
Figure 1. EFFECT OF PARTICLE VOLUME FRACTION AND SPHERICITY
C-N THERMAL CONDUCTIVITY RATIO FOR COPPER-WATER SYSTEM
3 U
1 h-
O k/ko
O P/Po
O 0
....&.
0
0
<?
-qr
<P
0
0
Q
4>
£>"
o
0
<?
!
0
~x>
10
k/k orP/P
o o
Figure 2. EFFECTS OF THERMAL CONDUCTIVITY AND PUMPING POWER
ON HEATTRANSFER
50
40
30
-
20
10
-
I I
o Conventional fluid
o Nanofluid
<j> <j>
o
i
Q....
o
\
0
.4
O
> 8 o
O i
O
;
o o 4> o o o o o
1.5 2 2.5 3
Heat transfer coefficient ratio,
h/h
3.5
Figure 3. POTENTIAL PUMPING POWER SAVINGS WITH NANOFLUIDS
