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Experimental Thermal and Fluid Science 37 (2012) 72–83
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science
journal homepage: www.elsevier .com/locate /et fs
Laminar convective heat transfer of alumina-polyalphaolefin
nanofluidscontaining spherical and non-spherical nanoparticles
Leyuan Yu a, Dong Liu a,⇑, Frank Botz ba Department of
Mechanical Engineering, University of Houston, Houston, TX 77204,
USAb METSS Corporation, Westerville, OH 43082, USA
a r t i c l e i n f o
Article history:Received 19 May 2011Received in revised form 27
September2011Accepted 12 October 2011Available online 19 October
2011
Keywords:NanofluidsConvective heat transferPressure dropThermal
conductivityViscosityMinichannel
0894-1777/$ - see front matter � 2011 Elsevier Inc.
Adoi:10.1016/j.expthermflusci.2011.10.005
⇑ Corresponding author.E-mail address: [email protected] (D.
Liu).
a b s t r a c t
As a potential candidate for advanced heat transfer fluid,
nanofluids have been studied extensively in theliterature. Past
investigations were largely limited to thermophysical property
measurements of aqueousnanofluids synthesized with spherical
nanoparticles. No comprehensive information is yet available
forconvective thermal transport of nanofluids containing
non-spherical particles, especially of the non-aqueous nanofluids.
In this work, an experimental study was conducted to investigate
the thermophys-ical properties and convective heat transfer of
Al2O3-polyalphaolefin (PAO) nanofluids containing bothspherical and
rod-like nanoparticles. The effective viscosity and effective
thermal conductivity of thenanofluids were measured and compared to
predictions from several existing theories in the literature.It was
found that, in addition to the particle volume fraction, other
parameters, including the aspect ratio,the dispersion state and the
aggregation of nanoparticles as well as the shear field, have
significantimpact on the effective properties of the nanofluids,
especially of those containing non-spherical parti-cles. The
pressure drop and convection heat transfer coefficient were also
measured for the nanofluidsin the laminar flow regime. Although
established theoretical correlations provide satisfactory
predictionof the friction factor and Nusselt number for nanofluids
containing spherical nanoparticles, they fail fornanofluids
containing rod-like nanoparticles. The results indicate that in a
convective flow, the shear-induced alignment and orientational
motion of the particles must be considered in order to
correctlyinterpret the experimental data of the nanofluids
containing non-spherical nanoparticles.
� 2011 Elsevier Inc. All rights reserved.
1. Introduction
Nanofluids have been studied extensively as a promising
candi-date of advanced heat transfer fluids for thermal
managementapplications in microelectronics, transportation, power
andmilitary systems [1]. While dramatic enhancement in thermal
con-ductivity was reported in the early literature, most recent
studiesfind the convective heat transfer of nanofluids is only
mildly aug-mented and the measured thermal properties can be well
corre-lated by the conventional effective medium theory (EMT)
[2,3].Wide discrepancies exist among different studies regarding
howthe dispersed nanoparticles alter the convective thermal
transportof nanofluids. Moreover, the past investigations were
conductedprimarily for water-based nanofluids synthesized with
sphericalnanoparticles. Due to the simple geometry of these
particles, it isreasonable to neglect the effects of the particle
distribution andorientation on the effective rheological and
thermal properties aswell as on the convective heat transfer of the
nanofluids. However,
ll rights reserved.
when non-spherical nanoparticles, such as carbon nanotubes(CNTs)
and titanate nanotubes (TNTs), are used in formulatingthe
nanofluids, these effects may no longer be ignored as the resultof
the hydrodynamic interactions between the particles and
thesurrounding fluid medium. Also, the use of aqueous nanofluids
be-comes infeasible in many practical applications due to their
limitsin the dielectric property and the operating temperature
range.Consequently, there is a need to systematically study the
convec-tive thermal transport of non-aqueous nanofluids synthesized
withnon-spherical nanoparticles.
Several experimental studies were performed to study
theeffective thermophysical properties and convective heat
transferof nanofluids containing non-spherical particles with
highlength-to-diameter ratio (aspect ratio). Cherkasova and Shan
[4]studied the effects of particle aspect-ratio and dispersion
state onthe effective thermal conductivity of aqueous nanofluids
with mul-ti-walled nanotubes (MWNTs). They found the effective
thermalconductivity decreases with reduced MWNT aspect ratio, and
theconductivity enhancement was primarily due to the presence
ofindividualized long nanotubes rather than the bundles of
aggre-gated low aspect ratio nanotubes. The measured conductivity
datashowed a good agreement with the EMT predictions, and no
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Nomenclature
A channel cross-sectional area, m2
f friction factorh heat transfer coefficient, W/m2 Kk thermal
conductivity, W/m Kl length of nanorod, nmL length of test tube, md
diameter of nanorods, nmD channel inner diameter, mCp specific
heat, kJ/kg KM fractal indexNu Nusselt numberP pressure, PaPe
Peclet numberPr Prandtl numberq00 heat flux, W/m2
Q volumetric flow rate, m3/sr aspect ratio of nanorodRb
interfacial resistance, m2 K/WRe Reynolds number
T temperature, �Cu velocity, m/sx axial position, mx� inverse of
Graetz number
Greek symbols/ volume concentrationl viscosity, N s/m2
q density, kg/m3
Subscriptsf base fluidin inleto outer wallout outletp particler
relativex localw wall
L. Yu et al. / Experimental Thermal and Fluid Science 37 (2012)
72–83 73
anomalous increase was observed. Ding and his co-workers
mea-sured the rheological properties of ethylene–glycol
(EG)-basednanofluids containing TNTs [5,6]. Strong shear thinning
behaviorwas found at high particle volume fractions in the EG-TNT
nanofl-uids. The initial high viscosity was attributed to the
resistance thatarises when the Brownian rotation of the rod-like
TNTs must beovercome for the nanotubes to align with the shear
field, as wellas the higher effective particle volume fraction
caused by the par-ticle aggregation than in a well-dispersed
solution. Ding et al. [7]conducted convective heat transfer
experiments of aqueous CNTnanofluids flowing through a circular
tube. The authors found thatthe heat transfer enhancement was
caused by the dynamic thermalconductivity of the nanofluids under
shear conditions, which wasmuch higher than the value measured at
static conditions. Theyalso suggested that the development of
thermal boundary layermay be affected by shear thinning and the
migration/aggregationof the long aspect ratio CNTs. Similar
observations were made byChen et al. [8] in their study of
convective heat transfer of water-TNT nanofluids. Yang et al. [2]
explored the effects of the Reynoldsnumber, temperature, particle
concentration on convective heattransfer of nanofluids through a
circular channel. Two kinds ofnanofluids were formulated by
dispersing disk-like graphite nano-particles in a commercial
automatic transmission fluid (ATF) and amixture of synthetic base
oils, respectively. The enhancement ofheat transfer coefficient was
much less than what was predictedby the Seider–Tate correlation
with the effective thermal conduc-tivity measured under static
conditions. It was hypothesized thatthe shear-induced nanoparticle
alignment disrupts the particle–particle interaction, which was
assumed to be the main energypathway in the nanofluids, and results
in the deterioration of con-vective heat transfer.
Polyalphaolefins (PAO) are a group of synthetic engine oils
thathave been used extensively as lubricants and coolants in
variousmilitary and aerospace applications [9]. As a heat transfer
fluid,their thermal performance and energy efficiency are seriously
lim-ited by the low intrinsic thermal conductivity of PAO (0.132
W/m Kvs. 0.6 W/m K for water). Therefore, it is of great practical
interestto develop PAO-based nanofluids with enhanced
thermophysicalproperties, which can also serve as a good sample for
the funda-mental study of convective thermal transport in
non-aqueousnanofluids. Yang et al. [10] measured the thermal and
rheologicalproperties of PAO-CNT nanofluids at different
dispersant
concentrations, dispersing energy levels and nanoparticle
concen-trations. They found nanoparticle aggregration was the
mostimportant factor contributing to the effective properties:
Largeragglomerates resulted in both higher thermal conductivity
andhigher viscosity. The thermal conductivity of nanofluids
increasedwith the CNT aspect ratio until the CNTs were long enough
to forma percolated network structure. Zhou et al. [11]
investigated thedependence of viscosity on the shear-rate and the
temperature inPAO-Al2O3 nanofluids. At low particle volume fraction
(1 vol%and 3 vol% for nanospheres and 1 vol% for nanorods), the
viscosityshowed a weak dependence on shear rate and the nanofluids
canbe approximated as a Newtonian fluid. The relative viscosity
(de-fined as lr = l/lf) was found to be independent of
temperature,indicating the rheological properties of nanofluids
were primarilydominated by the base fluid. Shaikh et al. [12]
measured the ther-mal conductivity of three types of PAO nanofluids
containing CNTs,exfoliated graphite (EXG) and heat treated
nanofibers (HTTs),respectively. They observed that the thermal
conductivityenhancement was the most significant for PAO-CNT
nanofluids,followed by EXG and HTT. Nelson et al. [9] conducted
convectiveheat transfer experiments of PAO nanofluids in a plain
offset finheat exchanger. The nanofluids were synthesized with
exfoliatedgraphite fibers. They showed the augmented Nusselt number
wasdue to the precipitation of nanoparticles on the wall of the
heat ex-changer which acted as nanoscale fins to enhance the
convectiveheat transfer.
The literature survey reveals that thermal transport of
non-aqueous nanofluids containing non-spherical particles has
notbeen well understood. Particularly, there is a clear call for
asystematic investigation on the effects of the particle–fluid
andparticle–particle interactions on the effective
thermophysicalproperty and convective heat transfer characteristics
of the nanofl-uids. In this work, an experimental study was
conducted to explorethe single-phase forced convection of PAO-Al2O3
nanofluids con-taining both spherical and rod-like nanoparticles
(nanorods)through a circular minichannel. The effective viscosity
and thermalconductivity were measured for the two types of
nanofluids, andthe data were compared to predictions from the
effective mediumtheory. The pressure drop and convective heat
transfer of the nano-fluids were characterized over the Reynolds
number range of110–630. It was found that the aspect ratio,
dispersion state andaggregation of the nanoparticles contribute
significantly to the
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74 L. Yu et al. / Experimental Thermal and Fluid Science 37
(2012) 72–83
effective thermophysical properties of nanofluids
containingnon-spherical particles, and the shear-induced alignment
andorientational motion of the non-spherical nanoparticles play
animportant role in affecting the pressure drop and heat
transfercharacteristics of the nanofluids.
Fig. 1. TEM image of the rod-like Al2O3 nanoparticles.
2. Experiments and methods
2.1. Preparation of nanofluids
The nanofluids were formulated by dispersing boehmitealumina
nanoparticles in 2 centiStokes (cSt) PAO under ultrasoni-cation.
Two types of nanofluids were prepared. The first type (re-ferred to
as NF1) contains spherical nanoparticles, and thesecond type
(referred to as NF2) contains nanorods. Due to thehydrophobic
nature of PAO, special dispersants of minusculeamount were added to
alleviate the aggregation of nanoparticlesto stabilize the
nanofluids. All the samples were found stable with-out
precipitation for at least 7 days during the experiment period.
The diameter of the spherical nanoparticles contained in NF1was
measured using a dynamic light scattering (DLS)
instrument(Brookhaven Instrument BI-200SM), and was found to be
about60 nm. The diameter and length of the nanorods contained inNF2
were obtained using transmission electron microscopy(TEM). Before
the TEM measurement, the sample was preparedby diluting the
nanofluid containing 0.65 vol% nanorods with pure2 cSt PAO at a
ratio of 1:10 and sonicating the mixture for 4 h. Fig. 1shows one
representative TEM image. The measured diameters ofthe individual
nanorods (d) range from 5 nm to 11 nm, and thelengths (l) range
from 80 nm to 106 nm. Taking the average mea-surements from 10 TEM
images, the mean diameter and lengthof the nanorods were d = 7.0 nm
and l = 85 nm, respectively, whichcorrespond to an average aspect
ratio of r = l/d � 12.
2.2. Viscosity and thermal conductivity measurements
Both the effective viscosity and thermal conductivity of
thenanofluids were measured under static conditions. The
viscositywas measured using a capillary viscometer
(Cannon-Ubbelohde9721-R53). The thermal conductivity was
characterized by a ther-mal property analyzer (KD2 Pro, Decagon
Devices). The manufac-turer specified measurement uncertainty was
5% for the thermalproperty analyzer, which was confirmed by
reproducing the liter-ature values for thermal conductivity of
deionized (DI) water.
2.3. Convective heat transfer experiments
The apparatus for the convective heat transfer experiments(shown
in Fig. 2) has been reported in details in Ref. [13]. In brief,a
gear pump (IDEX Micropump 67-GA-V21) was used to circulatethe
nanofluid through the test loop. The flow rate was measuredby a
turbine flowmeter (McMillan G111). A liquid–liquid heat ex-changer
(Lytron LL520G14) was used together with an air-cooledchiller
(Neslab MERLIN 25) to reduce the temperature of theheated nanofluid
to room temperature before it flows back to thereservoir. Readings
of the flow rate, temperature and pressuremeasurements were
collected by a data requisition system (Agilent34970A) and
processed in a computer.
The test tube is a circular minichannel made of stainless
steel,and it measures 1.09 mm in inner diameter (D) and 0.25 mm
inwall thickness. The total tube length (L) is 306 mm. The test
tubeis resistively heated by passing a DC current through it. The
voltagedrop across the channel was measured by the data acquisition
sys-tem, and the current was obtained by using an accurate
shuntresistor. Six copper–constantan (T-type) thermocouples
(Omega
5TC-TT-T40-36) were attached to the outer wall of the channel
at44 mm axial intervals (TC1 through TC6). The temperature
read-ings from these thermocouples were extrapolated to yield the
localtemperatures at the inner wall. To minimize the heat loss to
theambient, the test tube was wrapped heavily with thermal
insulat-ing materials. Two thermocouple probes (Omega TMT
IN-020G-6)were employed to measure the fluid temperatures at the
inlet andoutlet of the channel. Two absolute pressure transducers
(OmegaPX319-050A5V and PX319-030A5V) were installed to measurethe
pressure drop across the channel.
In the pressure drop experiments, the flow rate was adjusted bya
control valve. In each experiment run, the data were read into
thedata acquisition system after the flow rate and the pressure
signalsstabilized. The flow rate was then increased in small
increment andthe procedure repeated. In the heat transfer
experiments, thepower input to the test tube was maintained at a
constant level.The flow rate was first set to the maximum value and
graduallydecreased in subsequent experiments. In all experiments,
eachsteady-state value was calculated as an average of 100
readingsfor all flow rate, pressure, temperature, and power
measurements.
3. Data reduction
The pressure drop and the flow rate were measured to obtainthe
Reynolds number, Re, and the Darcy friction factor, f, whichare
defined as
Re ¼ quD=l ð1Þ
f ¼ ðDP=LÞDqu2=2
ð2Þ
In Eq. (2), DP is the pressure drop across the channel length,
and iscalculated by subtracting the inlet and outlet pressure
losses fromthe measured overall pressure drop [14,15].
In the heat transfer experiments, a uniform heat flux
boundarycondition is assumed on the channel wall. The wall heat
flux is cal-culated from the sensible heat gain by the fluid as
Q 00 ¼ qQCpðTout � TinÞ=A ð3Þwhere the fluid properties are
evaluated at the mean temperature
T ¼ ðTin þ ToutÞ=2 ð4Þ
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Fig. 2. Schematic of the experimental apparatus.
L. Yu et al. / Experimental Thermal and Fluid Science 37 (2012)
72–83 75
The local convective heat transfer coefficient is defined as
hxðxÞ ¼ q00=½TwðxÞ � TðxÞ� ð5Þ
where the local wall temperature Tw(x) is extrapolated from
thetemperature, Tw,o(x), measured at the outer wall of the channel,
fol-lowing [16]
TwðxÞ ¼ Tw;oðxÞ þqQCpðTout � TinÞ
4pkwL�
qQCpðTout � TinÞD2o2pkwðD2o � D
2ÞLln
DoD
ð6Þ
The local fluid temperature T(x) can be calculated from the
en-ergy conservation
TðxÞ ¼ Tin þ q00pDx=ðqQCpÞ ð7Þ
Accordingly, the local Nusselt number is
Nux ¼hx � D
kð8Þ
where the thermal conductivity is evaluated at the
correspondingfluid temperatures.
In the foregoing analysis (Eqs. (1)–(8)), the density and
specificheat of nanofluids were estimated as follows
qðTÞ ¼ / � qpðTÞ þ ð1� /Þ � qf ðTÞ ð9Þ
CpðTÞ ¼/ � ðqpCp;pÞðTÞ þ ð1� /Þ � ðqf Cp;f ÞðTÞ
qðTÞ ð10Þ
and the thermal conductivity and viscosity were from the
experi-mental measurements.
4. Measurement uncertainties
The measurement uncertainties for the temperature, flow rateand
pressure drop were ±0.3 �C, 1% of full scale and 2% of full
scale,respectively. A standard error analysis [17] revealed that
theuncertainties in the reported friction factor and heat transfer
coef-ficient were in the ranges of 5.2–13.8% and 1.6–3.5%,
respectively.
5. Results and discussion
5.1. Viscosity
Addition of particles, particularly anisotropic particles such
asspheroids, rods or disks, into a base fluid results in an
effectiveviscosity that is higher than the inherent viscosity of
the base fluid.This is due to the Brownian and hydrodynamic motions
of the dis-persing particles.
For suspensions of spherical particles, the relative viscosity
canbe expressed by the Batchelor equation as a function of
nanoparti-cle volume fraction
lr ¼llf¼ 1þ ½l�/þ kH/2 þ Oð/3Þ ð11Þ
where the intrinsic viscosity is [l] = 2.5 and the Huggins
coefficientis kH = 6.2 [18,19]. The first two terms at the RHS of
Eq. (11) are re-lated to the particle diffusion; the third term
arises in concentratedsuspensions, and the coefficient kH is very
sensitive to the rheolog-ical structure of the suspension [20]. At
infinite dilution, Eq. (11) re-duces to the well-known Einstein
equation, lr = 1 + 2.5/.
In static suspensions of rod-like particles, the impact of
transla-tional Brownian motion of the particles is negligible on
the viscos-ity, as compared to that due to the rotational Brownian
motion. Assuch, the effective viscosity is mainly affected by the
competitionbetween the shear force and the rotational Brownian
motion, rep-resented by the rotational Peclet number
Perot ¼_c
Drð12Þ
where _c is the shear rate, and Dr is the rotational diffusion
constantof the particles. It is easy to see the low shear limit (as
encounteredunder the static conditions) corresponds to Perot� 1. If
the particleconcentration is sufficiently high, the particles will
overlap andinteract hydrodynamically, and the rotational freedom is
restricted.Recasting the particle volume concentration / in terms
of the num-
ber density v, it yields v ¼ /= p4 d2l
� �for a dispersion of rod-like par-
ticles with a diameter d and a length l. The minimum
overlapconcentration is given by [21]
v� ¼ 1l3
ð13Þ
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76 L. Yu et al. / Experimental Thermal and Fluid Science 37
(2012) 72–83
If the particle dispersion is infinitely dilute (v < 0.1v�),
each particlecan rotate freely and the relative viscosity of the
nanofluid is
lr ¼ 1þ ½l�/ ð14Þ
where [l] can be calculated from one of the following
equations[22,23]
½l� ¼ 415
r2
ln rfor r � 1 ð15Þ
or
½l� ¼ r2
51
3ðln 2r � 1:5Þ þ1
ln 2r � 0:5
� �þ 1:6 for r > 15 ð16Þ
At higher shear rate, i.e., Perot P r3, the orientation
distribution ofthe particles due to shear forces dominates over the
Brownianmotion, and [l] can be estimated by the equation by Hinch
and Leal[24]
½l� ¼ 0:315 rln r
ð17Þ
If v P 0.1v�, the rod–rod hydrodynamic interaction starts
tocontribute to the effective viscosity of the suspension. For
instance,0.1v� corresponds to a particle volume concentration of
0.055 vol%for nanorods with l = 85 nm and d = 7 nm in this work.
When theparticle concentration falls in the range of 0.1v� < v
< v�, the suspen-sion can still be considered dilute. The
relative viscosity at lowshear limit (Perot� 1) is estimated from
the Berry–Russel equation[25]
lr ¼ 1þ ½l�/þ kH½l�2/2 ð18Þ
where kH ¼ 25 1� 0:00142Pe2rot
� �and [l] can be found from Eqs. (15)
or (16). At higher particle concentrations, v� < v <
(dl2)�1, or equiva-lently, 0.55 vol% < / < 6.5 vol% for the
PAO-nanofluids in the presentstudy, the particle suspension is
considered semi-dilute. In this con-centration range, the
rotational volumes of adjacent rods will over-lap and the rods are
entangled. The low-shear viscosity of suchparticle suspensions is
given by [21]
lr ¼ 1þr2
15 ln r/þ 36r
6
5p2b ln r/3 ð19Þ
where b is a numerical factor (b = 103–104). When the particle
con-centration further increases to the maximum packing fraction,
/m,the Krieger–Dougherty correlation [26] can be used to
estimatethe relative viscosity
lr ¼ ½1� ð/=/mÞ��½l�/m ð20Þ
where /m = 5.4/r for r� 1 [27,28].In addition to the rotational
interaction between particles, two
more effects must be considered in the study of the effective
vis-cosity of nanofluids: the particle aggregation and the shear
flow.Most nanoparticles naturally adhere to each other, and the
aggre-gation can only be suppressed to some degree with
stabilizingagents. As a consequence, the nominal particle volume
fraction, /, should be replaced by an effective volume fraction,
/a, as sug-gested by Chen et al. [29,30]
/a ¼ /aaa
� �3�Mð21Þ
where a is the primary nanoparticle size, aa is the effective
size ofthe aggregates; and M is the fractal index. The value of M
varies be-tween 1.6 and 2.3, and is approximately 1.8 for spherical
nanopar-ticles. Since (aa/a) > 1, the particle aggregation will
result in /a > /,which, in turn, leads to a higher viscosity of
the nanofluids, as canbe manifested by Eqs. (11)–(20). When a shear
flow is applied,the rod-like particles tend to align spontaneously
with the flowfield. As the shear rate increases, the impact of the
rotational
motion of nanoparticles on viscosity will diminish. In fact,
shearthinning behavior was observed in nanofluids of high particle
vol-ume fraction under high shear conditions [29,30]. As a
consequence,the effective viscosity of nanofluids in forced
convective flow is ex-pected to be lower than the values measured
at the staticconditions.
In this work, the viscosity of nanofluids was measured at 25
�Cunder static conditions for particle volume fractions of 0.33,
0.49,0.65, and 1.3 vol%, respectively. A capillary viscometer was
usedfor this purpose. The results are presented in Fig. 3 in terms
ofthe relative viscosity. Fig. 3a shows the measured data of NF1and
the comparison with theoretical predictions. The viscosity
ofnanofluids clearly increases with the nanoparticle volume
fraction.The original Batchelor equation (Eq. (11)) underpredicts
the exper-imental data; but when used in combination with the
effective vol-ume fraction calculated from Eq. (21), it provides a
betterprediction of the viscosity data. In doing so, aa/a must be
knownas a priori, however, it is employed as a fitting parameter
due tothe difficulty in obtaining the actual values for each
sample. It isfound that the selection of aa/a = 4.12 and M = 1.8
yields a goodagreement between the predictions and the measured
data witha coefficient of determination of R2 = 0.9843. For
simplicity, anempirical correlation is proposed for the nanofluids
containingspherical nanoparticles
lr ¼ 1þ 13:67/þ 185:42/2 for NF1 ð22Þ
Fig. 3b illustrates the measured lr of NF2 as a variation of /.
Ascompared to the results in Fig. 3a, the viscosity of NF2 is
distinctlyhigher than that of NF1 at the same particle
concentration and thedifference widens as the concentration
increases. Similar observa-tions were reported by Chen et al. [8]
and Zhou et al. [11]. The re-sults suggest the important role
played by the particle geometryand aspect ratio in the rheological
properties of nanofluids. Alsoshown in Fig. 3b are the predictions
from the theoretical modelsdeveloped for suspensions of rod-like
particles (Eqs. (14), (15),(18)–(20)). Unfortunately, they all
underestimate the measure-ment data. Considering the aggregation
effect, the effective volumefraction of the rod-like particles can
be estimated from Eq. (21),where aa/a = 1.48 and M = 1.95 were
chosen. With the effectivevolume fraction, the modified theoretical
predictions are examinedagain in Fig. 3c, which shows the dilute
suspension model yieldsthe best overall agreement (R2 = 0.9920)
with the experimentaldata. An empirical correlation similar to Eq.
(22) was proposedfor the nanofluids containing nanorods
lr ¼ 1þ 27:29/þ 296:92/2 for NF2 ð23Þ
It is noted that Eqs. (22) and (23) are valid for / 6 1.3%.The
viscosities of nanofluids at elevated temperatures were not
investigated in this work. They were estimated by
lðTÞ ¼ lr � lf ðTÞ ð24Þ
where the temperature-dependence of the viscosity of the
basefluid (PAO) is obtained from [31]
lf ðTÞ ¼ 10ð109:67=T3:923Þ � 0:7
� � 10�6 � 1360� 4:56T þ 0:0157T2
��0:28 10�4T3 þ 0:174 10�7T4
�ð25Þ
5.2. Thermal conductivity
For solid–liquid mixtures, the relative thermal conductivity
canbe estimated by the Hamilton–Crosser model [32]
kr ¼kkf¼ kp þ ðn� 1Þkf � ðn� 1Þðkf � kpÞ/
kp þ ðn� 1Þkf þ ðkf � kpÞ/ð26Þ
-
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.00
1.05
1.10
1.15
1.20
Rb = 6.5 x 10-8 m2K/W
k/k f
Volume fraction φ (v%)
Experiment (NF1)
Hamilton-Crosser model (Eq. (26)) Maxwell-Garnett model (Eq.
(28))
(a)
(b)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.00
1.05
1.10
1.15
1.20
Rb = 6.5 x 10-8 m2K/W
R2 = 0.9962
k/k f
Volume fraction φ (v%)
Experiment (NF1)
Hamilton-Crosser model (Eqs. (21) & (26))(aa/a = 4.12, M =
1.8) Maxwell-Garnett model (Eqs. (21) & (28))(aa/a = 4.12, M =
1.8))
Fig. 4. The relative thermal conductivity of NF1 as a function
of nanoparticlevolume fraction.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
R2 = 0.9843Rela
tive
visc
osity
μr
Volume fraction φ (v%)
Experiment (NF1) Batchelor model (Eq. (11)) Batchelor model
(Eqs. (11) & (21)) (aa/a = 4.12, M = 1.8)
(a)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Rela
tive
visc
osity
μr
Volume fraction φ (v%)
Experiment (NF2) Infinitely dilute (Eqs. (14) & (15)) Dilute
(Eqs.(15) & (18)) Semi-dilute (Eq. (19)) Concentrated (Eq.
(20))
(b)
(c)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
R2 = 0.9920
aa/a = 1.48, M = 1.95
Rela
tive
visc
osity
μr
Volume fraction φ (v%)
Experiment (NF2)
Infinitely dilute (Eqs. (14) & (15)) Dilute (Eqs. (15) &
(18)) Semi-dilute (Eq. (19)) Concentrated (Eq. (20))
Fig. 3. The relative viscosity of nanofluids at various
nanoparticle volume fractions.
L. Yu et al. / Experimental Thermal and Fluid Science 37 (2012)
72–83 77
where the shape factor is n = 3/w, and w is the sphericity
defined asthe ratio of the surface area of a sphere (with the same
volume asthe given particle) to the surface area of the particle.
For sphericalparticles, w = 1. Eq. (26) reduces to the classical
Maxwell model
kr ¼1þ 2b/1� b/ ð27Þ
where b = (kp � kf)/(kp + 2kf). To account for the interfacial
thermalresistance, the Maxwell–Garnett model [33] predicts
kr ¼ð1þ 2aÞ þ 2/ð1� aÞð1þ 2aÞ � /ð1� aÞ ð28Þ
where a = 2Rb kf/D and Rb is the interfacial resistance. The
actual va-lue of Rb is difficult to measure directly, but molecular
dynamicssimulations suggest it is typically on the order of
10�8–10�9 m2 K/W [15].
For dilute suspensions containing randomly dispersed spheroi-dal
particles, Nan et al. [33] developed a model for the
relativethermal conductivity
kr ¼ 1þ/ð2b11 þ b33Þ
3� /ð2b11L11 þ b33L33Þð29Þ
where
bii ¼ ðkii � kf Þ=½kf þ Liiðkii � kf Þ� ð30Þ
The depolarization factors for prolate spheroids, Lii (i = 1, 2
and 3),are
-
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.41.00
1.05
1.10
1.15
1.20
R2 = 0.9582
Rb = 1.24 x 10-8 m2K/W
k/k f
Volume fraction φ (v%)
Experiment (NF2)
Nan et al. model (Eq. (29)) Nan et al. model (Eqs. (21) &
(29)) (aa = 1.48 and M = 1.95)
Fig. 5. The relative thermal conductivity of NF2 as a function
of nanoparticlevolume fraction.
78 L. Yu et al. / Experimental Thermal and Fluid Science 37
(2012) 72–83
L11 ¼r2
2ðr2 � 1Þ �r
2ðr2 � 1Þ3=2cosh�1r and L33 ¼ 1� 2L11 ð31Þ
and the equivalent thermal conductivities along the two
spheroidalaxes are
k11 ¼kp
1þ 2kpRb=dand k33 ¼
kp1þ 2kpRb=l
ð32Þ
Fig. 4 illustrates the comparison of the measured relative
ther-mal conductivity of NF1 with the predictions from the
Hamilton–Crosser model and the Maxwell–Garnett model. In their
originalforms, both models significantly underpredict the
experimentaldata, as shown in Fig. 4a. If the particle aggregation
effect is consid-ered, the effective volume fraction used in the
viscosity calculationof NF1 (Eq. (21) with aa/a = 4.12 and M = 1.8)
can be applied in theestimate of the effective thermal
conductivity. The new results areplotted in Fig. 4b. The
Hamilton–Crosser model is seen to overesti-mate the thermal
conductivity. The accuracy of the Maxwell–Gar-nett model is
affected by the choice of Rb, which is used here as afitting
parameter. By using regression analysis, it is found that forRb =
6.5 10�8 m2 K/W, the Maxwell–Garnett model offers thebest
prediction of the experimental data with R2 = 0.9962. For
sim-plicity, the experimental data are correlated by a linear
function ofthe nanoparticle volume fraction
k=kf ¼ 1þ 7:6661/ for NF1 ð33Þ
Fig. 5 shows the comparison of the measured relative
thermalconductivity of NF2 with predictions from the Nan et al.
model[34]. Clearly, the original model fails to predict the
experimentaldata satisfactorily. However, when the effective volume
fraction(Eq. (21) with aa/a = 1.48 and M = 1.95) and Rb = 1.24 10�8
m2 K/W are used, the modified model offers a much betterprediction
of the experimental data (R2 = 0.9582). In light of thecomplexity
of the Nan et al. model, a simple correlation was pro-posed to
predict the effective thermal conductivity of nanofluidscontaining
nanorods
k=kf ¼ 1þ 9:4539/ for NF2 ð34Þ
In the above discussions, the nanofluids are regarded as a
ma-trix-based composite material whose effective thermal
conductiv-ity depends on the constituent materials, the volume
fraction andthe size/shape of the filler nanoparticles. On the
other hand, thethermal conductivity of nanofluids is also
critically affected by
the distribution and the relative orientation of nanoparticles
withrespect to the temperature field [40]. As depicted in Fig. 6,
thereare four possible particle configurations in the
particle–fluid sus-pension, namely, the parallel, series,
Hashin–Shtrikman (or H–S)and EMT configurations. In each
representative cell, the heat fluxis applied from the bottom
boundary to the top. When the particlesare continuously configured
in parallel with or perpendicular tothe direction of the
temperature gradient, the effective thermalconductivity can be
described by the parallel or the series model[35,36]
Parallel model k ¼ ð1� /Þkf þ /kp ð35Þ
Series model k ¼ 1ð1� /Þ=kf þ /=kpð36Þ
The parallel and series models represent the upper and
lowerbounds over all possible structures of a heterogeneous
material.In the H–S configuration, the discrete particles are
uniformly dis-tributed without direct contact with each other. The
correspondingeffective thermal conductivity is given by [37]
ke ¼ kp þ1� /1
km�kp þ/
3kp
ð37Þ
In real particle suspensions, the particle distribution is
neither con-tinuous nor uniform, but rather in the form of the EMT
structure,i.e., a random distribution. For such kind of particle
dispersion,the effective thermal conductivity is predicted by the
EMT model[38,39]
k ¼ ð3/� 1Þkp þ ½3ð1� /Þ � 1�kf�þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½ð3/�
1Þkp þ ½3ð1� /Þ � 1�kf �2 þ 8kf kp
q �=4 ð38Þ
For these four particle configurations of the Al2O3-PAO
nanofluids(kp/kf = 348), the theoretical predictions of the
relative thermalconductivity are plotted in Fig. 7 over the full
range of volume frac-tion (0 6 / 6 1). At any given particle
concentration, the highestthermal conductivity is obtained in the
parallel structure whereheat is conducted through the parallel
pathways formed by thealigned particles. In contrast, the lowest
possible thermal conduc-tivity occurs in the series structure.
In almost all heat transfer experiments of nanofluids
(includingthe present one), the effective thermal conductivity was
measuredunder static conditions, where the nanoparticles were
assumed todisperse either randomly or uniformly in the base fluid.
However,the thermal conductivity data of NF2 (shown as the inset in
Fig. 7)lie between the predictions of the parallel model and the
EMT/H–Smodel, suggesting that the actual distribution of the
nanorods isneither completely orderly nor completely random.
Furthermore,when the nanofluid flows through a circular channel, a
velocitygradient exists along the radial direction which gives rise
to a shearfield. The shear stress will align the non-spherical
particles withthe flow direction, as schematically depicted in Fig.
8 [20]. Afterthe flow becomes hydrodynamically fully developed, a
particle–fluid structure similar to the series configuration in
Fig. 7 will beformed. Consequently, it is reasonable to expect that
the actualthermal conductivity of nanofluids containing rod-like
particlesin the convective flow would be less than that is measured
understatic conditions. The reduced effective thermal conductivity
willadversely affect the convective heat transfer performance of
thenanofluids.
5.3. Pressure drop
Control experiments were first performed with the base
fluid(PAO) to obtain baseline information for single-phase
thermal
-
series TMElellarap H-S
q’’
particle
series TMElellarap H-S
q’’q’’
particle
Fig. 6. Four possible particle configurations in particle
suspensions.
φ(v%)
k/k f
0 20 40 60 80 1000
50
100
150
200
250
300
350kparallelkEMTkHashin-Shtrikmankseries
series
parallel
EMT
H-S
q’’q’’
particlemediumparticlemedium
0 0.5 1 1.51
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4Experiment (NF2)kparallelkEMTkHashin-Shtrikmankseries
Volume fraction φ (v%)
Fig. 7. Effective thermal conductivity for various particle
configurations.
L. Yu et al. / Experimental Thermal and Fluid Science 37 (2012)
72–83 79
transport of nanofluids. For laminar flow, the
Hagen–Poiseuilleequation [15] can be used to predict the friction
factor for hydrody-namically fully developed condition
f � Re ¼ 64 ð39Þ
and the Shah equation [40] is used to account for the
developinglength effect
fappRe 43:44ffiffiffi
1p þ 16þ 0:31251� 3:44=
ffiffiffi1p
1þ 2:12 10�4=12
!ð40Þ
where f = (x/D)/Re. Fig. 9 depicts the measured friction factor
of thePAO fluid as a variation of the Reynolds number. The
experiments inthis work were conducted over the same flow rate
range(50�200 mLPM) as for water in the previous work [13];
however,
u δ
δ
Hydrodynamic entrance reg
u δ
δ
Hydrodynamic entrance reg
Fig. 8. Shear-induced alignment of rod-like nanopar
the maximum Re achieved was much lower (Re 6 460) due to thehigh
viscosity of PAO. Consequently, the hydrodynamic entrancelength (L+
0.056 Re�D) is less than 9.2% of the total channel lengtheven at
the highest Reynolds number. Therefore, the entranceregion effect
is insignificant in all the experiments conducted.Fig. 9 shows the
experimental data agree quite well with the predic-tions from Eqs.
(39) and (40), except for the low Re region where themeasurement
uncertainty is relatively high (the maximum uncer-tainty is
13.8%.).
The pressure drop experiments were conducted for NF1 andNF2 with
volume concentrations of 0.65 vol% and 1.3 vol%, respec-tively.
Pressure drop across the length of the minichannel is
firstpresented in Fig. 10 as a function of the flow rate. It shows
nanofl-uids (both NF1 and NF2) incur higher pressure drop than the
basefluid at the same flow rate, and the difference enlarges
withincreasing particle volume fraction. Further, the pressure drop
ofNF2 is always greater than that of NF1 at the same volume
fraction,an observation consistent with the viscosity measurements
inFig. 3. Fig. 11 shows the measured friction factor of the
nanofluidsas a variation of the Reynolds number. At medium to high
Re, the fmeasurements of NF1 match the Shah prediction fairly well.
Incontrast, the data for NF2 show appreciable deviation in the
samerange of Re, i.e., dropping below the theoretical prediction.
Thismay be attributed to the strong alignment of the nanorods
underthe shear stress causing the effective viscosity of nanofluids
to de-crease in a manner similar to shear thinning.
5.4. Convection heat transfer
The local Nusselt number results of PAO are shown in Fig. 12 asa
function of x� (=x/(D Re Pr)). Due to the large Prandtl number
ofPAO (61.6 < Pr < 87.1), the thermally developing flow
behaviorcan be clearly identified: Nux approaches infinity at x� =
0 and rap-idly decays as x� decreases, and Nux does not reach the
asymptot-ical (fully developed) value, i.e., Nu = 4.36, over the
range of x�
studied in this work. The experimental data can be
reasonablycorrelated by the Shah–London equation [41].
ion
r
Fully developed region
q’’
ion
r
Fully developed region
q’’
ticles in the convective flow through a channel.
-
Flow rate Q (mLPM)
Pres
sure
drop
ΔP(k
Pa)
50 100 150 20060
80
100
120
140
160
180
200
220
240
260
PAO0.65 v% NF11.3 v% NF10.65 v% NF21.3 v% NF2
Fig. 10. Pressure drop across the minichannel versus flow
rate.
Reynolds number
Fric
tion
fact
or f
100 200 300 400 500
0.2
0.4
0.6
0.8
10.65 v% NF11.3 v% NF10.65 v% NF21.3 v% NF2Hagen-Poiseulle
equationShah equation
Fig. 11. Friction factor of nanofluids as a function of Reynolds
number.
x*
Loca
lNu
ssel
tnu
mbe
rN
u x
0 0.01 0.02 0.030
2
4
6
8
10
12
14
16
18
TC1TC2TC3TC4TC5Shah-London correlation
Nu = 4.36
Fig. 12. Local Nusselt number versus x� (heat flux q00 = 6.5
kW/m2).
Reynolds number
Fric
tion
fact
or f
100 200 300 400 500
0.2
0.4
0.6
0.8
1
PAOShah equationHagen-Poiseuille equation
Fig. 9. Friction factor of PAO versus Reynolds number.
80 L. Yu et al. / Experimental Thermal and Fluid Science 37
(2012) 72–83
Nux¼1:302=ðx�Þ1=3 � 1 for x� 6 0:000051:302=ðx�Þ1=3 � 0:5 for
0:0005 6 x� 6 0:00154:364þ8:68ð1000x�Þ�0:506e�41x� for x� P
0:0015
8><>:
ð41Þ
Convective heat transfer experiments were conducted for NF1and
NF2 with the volume concentrations of 0.65 and 1.3
vol%,respectively. The local heat transfer coefficients measured at
fiveaxial locations (TC1 through TC5) are presented in Fig. 13
forRe = 350 and 490. It is found that the convective heat transfer
ofnanofluids is enhanced as compared to the base fluid, and
theincrement increases proportionally to Re and /. Further, the
per-centile enhancement of local heat transfer coefficient is
higher nearthe channel entrance than at the downstream locations.
For in-stance, in Fig. 13a, the enhancement in hx for 1.3% NF2 is
28.7%near the entrance, but it decreases to less than 21% near the
chan-nel exit. This trend strengthens with increasing Re and /.
More interestingly, it can be observed that hx for 0.65 vol%
NF2always exceeds hx for NF1 at both concentrations (0.65 and1.3
vol%). This finding is unexpected because the measurementdata in
Figs. 5 and 6 suggest that the thermal conductivity for0.65 vol%
NF2 (k/kf = 1.076) is only slightly higher than that for0.65 vol%
NF1 (k/kf = 1.053), but is lower than that for 1.3 vol%NF1 (k/kf =
1.098). When the shear-induced particle alignment isconsidered, an
even larger discrepancy emerges. Since the seriesstructure can form
more easily in nanofluids containing rod-likeparticles (as shown in
Fig. 8), which represents the least effectivepathway for thermal
energy transport, the convective heat transferof NF2 would be lower
than that of NF1 at the same particlevolume concentration. However,
this conjecture is in direct contra-diction to the results shown in
Fig. 13.
The paradox may be explained qualitatively by examining
theperiodic orientational motions of rod-like particles in a shear
flow[42–45]. Single rod-like particle tends to align its long axis
with theflow direction. Unless perfectly aligned, the shear
velocities will be
-
(a)
(b)
x/D
h x(W
/m2 .K
)
0 50 100 150 2000
500
1000
1500
2000
PAO0.65 v% NF11.3 v% NF10.65 v% NF21.3 v% NF2
Re = 350
x/D
h x(W
/m2 .K
)
0 50 100 150 2000
500
1000
1500
2000
PAO0.65 v% NF11.3 v% NF10.65 v% NF21.3 v% NF2
Re = 490
Fig. 13. Local convective heat transfer of nanofluids (heat flux
q00 = 6.5 kW/m2).
(a)
(b)
x*
Loca
lNus
selt
num
berN
u x
0 0.01 0.02 0.030
2
4
6
8
10
12
14
16
18
TC1TC2TC3TC4TC5Shah-London correlationNu = 4.36
x*
Loca
lNus
selt
num
berN
u x
0 0.01 0.02 0.030
2
4
6
8
10
12
14
16
18
TC1TC2TC3TC4TC5Shah-London correlationNu = 4.36
Fig. 14. The local Nusselt number for NF1 as a function of x�
(heat flux q00 =6.5 kW/m2) for: (a) 0.65 vol%, and (b) 1.3
vol%.
L. Yu et al. / Experimental Thermal and Fluid Science 37 (2012)
72–83 81
slightly different at the two ends of the rod, causing the rod
torotate periodically about its center to trace out the so-called
Jefferyorbits [46]. In colloidal suspensions of sufficiently high
concentra-tion, the particles interact with their neighbors and are
forced toperform the orientational motion collectively, which can
be de-scribed by the ‘‘director’’, i.e., the average orientation of
the rods.At low shear rates, the director performs a ‘‘tumbling’’
or ‘‘kaya-king’’ motion in which the director rotates slowly when
it is nearlyaligned with the flow direction, and rotates rapidly
when its longaxis makes a non-zero angle with the shear plane. At
intermediateshear rates, the director will oscillate up and down in
the shearplane in a symmetrical way about the flow direction,
transitioninginto the ‘‘wagging’’ motion. At further increased
shear rate, thewagging motion is suppressed until the director is
arrested makinga stationary orientation at a small angle with
respect to the flowdirection. Clearly, the periodic orientational
motions of the rod-likeparticles, either tumbling, kayaking or
wagging, will create distur-bances to the local flow field, acting
in the role of turbulent eddiesto promote the convective heat
transfer. Furthermore, when thenanorods rotate in the thermal
boundary layer, their two endsexperience periodically higher
temperature in the near-wall regionand lower temperature in the
near-bulk region. Since heat can be
conducted effectively from the hot end to the cold end of the
highlyconductive nanorods, they may act as nanoscale heat pumps
totransfer heat into the bulk of the fluid. Indeed, the results
inFig. 13 suggest that the heat transfer enhancement due to the
peri-odic orientational motion of the nanorods in NF2 not only
offsetsthe adverse effect of reduced effective thermal conductivity
dueto the shear-induced particle alignment, but it also surpasses
theheat transfer augmentation in NF1 due to higher particle
volumefraction.
Finally, the local Nusselt number measurements are plotted
inFigs. 14 and 15 as a function of x⁄ for NF1 and NF2,
respectively.Fig. 14 shows that the experimental data of NF1
closely matchthe predictions from Shah–London’s correlation at both
volumefractions of 0.65 and 1.3 vol%. In Fig. 15, the measured Nux
initiallyfollows the Shah–London prediction, but drops rapidly with
a slopemuch steeper than the theoretical curve as x� increases.
Unlike PAOand NF1, the Nux results for NF2 at different axial
locations are dis-persive and no common trend line can be found.
Rather than a newphysical phenomenon, this should be interpreted as
an artifactwhich may be attributed to the effects of shear-induced
motionof rod-like particles on the effective thermal conductivity.
In
-
(a)
(b)
x*
Loca
lNus
selt
num
berN
u x
0 0.01 0.02 0.030
2
4
6
8
10
12
14
16
18
TC1TC2TC3TC4TC5Shah-London correlationNu = 4.36
x*
Loca
lNus
selt
num
berN
u x
0 0.01 0.02 0.030
2
4
6
8
10
12
14
16
18
TC1TC2TC3TC4TC5Shah-London correlationNu = 4.36
Fig. 15. The local Nusselt number for NF2 as a function of x�
(heat flux q00 =6.5 kW/m2) for: (a) 0.65 vol%, and (b) 1.3
vol%.
82 L. Yu et al. / Experimental Thermal and Fluid Science 37
(2012) 72–83
calculating Nux (=hxD/k), hx is taken from the data of
convectiveheat transfer experiments using Eq. (5), but k is from
conductivitymeasurements obtained under static conditions. As
already dis-cussed, the actual thermal conductivity of NF2 depends
stronglyon the shear field as the result of the shear-induced
alignmentand orientational motion of the nanorods. Hence it is the
use ofstatic measurement of k that leads to the artifact shown
inFig. 15. Consequently, certain caution must be exercised whenthe
convective heat transfer performance is evaluated on the basisof
conventional dimensionless numbers, such as Nu, for
nanofluidscontaining non-spherical particles.
6. Conclusions
An experimental study was conducted to investigate the
ther-mophysical properties and convective heat transfer
characteristicsof Al2O3-PAO nanofluids containing both spherical
and rod-likenanoparticles. The effective viscosity and thermal
conductivity ofthe nanofluids were measured, and the results were
comparedwith predictions from several existing theories in the
literature.It was found that, in addition to the particle volume
fraction, other
parameters including the aspect ratio, dispersion state and
aggre-gation of nanoparticles as well as the shear field have a
significantimpact on the effective properties, especially for
nanofluids con-taining non-spherical particles. The pressure drop
and convectionheat transfer coefficient were also measured for the
nanofluids inthe laminar flow regime. Although established
theoretical correla-tions provide satisfactory prediction of the
friction factor and Nus-selt number for nanofluids containing
spherical nanoparticles, theyfail for nanofluids containing
rod-like nanoparticles. The resultsindicate that in a convective
flow, the shear-induced alignmentand orientational motion of the
particles must be considered inorder to correctly interpret the
experimental data of nanofluidscontaining non-spherical
nanoparticles. Findings from this studyimply that, if external
means (such as electromagnetic force orshear field) are applied to
manipulate the states of dispersionand orientation of the
nanoparticles in the base medium, thermaltransport of the
nanofluids can be strategically controlled to yieldoptimal
performance.
Acknowledgments
The authors are grateful to Prof. Suresh Garimella at
PurdueUniversity and Dr. Lois Gschwender at Air Force Research
Labora-tory for their assistance with initiating this work. They
acknowl-edge the financial supports from the University of Houston,
theCooling Technologies Research Center (a National Science
Founda-tion Industry/University Cooperative Research Center) at
PurdueUniversity and the National Science Foundation (Grant
No.0927340).
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Laminar convective heat transfer of alumina-polyalphaolefin
nanofluids containing spherical and non-spherical nanoparticles1
Introduction2 Experiments and methods2.1 Preparation of
nanofluids2.2 Viscosity and thermal conductivity measurements2.3
Convective heat transfer experiments
3 Data reduction4 Measurement uncertainties5 Results and
discussion5.1 Viscosity5.2 Thermal conductivity5.3 Pressure drop5.4
Convection heat transfer
6 ConclusionsAcknowledgmentsReferences