This study presents an experimental study of the effect of solid volume fraction and Reynolds number on heat transfer coefficient and pressure drop of CuO-Water nanofluid. Pure Water and nanofluid with particle volume fractions of 0.0625%, 0.125%,

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Experimental study of the effect of solid volume fraction and Reynoldsnumber on heat transfer coefﬁcient and pressure drop of CuO–Waternanoﬂuid
Majid Zarringhalam
a
, Arash Karimipour
b
, Davood Toghraie
a,
⇑
a
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
b
Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
a r t i c l e i n f o
Article history:
Received 25 October 2015Received in revised form 25 March 2016Accepted 27 March 2016Available online 30 March 2016
Keywords:
CuO–Water nanoﬂuidHeat transfer coefﬁcientPressure dropSolid volume fraction
a b s t r a c t
Thisstudy presentsanexperimental studyof theeffect of solidvolume fractionandReynolds numberonheat transfer coefﬁcient and pressure drop of CuO–Water nanoﬂuid. Pure Water and nanoﬂuid with par-ticle volume fractions of 0.0625%, 0.125%, 0.25%, 0.5%, 1%, 1.5% and 2% are used as working ﬂuids.Nanoﬂuids were ﬂowed inside a horizontal double-tube counter ﬂow heat exchanger under turbulentﬂow regime. Flow Reynolds numbers of each volume fraction of nanoﬂuid were between from 2900 to18,500 during the experiments. The Result shows that generally heat transfer coefﬁcient of nanoﬂuidsis higher than that of base ﬂuid. Moreover, it is observed that heat transfer coefﬁcient and Nusselt num-berofnanoﬂuidsincreaseswithanincreaseinsolidvolumefractionandReynoldsnumber.Buttherateof thisincreaseinlowReynoldsnumberswasmorethanthatathighReynoldsnumbers.Themeasurementsalso show that the pressure drop of nanoﬂuid is slightly higher than that of the base ﬂuid and increaseswith anincrease inthe nanoparticles volume fraction. But the rateof this increase in lowReynolds num-bers was more than that at high Reynolds numbers. Therefore, it can be concluded that the effect of increasing percentage of nanoparticle in low Reynolds number of this research is stronger than that of high Reynolds number. Moreover, friction factors were calculated and compared with blasious correla-tion. Finally, in order to ﬁnd the optimum condition of this nanoﬂuid for practical applications, thermalperformance factor was deﬁned to consider increasing Nusselt ratio besides increasing friction ratiosimultaneously. The results show that the maximum thermal performance factor of this nanoﬂuid was1.266, which was calculated for 2% nanoparticle volume fraction at Reynolds number 3677.
2016 Elsevier Inc. All rights reserved.
1. Introduction
Nowadays, cooling and heating of industrial systems with highheat ﬂux such as nuclear fusion, microelectronics mechanicalsystem (MEMS) and micro chemical reactions are the reasons forstrong challenges among engineering designers. On the one side,convective properties of conventional ﬂuids such as water, differ-ent types of oils and ethylene glycol play an important role inexchanging thermal energy for efﬁcient heat exchangers; on theother hand, poor thermal properties of these ﬂuids are an obstaclefor designers to increase heat transfer and reduce the size of heatexchangers. One of the best solutions to the aforementionedproblemis suspendingsmall amounts of nanoparticlesinto formerconventional heat ﬂuids. This type of ﬂuid is called nanoﬂuid. Inrecent years, many researchers have investigated heat transfercharacteristics of different nanoﬂuids. Experimental study of researchers shows that effects of some parameters such as solidvolume fraction, shape, size and material characteristics of nanoparticlesbesidesexperimentalconditionsplayveryimportantroles in heat transfer coefﬁcients.In an experimental investigation, Pak and Cho [1], studied theconvective heat transfer of Al
2
O
3
–Water and TiO
2
–Water nanoﬂu-ids under laminar and turbulent ﬂow regimes. They showed thatNusselt number (Nu) enhanced with increasing particle volumefraction as well as Reynolds number augmentation. They alsoreported reduction range of 3–12% of heat transfer coefﬁcient forTiO
2
–water nanoﬂuid with 3% volume concentration of nanoparticles.Xuan and Li [2] experimentally investigated heat transfer char-acteristics of Cu–Water nanoﬂuid, ﬂowing straight through a tube
http://dx.doi.org/10.1016/j.expthermﬂusci.2016.03.0260894-1777/
2016 Elsevier Inc. All rights reserved.
⇑
Corresponding author.
E-mail addresses:
st_m_zarringhalam@azad.ac.ir (M. Zarringhalam),Arashkarimipour@gmail.com (A. Karimipour), Toghraee@iaukhsh.ac.ir(D. Toghraie).Experimental Thermal and Fluid Science 76 (2016) 342–351
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science
journal homepage: www.elsevier.com/locate/etfs
with constant heat ﬂux under both laminar and turbulent ﬂowconditions, and foundthat suspendednanoparticles withdiameterbelow100nminbaseﬂuidcanincreaseheattransfercoefﬁcientof conventional base ﬂuid considerably; while friction factor did notincrease remarkably during the experiment. According to theirresult, heat transfer coefﬁcient of conventional base ﬂuid canenhanceabout60%bysuspending2%nanoparticlevolumefractionwithout signiﬁcant augmentation of pressure drop. Furthermore,theyproposedanewconvectiveheattransfercorrelationtopredictheat transfer coefﬁcient of the nanoﬂuid under turbulent and lam-inar ﬂow conditions.WenandDing[3]carriedoutanexperimentalstudyontheheattransfer characteristics of Al
2
O
3
–Water nanoﬂuid in a copper tubewith constant heat ﬂux under laminar ﬂow. Diameter range of nanoparticles was 27–56nm. They observed that the convectiveheat transfer increases by enhancement of nanoparticles volumeconcentrationandReynoldsnumber.Moreover,inentranceregion,heat transfer augmentation is high and decreases by increment of axial distance. They also reported that those nanoparticles candecline thermal boundary layer thickness.He et al. [4] investigated heat transfer and ﬂow behavior of aqueous suspensions of TiO
2
nanoparticles ﬂowing upwardthrough a vertical pipe under both laminar and turbulent ﬂowregimes. They observed that in speciﬁed nanoparticles size andReynolds number, the convective heat transfer coefﬁcientincreased with enhancement of volume concentration of nanopar-ticle while pressure drop did not increase remarkably. They alsoreported that heat transfer coefﬁcient is sensible with nanoparti-cles size.Herisetal. [5,6]reportedanexperimentwhichstudiedthecon-vective heat transfer coefﬁcient of CuO–Water and Al
2
O
3
–Waternanoﬂuids under laminar and turbulent ﬂow condition ﬂowing ina circular tube exposed to saturated vapor due to ﬁx constant walltemperature boundary condition. The result of this experimentshowed that convective heat transfer coefﬁcient (
h
) of bothnanoﬂuids increased with increasing Peclet number and volumeconcentration of nanoparticles. Moreover, this increase (h) inAl
2
O
3
–Water nanoﬂuid was more than that in CuO–Waternanoﬂuid.DangthongsukandWongwises[7]experimentallyprobednano-ﬂuid with 2% volume concentration of suspended TiO
2
nanoparti-cles into water base ﬂuid ﬂowing in a double tube counter ﬂowheat exchanger and found that the convective heat transfer coefﬁ-cient of nanoﬂuid was higher than that of the water base ﬂuid byabout 6–11% with a little penalty of pressure drop. Moreover theypublished their next experiment [8] with the same test set up andnanoﬂuidas thatinthelast experiment[7] reportingthatdifferentthermo physical models have no strong effects on the predicationof convective heat transfer coefﬁcient of the nanoﬂuid, and thatcredibility and precision of experimental heat transfer coefﬁcientis related to calibration of experimental system more thanthermo-physical models of nanoﬂuid.Nguyen et al. [9] and Anoop et al. [10] experimentally investi-
gated the effect of nanoparticle size of Al
2
O
3
–Water nanoﬂuidandconcludedthatsmallersizeofsuspendednanoparticlesincon-ventional base ﬂuid causes higher heat transfer coefﬁcient thantheir larger sizes.In an experimental study, Ding et al. [11] considered the con-vective heat transfer of CNT-distilled Water nanoﬂuid under lami-nar ﬂow condition and concluded that the local convective heattransfer coefﬁcient may be as a function of ﬂow characteristics,CNT concentration and PH value. But among prementioned effec-tive parameters, pH value has the least effect on the convectiveheat transfer coefﬁcient of the nanoﬂuid.Chandrasekar et al. [12] experimentally studied Al
2
O
3
–Waternanoﬂuid ﬂowing inside a tube with and without wire coil insertsunder both laminar and turbulent ﬂow conditions. They reportedthat the heat transfer performance of Water base ﬂuid increasesevenwithsmallamountsofnanoparticles(0.1%volumeconcentra-tion). Furthermore, wire coil inserts with different pitch ratioscouldbeeffectiveontheheattransferperformance;whilepressuredrop was approximately as much as base liquid for givenconditions.Dangthongsuk and Wongwises [13] experimentally investi-gated heat transfer performance for the nanoﬂuid, which containsdifferentvolumefractions(0.2–2%)ofTiO
2
nanoparticleandWaterbase ﬂuid ﬂowing inside a double tube counter ﬂow heat exchan-gerunderturbulentﬂowcondition.Theyreportedtheheattransfercoefﬁcient of nanoﬂuids is higher than that of the conventionalbase ﬂuid and increases with enhancement of Reynolds numberand volume concentration of nanoparticles. But the heat transfercoefﬁcient of the nanoﬂuid with 2% particle concentration wasabout14%lowerthanthatofthebaseﬂuid;whereas,pressuredropwas higher. They also presented new correlations for the predic-tion of Nusselt number and friction factor of the nanoﬂuid.Fotukian and Nasr Esfahani [14] experimentally investigatedturbulent convective heat transfer and pressure drop of diluteCuO–Water nanoﬂuid inside a circular tube. Results showed thatheat transfer coefﬁcient increased by suspending small amountsof nanoparticles to the base ﬂuid. They reported average 25%enhancement of heat transfer coefﬁcient and 20% pressure dropaugmentation.
Nomenclature
Cp
speciﬁc heat, J/kg K
k
thermal conductivity, W/m K
L
tube length, m
Nu
Nusselt number
Re
Reynolds number
T
temperature, K
V
mean velocity, m/s
m
mass ﬂow rate, kg/s
d
tube diameter, m
h
heat transfer coefﬁcient, W/m
2
K
f
friction factor
Greeks
D
p
pressure drop, pa
u
nanoparticles volume fraction
t
viscosity, m
2
s
q
density, kg/m
3
g
thermal performance factor
Subscriptsbf
base ﬂuid
nf
nanoﬂuid
in
inlet
out
outlet
m
mean
b
bulk
p
nanoparticle
w
water
U
uncertainty
M. Zarringhalam et al./Experimental Thermal and Fluid Science 76 (2016) 342–351
343
In an experimental investigation Amrollahi et al. [15] studiedconvection heat transfer of functionalized MWNT in aqueous ﬂuidﬂowing at the entrance region of horizontal tube under laminarand turbulent ﬂow condition. They reported heat transfer coefﬁ-cient enhancement by about 33–40% compared to base ﬂuid atgiven conditions.Hashemi and Akhavan-Behabadi [16] reported an experimentalstudy of heat transfer and pressure drop characteristics of CuO–base Oil nanoﬂuid ﬂowing in a horizontal helically coiled tubeunder constant heat ﬂux and found that heat transfer coefﬁcientand pressure dropincreasedby increasingnanoparticleconcentra-tion. Moreover, theyreportedthatusingahelical tube, insteadof astraighttubeisamoreeffectivewaytoincreaseheattransfercoef-ﬁcient compared to suspending nanoparticles to the base ﬂuid.Hojjat et al. [17] experimentally studied convective heat trans-ferofnonNewtoniannanoﬂuidsthroughauniformlyheatedcircu-lar tube and observed that convective heat transfer increases byincreasing nanoparticles concentration and decreases with axialdistance from the entrance region.Kayhanietal. [18], inanexperimentalstudy, probedconvectiveheattransferandpressuredropofTiO
2
–Waternanoﬂuidthroughauniformly heated horizontal circular tube. They reported that heattransfer coefﬁcient ratio increases by increasing nanoparticles vol-umeconcentration.Butit doesnotalterwithvariationof Reynoldsnumber.Syam Sundar et al. [19] carried out an experimental investiga-tion on the effect of twisted tape insert on the heat transfer andfriction factor enhancement with Fe
3
O
4
magnetic nanoﬂuid insidea plain tube, and concluded better heat transfer rate when the cir-cular tube contains a twisted tape insert.HemmatEsfeetal.[20]investigatedexperimentallytheconvec-tive heat transfer performance of MgO–Water nanoﬂuid with dif-ferent volume fractions of particle under turbulent ﬂowcondition.Theyreportedthatadditionof smallamountsofparticleinto Water base ﬂuid can increase heat transfer. They also com-pared experimental friction factor with Blasious equation.Inthisstudy, calculationof thermal performancefactorshowedthat the nanoﬂuid is a good choice for practical applications.Hemmat Esfe et al. [21] reported an experiment on the heattransfer characteristics and pressure drop of COOH-functionalized DWCNTs–Water nanoﬂuid in turbulent ﬂow atlow concentration range of particle. They observed by about 32%heat transfer enhancement with about 20% penalty of pressuredrop for 0.4% volume concentration of nanoparticles. Furthermore,the result of thermal performance factor revealed that the nano-ﬂuid with 0.4% particle concentration is a good choice to utilizein double tube heat exchangers.Saeednia et al. [22] presented an experimental study on CuO–base oil nanoﬂuid with different particle weight fraction ﬂowinginside a circular tube. They reported that heat transfer coefﬁcientincreases by with increasing nanoparticles weight fraction.Abbasian and Amani [23] published an experimental study onthe effect of diameter on heat transfer performance and pressuredrop of TiO
2
–Water nanoﬂuid ﬂowing in a horizontal double tubecounter ﬂow heat exchanger. They reported that Nusselt numberdoesnotgenerallyincreasebydecreasingthediameterofnanopar-ticles. They also achieved the highest thermal performance factorwith 20nm particle size diameter.It can be noted that previous studies, did not considered differ-enthighvolumeconcentrationofCuO–Waternanoﬂuid.Since,thisarticle analyze and compared the results of heat transfer coefﬁ-cient, Nusselt number, pressure drop and friction factor of eightdifferent volume fractions (0–2%) of CuO–Water nanoﬂuid, is veryinterestingissueforfurtherstudy.Also, ﬁnalresultofthisarticleispresent by thermal performance factor which is as a reliable crite-ria to aim for utilizing this nanoﬂuid for practical application.
2. Experiments
2.1. Experimental setup and method
Anexperimentalsetupwasappliedtomeasureconvectiveheattransfercoefﬁcientandpressuredropcharacteristicsinthepresentwork.Fig.1showsaschematicdiagramoftheexperimentalinstru-ment. The apparatus was mainly composed of two centrifugalpumps, a heat transfer test section, a counter ﬂow heat exchanger,a ﬂow meter, a differential pressure transmitter, a bypass valve, areservoir, and a digital data logger. The test section is designedso that a small volume of nanoﬂuid (about 2.7L) will be sufﬁcientto investigate the heat transfer performance of nanoﬂuids to holddown costs. This implement is basically provided by three closedloopcycles.Thenanoﬂuidloopiscomposedofapump,acollectiontank, a test section and a Water heat exchanger for cooling theworkingﬂuid.Theheatexchangertestsectionissuppliedbyadou-ble concentric tube. Two calibrated RTD-PT100 types with digitalindicators are mounted at the inlet and outlet of the test sectionto measure the temperatures of the nanoﬂuid with an accuracyof0.1
C.Moreover,eightK-type(Chromel–Alumel)thermocouplesare assembled on the copper tube wall at equal intervals of 13cmto measure the wall temperature with an accuracy of 0.5
C. Twoplastic ﬁttings at inlet and outlet sections of the copper tube pro-vide a thermal blockage against axial heat conduction. In accor-dance with the equation
ð
L
e
=
D
4
:
4
Re
1
=
6
Þ
, the length of thetube in order to create fully developed turbulent ﬂow at Reynoldsnumber of 29,000, is estimated to be about 15cm. The heatedlength of the test section is 111cm. Therefore, it can be concludedthat the ﬂow becomes developed turbulent for all cases studied.The test section is protected by 7cm of ﬁberglass to reduce heatloss to the ambient. To minimize heat loss to the surrounding(ambient air), the test section was insulated with 7cm of ﬁber-glass. The test section was heated by hot Water which ﬂows overa copper tube. The second cycle contains equipment to ﬂow andcontrol the hot Water ﬂowrate at the desired temperature. Atem-perature controller with PT100 sensor was utilized to control thetemperature of hot Water. Two K-type thermocouples wereinserted into the ﬂow at the inlet and outlet of the test section tomeasure bulk temperatures of hot Water. Furthermore, a ﬂowmeter was used to adjust the hot Water ﬂow rate. The third cycleincluded a pump, a nanoﬂuid heat exchanger, a bypass line, a con-densing unit and a temperature controller with a PT100 sensor.This unit controls the temperature of the nanoﬂuid at the inletand outlet of the test section by changing the power of the con-densing unit.Moreover, two valves control the ﬂow rate of this loop cycle atthebypasslineandinletofthetestsection.Adifferentialtransmit-terRosemount3051cd(Rosemount,Inc.USA)measuresﬂowstaticpressure drop of nanoﬂuid along the test section with an accuracyof up to 0.1%. This instrument measured the pressure dropbetween the inlet and outlet of the test section during each exper-iment. The essential parameters that are measured include hotWater and nanoﬂuid ﬂow rate, temperatures and pressure drop.It should be mentioned that all of the thermocouples and temper-aturesensors werecalibratedbefore being insertedtothe test sec-tion. Meanwhile, an ordinary thermometer measures the ambienttemperature.
2.2. Preparation of nanoﬂuid
Preparation of nanoﬂuids is the ﬁrst key step in experimentalstudies with nanoﬂuids. Nanoﬂuids are not simply liquid–solidmixtures. Some special requirements are essential e.g. even andstable suspension, durable suspension, negligible agglomeration
344
M. Zarringhalam et al./Experimental Thermal and Fluid Science 76 (2016) 342–351
of particles, no chemical change of the ﬂuid, etc. In this paper, theCuO–Water nanoﬂuids were supplied by dispersingCuO nano par-ticles in pure Water as base liquid at ambient conditions. Thedesired particles volume concentrations dispersed in this studywere 0.000625 (0.0625%), 0.00125 (0.125%), 0.0025 (0.25%), 0.005(0.5%), 0.01(1%), 0.015 (1.5%) and 0.02 (2%). Total volume of eachnanoﬂuids was about 6L. In this study, CuO–Water nanoﬂuidwas supplied utilizing a two-step method. The two-step methodis extensively used in the synthesis of nanoﬂuids considering theavailable Nano powders. In this method, ﬁrstly, nanoparticles areproduced. Secondly, they are dispersed into conventional baseﬂuid.Duetoadeclineinagglomerationofnanoparticlesinthebaseﬂuid, an ultrasonic vibrator is used to disperse nanoparticlesagainstlargeagglomerates.Theappliednanoparticleswithaveragediameters40nmwereproducedbyUSResearchNanomaterial,Inc.Properties of the applied nanoparticles to the base ﬂuid have beendescribed in Table 1. In this research, nanoﬂuids were prepared bydispersing a speciﬁc amount of CuO in pure Water by using anultrasonic vibrator (Hielscher Company, Germany) for 180min inorder to obtain a dispersed solution which is uniform and stableand break down agglomeration of the nanoparticles. No surfactantwasusedastheymayhavesomeinﬂuenceontheeffectivethermalconductivity of nanoﬂuids. Then nanoﬂuids were poured into thenanoﬂuid reservoir immediately and tests were carried out afterabout 180min when nanoﬂuid ﬂows at its maximum ﬂow rate.As presented by Nasiri et al. [24], in turbulent ﬂow condition, par-ticlessedimentationislessimportantduetogreaterimposedshear
Fig. 1.
Schematics of experimental setup.
Table 1
Properties of CuO nanoparticles with diameter of 40 nm.
Purity (metal basis) 99.5+%Color BlackAPS (nm) 40Morphology Spherical
M. Zarringhalam et al./Experimental Thermal and Fluid Science 76 (2016) 342–351
345
which breaks down agglomeration of particles. Hence, it can bementionedthat turbulenceof ﬂowhelps thestabilityof nanoparti-cles during the tests. Moreover, it is important to note that duringexperiments, no sedimentation was observed even at low ﬂowrates. As noted above, in order to achieve a proper dispersion, itis necessary to repeat mechanical mixing and ultrasonic vibration.After 16h no sedimentation was obvious in any samples of nanoﬂuids.The typical TEM (transmission electron microscope) micro-graph of the CuO nanoparticles with nominal particle size of 40nm is shown in Fig. 2. It was observed that the CuO nanoparti-cles have spherical shapes.The XRD (X-ray diffraction) of the prepared sample are shownin Fig. 3. As shown in Fig. 3, the powder XRD was carried out with
a Rigaka X-ray diffractometer by CuO K
a
1
radiation in the range of 10–90
.
2.3. Data processing
Using the conservation of energy law (ﬁrst law of thermody-namic),convectiveheattransfercoefﬁcient(
h
)andNusseltnumber(
Nu
) of inner tube can be acquired in the equation below:
dT
b
dx
¼
p
_
mC
p
h
ð
T
s
T
b
Þ ð
1
Þ
Separating variables and integrating from the tube inlet to theoutlet, the equation is as follows:
ln
ð
D
T
0
Þ
D
T
i
¼
pL
_
mCp
1
L
Z
L
0
hdx
ð
2
Þ
The following expression is used to calculate the mean heattransfer coefﬁcient,
h
¼
1
L
Z
L
0
hdx
where
h
is the average value of
h
for the entire tube. From the def-inition of the average convection heat transfer coefﬁcient and aftersimplify,
D
T
0
D
T
i
¼
T
s
T
b
;
o
T
s
T
b
;
i
¼
exp
pLmC
p
h
ð
3
Þ
Rearranging Eq. (3) results in:
h
¼
_
mC
p
pL ln T
s
T
b
;
i
T
s
T
b
;
o
ð
4
Þ
Bulk temperature is calculated by:
T
b
¼
T
b
;
i
þ
T
b
;
o
2
ð
5
Þ
Also, Reynolds and Nusselt number are deﬁned as follows:
Re
¼
Vd
m
Nu
¼
hdk
ð
6
Þ
2.4. Uncertainty analysis
Tobesureaboutthereliabilityofexperimentresults,measuringeach data was done for twice. Moreover, for each set of the exper-iment, nanoﬂuid was reﬁlled.The uncertainty of the experimental results was determined bythe measurement errors of the major heat transfer parameters byusing the values presented in Table 2, and based on the methodobtained by Kline and Mcclintock [25]. This method also has beenused by Fakoor et al. [26] and Hemmat Esfe et al. [20]. Assume the
followingequationtocalculatetheuncertaintyof the parameter
R
.
U
R
¼
X
ni
¼
1
@
R
@
V
i
U
V
i
2
"#
12
ð
7
Þ
where
U
R
and
U
V
i
are the uncertainties associated with theparameter
R
and independent variables (
V
i
), respectively. In addi-tion, n is the number of the independent variables. Eqs. (8)–(11)were taken into account to calculate the uncertainty of Reynoldsnumber, convective heat transfer coefﬁcient, Nusselt number andfriction factor,
U
Re
¼
d
m
U
V
2
þ
V
m
U
d
2
þ
Vd
m
2
U
m
2
"#
12
ð
8
Þ
U
h
¼
VdC
p
L U
q
Ln
D
T
i
;
s
D
T
o
;
s
2
þ
q
dC
p
U
V
Ln
D
T
i
;
s
D
T
o
;
s
2
"
þ
q
VC
p
L U
d
Ln
D
T
i
;
s
D
T
o
;
s
2
þ
q
VdC
p
L
2
U
L
Ln
D
T
i
;
s
D
T
o
;
s
2
þ
q
VdC
p
L U
D
T
i
;
s
1
D
T
i
;
s
2
þ
q
VdC
p
L U
D
T
o
;
s
1
D
T
o
;
s
2
#
12
ð
9
Þ
U
Nu
¼
dkU
h
2
þ
hkU
d
2
þ
hdk
2
U
k
2
"#
12
ð
10
Þ
U
f
¼
2
d
q
LV
2
U
D
P
!
2
þ
2
D
P
q
LV
2
U
d
!
2
þ
2
D
Pd
q
2
LV
2
U
q
!
2
þ
2
D
Pd
q
L
2
V
2
U
L
!
2
24
þ
4
D
Pd
q
LV
3
U
v
!
2
35
12
ð
11
Þ
After computing the uncertainty of the Reynolds and Nusseltnumbers, heat transfer coefﬁcient and friction factor at the righthand side of Eqs. (8)–(11), the uncertainty of key parameters wascalculated. Findings are presented in Table 2.
3. Measurements of thermo physical properties of nanoﬂuid
To calculate the heat transfer coefﬁcient for nanoﬂuid, it is nec-essary to apply thermo-physical property models for nanoﬂuids.Thenecessarythermo-physicalpropertiesinthispaperaredensity,
Fig. 2.
Transmission electron microscopy (TEM) image of CuO nanoparticles.346
M. Zarringhalam et al./Experimental Thermal and Fluid Science 76 (2016) 342–351

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