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Journal of Thermal Analysis andCalorimetryAn International Forum for ThermalStudies ISSN 1388-6150Volume 131Number 2 J Therm Anal Calorim (2018)131:1605-1613DOI 10.1007/s10973-017-6694-5
New experimental correlation for thethermal conductivity of ethylene glycolcontaining Al2O3–Cu hybrid nanoparticles
Amir Parsian & Mohammad Akbari
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New experimental correlation for the thermal conductivityof ethylene glycol containing Al2O3–Cu hybrid nanoparticles
Amir Parsian1• Mohammad Akbari2
Received: 23 May 2017 / Accepted: 5 September 2017 / Published online: 21 September 2017
� Akademiai Kiado, Budapest, Hungary 2017
Abstract In the present study, the thermal conductivity of
the Al2O3–Cu/EG has been experimentally investigated.
For this purpose, a mixture of Al2O3 and Cu nanoparticles
with a ratio of 50:50 was dispersed in ethylene glycol at
different concentrations (0.125, 0.25, 0.5, 1.0, 1.5 and 2.0)
and temperatures (25–50 �C). The two-step method is used
for dispersing nanoparticles in the base fluid. Results show
that the thermal conductivity of nanofluid is more than the
base fluid, and it depends on volume concentration and
temperature. Experimental results have been compared
with some of the most famous models, and it has been
found that these models are unable to predict the thermal
conductivity of investigated nanofluid. Finally, based on
the experimental data, a correlation is presented as a
function of the temperature and volume fraction of
nanoparticles.
Keywords Nanofluid � Volume concentration �Temperature � Thermal conductivity � Experimental
correlation
Introduction
Heat transfer plays an essential role in different applica-
tions, such as transportation, power generation, air condi-
tioning, electronic, etc. In most of these applications, heat
transfer is realised through some heat transfer devices such
as heat exchangers, evaporators and condensers. Increasing
the heat transfer efficiency of these devices is highly
important because by increasing the efficiency, the space
occupied by the device and pumping power required for
circulating fluids can be optimised. Consequently, numer-
ous studies and researchers are aimed to increase cooling
performance of the working fluids. One of the most com-
mon methods used to improve the heat transfer efficiency is
increasing the thermal conductivity of the working fluids.
Frequently used heat transfer fluids such as water, oil, and
ethylene glycol have comparatively low thermal conduc-
tivities when compared to the thermal conductivity of solid
particles. By adding proper small solid particles to afore-
mentioned fluids, the thermal conductivity of working
fluids can be increased considerably. The feasibility of
using millimetres or micrometres solid particles was pre-
viously investigated by several researchers. However, the
concept of improving heat transfer by adding convenient
nanoparticles to conventional heat transfer fluids was first
proposed by Chol [1] in 1995.
A variety of nanoparticles such as metallic particles (Al,
Cu, Fe and Ag), nonmetallic particles (Al2O3, TiO2, CuO
and Fe3O4) and carbon nanotubes have been studied by
researchers [2–4]. Wang et al [5] measured the thermal
conductivity of Al2O3/water and Al2O3/ethylene glycol
nanofluids in which the size of particles was 28 nm. They
reported that the thermal conductivity enhancement was
approximately 16 and 24% for the volume fraction of 5.5%
in water and volume fraction of 5% in ethylene glycol,
respectively. Lee et al. [6] performed an experiment to
measure the thermal conductivity of Al2O3 and CuO dis-
persed in water and ethylene glycol for volume fraction
range of 1–4%. Particle sizes of Al2O3 and CuO were 23.6
and 38.4 nm, respectively. Their results revealed that
& Mohammad Akbari
1 Department of Mechanical Engineering, Khomeinishahr
Branch, Islamic Azad University, Khomeinishahr, Iran
2 Department of Mechanical Engineering, Najafabad Branch,
Islamic Azad University, Najafabad, Iran
123
J Therm Anal Calorim (2018) 131:1605–1613
https://doi.org/10.1007/s10973-017-6694-5
Author's personal copy
nanofluids had higher thermal conductivity than the base
fluid, and it relates to the level of volume fraction.
Eastman et al. [7] conducted an experiment to measure the
thermal conductivity of Cu–ethylene glycol nanofluid with
an approximate copper particle size of 10 nm and volume
fraction level of 0.6%. A transient hot–wire method was
used for measurement. They observed that nanofluids had
higher thermal conductivity when the volume fraction level
increased. Chon and Kihm [8] investigated the increase in
thermal conductivity of a nanofluid due to Brownian
motion. Al2O3–water nanofluid with the volume fraction of
1% and particle sizes of 11 nm, 47 nm and 150 nm were
used in this experiment while temperature range was
20–70 �C. They reported that thermal conductivity of the
nanofluid increases more than the base fluid with an
increase in nanoparticles, and rises with the increase in
temperature. They also establish that smaller particle sizes
give higher thermal conductivity. They asserted that the
increase in thermal conductivity of the nanofluid resulted
from Brownian motion or microconvection mechanism.
Chopkar et al. [9] measured the thermal conductivity of
Al2Cu and Ag2Al nanoparticles with the approximate
volume fraction of 0.2–1.5% dispersed in water. The
results indicated the thermal conductivity enhancement of
50–150%. The experimental results and the analytical
study showed that the quality of enhancement extremely
depends on size, volume fraction and shape of the dis-
persed nanoparticles. Sundar and Sharma [10] reported
thermal conductivity enhancement of 6.52% with Al2O3
nanofluid, 24.6% with CuO nanofluid at a volume fraction
of 0.8% compared to water. Yu et al. [11] studied the
thermal conductivity enhancement of stable Cu/EG nano-
fluid. For the concentration of 0.5 vol% at 50 �C, the
enhancement ratio was up to 46%. They concluded that
thermal conductivity depends strongly on the temperature
of the fluid and enhancement ratio increases along with the
rise in temperature. They also discovered that Brownian
motions of Cu nanoparticles have a very important role in
determining the effects of the temperature on thermal
conductivity enhancement of nanofluids.
Chandrasekar et al. [12] measured the thermal properties of
Al2O3–water nanoparticles including effective thermal
conductivity and dynamic viscosity. The results indicated
that the viscosity increase is considerably higher than the
increase in thermal conductivity and that the thermal
conductivity increases linearly by adding more particles.
Khedkar et al. [13] determined the thermal conductivities
of CuO–MEG and CuO–water nanofluids. The results
indicated that by increasing the volume fraction of
nanoparticles, the effective thermal conductivity of the
nanofluid also increased. They also found that the thermal
conductivity of nanofluids was further enhanced as the
sonication time increased until certain limits. The cause of
this phenomenon was believed to be the increase in
Brownian motion and agglomeration of small particles.
Sundar et al. [10] conducted experiments on dispersion
behaviour of Al2O3 and CuO nanoparticles in 50:50% of
EG/water mixture. The thermal conductivity of nanofluids
was measured as a function of nanoparticle concentration
and temperature. The thermal conductivity of Al2O3 and
CuO nanofluids increases with the increase in volume
concentration. The thermal conductivity of both nanofluids
increases with the rise in temperature compared to the base
fluid. The thermal conductivity enhancement varies from
9.8 to 17.89% and 15.6 to 24.56% with the temperature
range of 15–50 �C at 0.8% volume concentration compared
to the base fluid, respectively. The CuO nanofluid showed
more thermal conductivity enhancement compared to
Al2O3 nanofluid under the same temperature and volume
concentration. Esfe et al. [14] conducted an experiment on
the effect of diameter on thermal conductivity and dynamic
viscosity of Fe/water nanofluids. They studied different
magnetic nanoparticles with diameters of about 37, 71 and
98 nm. Results indicated that thermal conductivity
increases as volume fraction increases and thermal con-
ductivity of the nanofluid increases with a decrease in
nanoparticle’s size. Furthermore, the nanofluid dynamics
viscosity ratio increases with the addition of particles and
increasing nanoparticle’s diameter.
Although many types of research have been carried out
regarding metallic and nonmetallic nanofluids, the mixture
of both particles dispersed in a working fluid is an ongoing
investigation [15–25].
Vasu et al. [26] measured the thermal conductivity and
viscosity of vegetable oil-based Cu, Zn and Cu–Zn hybrid
nanofluids. The particle size was 60 nm for Zn, 60 nm for
Cu and 70 nm for Cu–Zn alloy. They reported the thermal
conductivity enhancement of 36, 42 and 48% for Zn, Cu
and Cu–Zn nanofluids, respectively, with a volume con-
centration of 0.5%, compared to base fluid (vegetable oil).
The enhancement in viscosity for Zn, Cu and Cu–Zn
nanofluids were 47, 53 and 61%, respectively, at the same
volume fraction. Esfe et al. [27] studied the effect of
nanoparticle volume fraction on thermal conductivity and
dynamic viscosity of Ag–MgO/water hybrid nanofluid with
the particle diameter of 40 and 25 nm and nanoparticle
volume fraction range between 0 and 2% for MgO and Ag,
respectively. Results indicated that by increasing the
nanoparticle volume fraction, thermal conductivity and
dynamic viscosity of nanofluid will increase. They also
proposed new correlations for both thermal conductivity
and dynamic viscosity.
In the recent studies, neural network modelling was used
to deliver the most accurate correlations to estimate both
thermal conductivity and viscosity of the nanofluids
[18, 28–33]. Esfe et al. [34] proposed new correlations for
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thermal conductivity of alumina nanoparticle dispersed in
pure ethylene based on neural network modelling using
experimental data. Results showed that the ANN model can
predict the thermal conductivity of Al2O3–EG nanofluid
accurately with a maximum deviation of 1.3% and high
correlation coefficient.
The aim of the present paper is to investigate the thermal
conductivity of Al2O3–Cu/EG nanofluids at the solid
volume fraction range of 0.125–2.0% and a temperature
range between 25 and 50 �C. Measured data were com-
pared with some theoretical models. At the end, a new
correlation is presented for the thermal conductivity as a
function of temperature and solid volume fraction.
Nanofluid preparation
The two-step method was implemented to prepare the
Al2O3–Cu/EG nanofluid with different concentrations. Due
to the sedimentation and agglomeration of nanoparticles in
the base fluid, special techniques should be utilised to make
sure that an adequate suspension and stability is attained. In
the present study, the nanofluids at volume concentrations
of 0.125, 0.25, 0.5, 1.0, 1.5 and 2.0% were prepared by
dispersing the mixture of Al2O3 and Cu nanoparticles in
ethylene glycol as the base fluid. Al2O3 and Cu nanopar-
ticles with a diameter of 5 and 50 nm, respectively, were
purchased from US Research Nanomaterial, Inc. Properties
of the nanoparticles are presented in Table 1. A transmis-
sion electron microscope (TEM) was used to determine the
shape and size of the particles. Figure 1 illustrates that the
particles are approximately spherical in shape for both
Al2O3 and Cu. This method was commonly used by many
researchers [35–37].
Nanoparticles weighed carefully for each volume con-
centration and then gradually added to the base fluid. The
suspensions were subjected to an ultrasonic vibrator for 7 h
in order to attain a uniform/proper dispersion and
stable suspension. No sedimentation in the samples was
observed within 3 days.
Various techniques including transient hot wire [38],
parallel state [39], temperature oscillation [40], cylindrical
cell [41] and 2x [42] have been utilised to measure the
thermal conductivity of nanofluids. In present study, tran-
sient, hot wire technique [43] is applied to measure the
thermal conductivity of Al2O3–Cu/EG nanofluid for its
accuracy and speed.
Measurement of thermal conductivity
The thermal conductivity of Al2O3–Cu/EG nanofluid was
measured in various solid volume fractions and tempera-
tures (ranging from 25 to 50 �C), using a KD2 Pro
instrument (Decagon Devices, Inc., USA). The accuracy of
the instrument is ±5%. The KD2 Pro is operating base on
the transient hot wire method, and it consists of a handheld
microcontroller and sensor needles. The KD2’s sensor
needle is equipped with a heating element and a thermistor.
The sensor needle used in this study was KS-1 which is
60 mm in length and 1.3 mm in diameter. This needle
closely approximates the infinite line heat source. Each
measurement cycle is 90 s. The first 30 s, the instrument
will equilibrate and the next two 30 s are followed by
heating and cooling of sensor needle. After the reading, the
controller computes thermal conductivity using the change
in temperature (rT). The thermal conductivity of fluids can
be determined from [44]:
K ¼ q ln t2 � ln t1ð Þ4 rT2 �rT1ð Þ ð1Þ
where q is constant heat rate, rT1 and rT2 are the changes
in temperature at times t1 and t2, respectively.
To make sure of the experimental accuracy, each
experiment is repeated three times and the average value is
calculated. It worth to mention that the hot water bath is
used to stabilise the temperature of nanofluid.
Results and discussion
An accurate experimental thermal conductivity measure-
ment of nanofluids is considered to be a very difficult and
time-consuming task due to some errors arising during the
measurement operation. In addition, cost and expenses of
doing reproducible experiments are immense. Therefore,
enlisting accurate models to predict thermal conductivity of
nanofluid with regards to easily measurable properties such
as volume fractions, temperature and particle size were
investigated in many studies.
Hamilton–Crosser is one of the basic models to predict
thermal conductivity of dilute dispersions of solid
nanoparticles, in which the thermal conductivity ratio of
Table 1 Nanoparticles’ characteristics
Al2O3 Cu
Nanoparticles purity 99.99/% 99.9/%
Nanoparticles APS 5/nm 70/nm
Nanoparticles SSA [150/(m2 g-1) *10–14/(m2 g-1)
Nanoparticles morphology Nearly spherical Spherical
Nanoparticles colour White Saddle brown
Specific heat capacity 880/[J kg-1 K-1] 386/[J kg-1 K-1]
Nanoparticles bulk density 0.18/(g cm-3) 8.9 g cm-3
New experimental correlation for the thermal conductivity of ethylene glycol containing… 1607
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the solid phase to the liquid phase is more than 100 [45].
This model is described as follows:
keff
kbf
¼ knf þ n� 1ð Þkbf � n� 1ð Þu kbf � knfð Þknf þ n� 1ð Þkbf þ u kbf þ knfð Þ ð2Þ
where knf and kbf are the thermal conductivity of particles
and fluid, respectively, u is the volume fraction of
nanoparticles and n = 3 w-1 in which w is the particle
sphericity. For spherical and cylindrical particles, the value
of n is assumed 3 and 6, respectively.
Another model to predict the thermal conductivity of
nanofluid was proposed by Yu–Choi [46]. The relation can
be expressed as:
keff
kbf
¼ knf þ 2kbf � 2u kbf � knfð Þ 1 þ bð Þ3
knf þ 2kbf � u kbf � knfð Þ 1 þ bð Þ3ð3Þ
where b is the ratio of the nanolayer thickness to the
original particle radius.
Lu and Lin [47] also proposed a model to calculate the
thermal conductivity of nanofluids with spherical particles.
The relation reads as:
keff
kbf
¼ 1 þ 2:25uþ 2:27u2 ð4Þ
A comparison between the experimental data as relative
thermal conductivity (knf/kbf) and the results obtained by
the H–C, Yu–Choi and Lu–Lin models at different tem-
peratures are shown in Fig. 2. Looking at Fig. 2a, the
closest prediction took place by Yu–Choi model which
underestimates the measured data by about 11% at the
temperature of 298 K. This deviation even increases at the
higher temperatures (Fig. 2b–d). It is evident that above-
mentioned models are unable to calculate the thermal
conductivity of Al2O3–Cu/EG nanofluid. This is caused by
not considering the effects of significant factors on the
thermal conductivity of nanofluids such as the temperature,
particle size and interfacial layer. It is vital to note that the
various parameters may affect the thermal conductivity of
nanofluids including thermal conductivity of the solid
particles and base fluid, the shape of particles, the thermal
conductivity of nanolayer [48], the stability of nanofluid,
clustering [49–52] and temperature.
Also, Fig. 2 reveals that the increasing rate of thermal
conductivity at low concentrations is greater than that at
high concentrations. The reason for this phenomenon may
be that the increase in nanofluid viscosity is much greater
than the enhancement of thermal conductivity at higher
concentrations [53–68]; in other words, space for mole-
cules to collide and transfer energy reduces by adding more
solid particles.
Figure 3 demonstrates the enhancement of thermal con-
ductivity at the different concentration with respect to the
temperature. The enhancement of 24–28% was observed at
the volume concentration of 2.0% compared to the base fluid.
It can be concluded that the higher temperatures result in
bigger thermal conductivity enhancements.
Figure 4 shows relative thermal conductivity with the
temperature at different concentrations. As it can be seen,
the increase in temperature slightly affects the increase in
thermal conductivity as it can be noticed from the slope of
the graph. Particularly, for concentrations lower than 0.5%
the enhancement of thermal conductivity with respect to
temperature is negligible. A collision between solid parti-
cles plays an essential role in increasing of nanofluid
thermal conductivity. The increase in molecules collisions
and Brownian motion leads to increase in internal energy
of particles and hence enhancement of the thermal con-
ductivity. At the lower concentrations, the space between
solid molecules is bigger than high concentration due to
fewer particles at the same volume of nanofluid. Conse-
quently, the probability and number of collisions particles
decrease due to heating.
In this study, a new correlation has been proposed for
calculating the thermal conductivity of Al2O3–Cu/EG
nanofluid. This correlation is based on temperature and
solid volume fraction as follows:
Knf
Kbf
¼ 9:6128 þ uð Þ9:3885 � 0:00010759 T2
� 0:0041099
uð5Þ
To investigate the accuracy of proposed correlation, the
margin of deviation can be expressed as follows:
Margin of deviation %ð Þ ¼ Kc � Kexp
Kexp
� 100 ð6Þ
where kc is the thermal conductivity computed from the
proposed correlation and kexp is the thermal conductivity of
measured data. Figure 5 shows a good correspondence
between experimental data and proposed correlation based
on solid volume fraction with regards to temperature. Also,
the margin of deviation at the different temperatures is
presented in Fig. 6. Calculations show only 1.6% margin of
deviation which suggests that the accuracy of proposed
correlation is in the acceptable range.
Fig. 1 A transmission electron microscope (TEM) of Al2O3 (a) and
Cu (b)
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1.4
1.3
1.2
1.1
1.0
0.9
1.4
1.3
1.2
1.1
1.0
0.9
1.4
1.3
1.2
1.1
1.0
0.9
1.4
1.3
1.2
1.1
1.0
0.9
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
Nanoparticles volume fraction/% Nanoparticles volume fraction/%
Nanoparticles volume fraction/%Nanoparticles volume fraction/%
The
rmal
con
duct
ivity
rel
ativ
e
The
rmal
con
duct
ivity
rel
ativ
eT
herm
al c
ondu
ctiv
ity r
elat
ive
The
rmal
con
duct
ivity
rel
ativ
e
Experimental (T = 25 °C)H–C modelYu and Choi modelLu and Lin model
Experimental (T = 35 °C)H–C modelYu and Choi modelLu and Lin model
Experimental (T = 45 °C)H–C modelYu and Choi modelLu and Lin model
Experimental (T = 50 °C)H–C modelYu and Choi modelLu and Lin model
(a) (b)
(c) (d)
Fig. 2 Comparison between the
measured data and the theatrical
models
1.30
1.25
1.20
1.15
1.10
1.05
1.000.0 0.5 1.0 1.5 2.0
Nanoparticles volume fraction/%
Rel
ativ
e ef
fect
ive
ther
mal
con
duct
ivity
T = 25 °CT = 30 °CT = 35 °CT = 40 °CT = 45 °CT = 50 °C
Fig. 3 Relative thermal conductivity with concentration at different
temperature
1.4
1.3
1.2
1.1
1.020 25 30 35 40 45 50 55
Temperature/°C
Rel
ativ
e ef
fect
ive
ther
mal
con
duct
ivity
ϕ = 0.125%ϕ = 0.25%ϕ = 0.5%ϕ = 1.0%ϕ = 1.5%ϕ = 2.0%
Fig. 4 Relative thermal conductivity with temperature at different
concentrations
New experimental correlation for the thermal conductivity of ethylene glycol containing… 1609
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Conclusions
In this paper, an experimental investigation has been
performed to measure the thermal conductivity enhance-
ment of Al2O3–Cu/EG hybrid nanofluid using the transient
hot wire method. For this purpose, a mixture of Al2O3 and
Cu particles with a ratio of 50:50 was carefully measured
and dispersed in ethylene glycol to achieve a desirable
solid volume fraction. The thermal conductivity of
investigated nanofluid was studied with the various con-
centrations from 0.125 to 2.0% and the temperature range
of 25–50 �C. It was found that the thermal conductivity
enhancement of nanofluids with solid volume fraction at
higher temperatures is greater than that at lower temper-
atures. Furthermore, the thermal conductivity enhance-
ment of nanofluids with temperature at higher solid
volume fraction is more than that at lower solid volume
fraction. The results indicate that the maximum enhance-
ment of thermal conductivity of Al2O3–Cu/EG hybrid
nanofluid was 28%, which occurred in a solid volume
fraction of 2.0% and temperature of 50 �C. In addition, it
1.30
1.25
1.20
1.15
1.10
1.05
1.00
1.30
1.25
1.20
1.15
1.10
1.05
1.00
1.30
1.25
1.20
1.15
1.10
1.05
1.00
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5
Nanoparticles volume fraction/% Nanoparticles volume fraction/%
Nanoparticles volume fraction/%Nanoparticles volume fraction/%
The
rmal
con
duct
ivity
rat
io
The
rmal
con
duct
ivity
rat
ioT
herm
al c
ondu
ctiv
ity r
atio
The
rmal
con
duct
ivity
rat
io
CorrelationExperimental
CorrelationExperimental
CorrelationExperimental
CorrelationExperimental
T = 25 °C T = 35 °C
T = 50 °CT = 45 °C
(a) (b)
(c) (d)
Fig. 5 Comparison between experimental data and proposed correlation at different temperatures
3
2
1
0
–1
–2
–30.0 0.5 1.0 1.5 2.0 2.5
Nanoparticles volume fraction/%
Mar
gin
of d
evia
tion/
%
T = 25 °CT = 30 °CT = 35 °CT = 40 °CT = 45 °CT = 50 °C
Fig. 6 Margin of deviation of presented correlation
1610 A. Parsian, M. Akbari
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shows that the effect of temperature was negligible at the
concentration lower than 0.5%.
The measured data were compared with some of the
famous models including Hamilton–Crosser, Yu–Choi and
Lu and Lin. The comparison revealed that none of these
models were able to predict the thermal conductivity of
Al2O3–Cu/EG nanofluid with acceptable accuracy. Finally,
based on the experimental data, a correlation was proposed as
a function of the solid volume fraction and temperature to
predict the thermal conductivity ratio of Al2O3–Cu/EG hybrid
nanofluid. The calculations of the thermal conductivity ratio
showed that the maximum value of margin of deviation was
only 1.6% for proposed correlation which indicates a good
accuracy. Thus, the proposed correlation can be used for
predicting the thermal conductivity ratio of Al2O3–Cu/EG
hybrid nanofluids at solid volume fractions ranging from
0.125 to 2.0% for temperature range of 25–50 �C.
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