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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

[email protected]

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

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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

1606 A. Parsian, M. Akbari

123


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

123


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




(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


123


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




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


123


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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