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Experimental investigation of diameter effect on heat transfer performance

and pressure drop of TiO2–water nanofluid

A.A. Abbasian Arani ⇑, J. Amani

Department of Mechanical Engineering, University of Kashan, Iran

a r t i c l e i n f o

Article history:

Received 24 May 2012

Received in revised form 13 August 2012

Accepted 14 August 2012

Available online 24 August 2012

Keywords:

Experimental study

TiO2–water nanofluid

Pressure drop

Nusselt number

Nanoparticle diameter

Turbulent flow

a b s t r a c t

In this paper, an experimental study performed to investigate the convection heat transfer characteristics

in fully developed turbulent flow of TiO2–water nanofluid. The effect of mean diameter of nanoparticles

on the convective heat transfer and pressure drop studied at nanoparticle volume concentration from

0.01 to 0.02 by volume. The experimental apparatus is a horizontal double tube counter-flow heat

exchanger. The nanoparticles of TiO2 with diameters of 10, 20, 30 and 50 nm dispersed in distilled water

as base fluid. The results indicated higher Nusselt number for all nanofluids compared to the base fluid. It

is seen that the Nusselt number does not increase by decreasing the diameter of nanoparticles generally.

In this study both Nusselt number and pressure drop were considered in definition of thermal perfor-

mance factor. The results show that nanofluid with 20 nm particle size diameter has the highest thermal

performance factor in the range of Reynolds number and volume concentrations were studied.

2012 Elsevier Inc. All rights reserved.

1. Introduction

Heat transfer loads have rapid growth at various equipments

used in industry, transportation, electronic and microelectronic,

defense weaponry, etc. Conventional fluids such as oils and water

are used widely in industries in order to heat transfer. In general,

these fluids have poor thermal properties that restricted the heat

transfer performance compared to those of most solids. Many tech-

niques could be used to enhance heat transfer rate that results in

reduction in the size of the heat transfer equipments. In recent

years, many researchers developed new classes of fluids to en-

hance heat transfer rate by suspending small particles of solids

in the ordinary fluids. Different types of nanoparticles, such as

metallic, ceramics, ceramic oxides, ceramic nitrides, semi conduc-

tive material and carbon nanotubes (CNTs) can be used as solid.

In the primitive studies in many years ago, uses of particles in size

of millimetre or even micrometre in the fluid, results high thermal

enhancement. But some problems such as poor stability of the sus-

pension, clogging and high pressure drop creates. A decade ago,

with the rapid development of nanotechnology, particles in order

of micrometre (commonly between 1 nm and 100 nm) were re-

placed by nanometre-size particles. Choi [1] called this type of fluid

by nanofluid. By using the nanofluid, compared with suspensions

contains particles in size of millimetre or micrometre, heat transfer

area decreases because of an enhancement in the heat transfer

rate. Many experimental studies have been done by researchers.

They reported that nanofluids have shown special advantages,

such as better stability, greater thermal conductivity, and lower

pressure drop. Although all of these benefits might does not occur

at the moment. Some of these studies are expressed as follows.

Pak and Cho [2] studied on the heat transfer performance and

pressure drop of c-Al2O3 (13 nm) and TiO2 (27 nm) nanoparticles

suspended in water in turbulent flow through a horizontal circular

tube. They observed that the heat transfer rate increases by in-

crease in Reynolds number and nanoparticle volume fraction up

to 3%, and it decreases for volume fraction of 3%.

Wen and Ding [3] studied on the convective heat transfer of

water–Al2O3 nanofluid flowing through a copper tube in the lami-

nar flow regime. Using the nanofluid showed considerable

enhancement of convective heat transfer. The enhancement was

particularly significant in the entrance region. Yang et al. [4] inves-

tigated the convective heat transfer coefficients of several nanofl-

uids under laminar flow in a horizontal tube heat exchanger. The

nanoparticles used in this research were graphitic in nature, with

different aspect ratios. The graphite nanoparticles increased the

convective heat transfer and static thermal conductivities signifi-

cantly at low weight fraction loadings. He et al. [5] reported that

addition of TiO2 nanoparticles into the water or decreasing

agglomerate size, enhances the thermal conductivity. The convec-

tive heat transfer coefficient increases with nanoparticle concen-

tration in both the laminar and turbulent flow regimes through a

vertical pipe at Reynolds <6500. The convective heat transfer coef-

ficient does not change by average agglomerate size. The nanofluid

pressure drop is very close to that of the water.

0894-1777/$ - see front matter 2012 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.expthermflusci.2012.08.014

⇑ Corresponding author. Tel.: +98 3615912413; fax: +98 3615912475.

E-mail address: [email protected] (A.A. Abbasian Arani).

Experimental Thermal and Fluid Science 44 (2013) 520–533

Contents lists available at SciVerse ScienceDirect

Experimental Thermal and Fluid Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e t f s

http://dx.doi.org/10.1016/j.expthermflusci.2012.08.014

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Kulkarni et al. [6] performed a study on the convective heat

transfer and viscosity of nanofluids. The nanoparticles CuO, Al2O3

and SiO2 were used each in mixture of ethylene glycol and water.

The results indicated that the heat transfer coefficient of nanofluid

increases by increasing volume concentration. Kim et al. [7] inves-

tigated the convective heat transfer of nanofluid through a straight

circular tube in the laminar and turbulent flow regimes. The base

fluid was water and the nanoparticles were separate alumina and

amorphous carbonic nanoparticles. Thermal conductivity and con-

vective heat transfer coefficient at 3 vol.% Al2O3–water nanofluid

were 8% and 20%, respectively. For amorphous carbonic nanofluid,

the thermal conductivity was similar to that of water, and the con-

vective heat transfer coefficient increased only 8% in laminar flow.Sharma et al. [8] evaluated heat transfer coefficient and friction

factor in a tube with twisted tape at different twist ratio of nano-

fluid flows with Al2O3 nanoparticles. The results showed that heat

transfer coefficient of nanofluid with 0.1% volume concentration is

23.7% higher than that of water in a tube at Reynolds number of

9000. The maximum friction factor with twisted tape at 0.1% nano-

fluid volume concentration was 1.21 times that of water flowing in

a plain tube. Anoop et al. [9] studied on the effect of Al2O3 particle

size in water base nanofluid on the heat transfer characteristics in

the developing region of tube flow. Selected particle sizes were 45

and 150 nm. The nanofluid contains 45 nm particles have higher

heat transfer coefficient compared with 150 nm particles. Both

nanofluids showed higher heat transfer characteristics compared

to the base fluid.Duangthongsuk and Wongwises [10] studied the heat transfer

coefficient and friction factor of the TiO2 (21 nm)–water nanofluid

with 0.2–2 vol.% in a horizontal double tube counter-flow heat ex-

changer under turbulent flow conditions. The heat transfer coeffi-

cient of nanofluid with 1 vol.% was approximately 26% greater

than that of base fluids, while for volume concentration of

2.0 vol.% was approximately 14% lower than that of base fluids.

The pressure drop of nanofluid was slightly higher than the base

fluid and increases with increasing the volume concentrations.

Teng et al. [11] studied on the effect of particle size, tempera-

ture, and weight fraction on the thermal conductivity ratio of

Al2O3–water nanofluid up to 2.0 wt.% and different nominal diam-

eter 20, 50, and 100 nm. The results showed a correlation between

high thermal conductivity ratios and enhanced sensitivity, small

nanoparticle size and higher temperature. Xie et al. [12] investi-

gated the convective heat transfer enhancement of nanofluid in

laminar flows inside a tube. Nanofluid containing nanoparticles

of Al2O3, ZnO, TiO2, and MgO separately in a base fluid contains

55 vol.% distilled water and 45 vol.% ethylene glycol. They reported

that the nanofluid heat transfer rate highly depended on several

parameters such as the nanoparticle volume fraction, average size

of nanoparticles, and the flow conditions. All nanofluids have high-

er heat transfer coefficient than that of water, and up to 252%

enhancement occurs at a Reynolds number of 1000 for MgO

nanofluid.

Farajollahi et al. [13] reported the heat transfer characteristics

of aqueous nanofluid contains c-Al2O3 and TiO2 nanoparticles sep-

arately under turbulent flow condition in a shell and tube heat ex-changer. The results showed that by uses the nanofluid, significant

enhancement of heat transfer characteristics obtained and differ-

ent optimum nanoparticles concentrations exist for nanofluid.

Some of other researchers studied on the effect of some parameters

such as nanoparticles volume fraction and type of nanoparticles on

the convective heat transfer and the friction factor or pressure drop

of nanofluid in turbulent flow condition [14–17].

Sajadi and Kazemi [18] investigated turbulent heat transfer

characteristics of TiO2–water nanofluid in a circular pipe for max-

imum nanoparticles volume concentration of 0.25%. The results

indicated that addition of small amounts of nanoparticles to the

base fluid considerably augmented heat transfer, while Nusselt

number are approximately the same for all nanoparticles volume

concentration. The pressure drop of nanofluid increased withincreasing the volume concentration while are slightly higher com-

pared to the base fluid. Ji et al. [19] were investigated the effect of

Al2O3–water particle size on the heat transfer performance of an

oscillating heat pipe. Four nanoparticles with average diameters

of 50 nm, 80nm, 2.2 lm, and 20lm were used. The results

showed that all the nanofluids significantly affect the heat transfer

performance and it depends on the particle size. The best heat

transfer performance observed for nanoparticles with diameter of

80 nm. Zamzamian et al. [20] studied on the effect of nanofluid

of aluminium oxide and copper oxide were prepared in ethylene

glycol on the forced convective heat transfer coefficient in turbu-

lent flow within a double pipe and plate heat exchangers. They

found up to 50% enhancement in convective heat transfer coeffi-

cient of the nanofluid compared to the base fluid. Moreover, the re-

sults indicated that with increasing nanoparticles concentration

Nomenclature

A area of heat transfer (m2)c p specific heat (J/kg K)d diameter of particles (nm)D inner diameter of inner tube (m) f friction factor

g gravitational acceleration (m/s2)h height differences of Hg column (m)h average heat transfer coefficient (W/m2 K)k thermal conductivity (W/mK)L test section length (m)_m mass flow rate (kg/s)Nu average Nusselt number p pressure (Pa)Pr Prandtl number_Q heat transfer rate (w)Q flow rate (m3/s)Re Reynolds numberT wall average of inner tube surface temperatures (K)

u mean velocity of nanofluid (m/s)

Greeksa thermal diffusivity (m2/s)g thermal performance factorl dynamic viscosity (kg/ms)q density (kg/m3)d uncertaintyu nanoparticle volume fraction

Subscripts f base fluidnf nanofluid p particlesm meanw hot waterin inletout outlet

A.A. Abbasian Arani, J. Amani / Experimental Thermal and Fluid Science 44 (2013) 520–533 521



and nanofluid temperature, the convective heat transfer coefficient

of nanofluid increases.

Recently Abbasian Arani and Amani [21] presented an experi-

mental study on heat transfer and pressure drop of TiO2–water

in turbulent flow regime for 30 nm particle size diameter. They

carried out their experiment investigation for Reynolds number

range between 8000 and 51,000 and 0.002–0.02 volume concen-

trations. They concluded that by using the nanofluid at high Rey-

nolds number (greater than 30,000) more power compared to

low Reynolds number needed to compensate the pressure drop

of nanofluid, while increments in the Nusselt number for all Rey-

nolds numbers are approximately equal. Therefore using nanofl-

uids at high Reynolds numbers compared with low Reynolds

numbers, have lower benefits.

Wang and Mujumdar [22], in their review article, explained that

many factors such as particle size, shape and distribution, pH va-

lue, and the particle–fluid interactions may have important effect

on the heat transfer performance of the nanofluids. The purpose

of this study is to disclose the thermal fluid flow transport phe-

nomenon of TiO2–water nanofluid by studying the pressure drop,

and the convective heat transfer performance for various diameter

and concentrations of TiO2–water nanofluids. TiO2–water nano-

fluid is used as the working fluid under the constant heat flux

boundary.

From the above literature review it must be mentioned that

considerable enhancement in heat transfer coefficients were re-

ported in the turbulent regime but studies on the effect of particle

sizes in this regime has not been investigated comprehensively.

Hence, the present investigation concentrates on the heat transfer

enhancement in the turbulent flow regime with varying particle

sizes and concentrations. The nanofluid used in this study is

TiO2–water with average particle sizes of 10 nm, 20 nm, 30 nm

and 50 nm. The particle concentrations used in the experiments

were of 1 vol.%, 1.5 vol.% and 2 vol.%.

We focus on titanium dioxide as a nanoparticle that was not

studied extensively in literature such as aluminium and copper.

Also titanium dioxide has important characteristics as safe mate-rial for human and excellent chemical and physical stability [9,23].

In addition based on our literature review, it can be seen that all

of the previous works on nanofluid heat transfer focused on heat

transfer characteristics or pressure drop separately. Hence, the an-

other aim of the present experimental investigation is to study

both the convective heat transfer and friction factor characteristics

in the fully developed turbulent flow of TiO2–water nanofluid in a

Reynolds number range of 9000–55,000 with 1–2 vol.%

concentration.

2. Experimental design

2.1. Sample preparation

The schematic of the experimental apparatus is shown in Fig. 1.

This set up have three closed-loop cycles. The nanofluid cycle con-

tains a collection tank, a pump with bypass line, heat transfer test

section, and a water heat exchanger in order to cool nanofluid. The

heat transfer section was made of two centric tubes. According to

equation (Le/D 4.4 Re1/6) [24] the length of tube in order to cre-

ate fully developed turbulent flow at Reynolds number of 51,000

(near maximum Reynolds number) calculated about 22 cm (The

heated length of test section is 98.8 cm). Thus the flow becomes

developed turbulent for all cases studied. Two K-type thermocou-

ples were measured bulk temperature of the flow at the inlet and

outlet of the test section. Also eight other K-type thermocouples

were installed with distance about 12 cm from each other on thesurface of the test section. The test section was heated by hot water

which flows over copper tube. The second cycle contains equip-

ments to create and control the flow rate of hot water at desired

temperature. A temperature controller with PT100 sensor used to

control the temperature of hot water. Two K-type thermocouples

measured inlet and outlet bulk temperature of hot water to the test

section. In addition a rotameter used to measure and adjust the hot

water flow rate. The third cycle contains a pump, nanofluid heat

exchanger, bypass line, condensing unit and temperature control-

ler with a PT100 sensor. This unit controls the temperature of

nanofluid at the inlet of the test section by changing the power

of the condensing unit. In this experimental apparatus a slop mer-

cury manometer was used to measure the pressure drop. The angle

of manometer with horizontal line was 48.5.

The essential parameters that were measured include hot water

and nanofluid flow rate, temperatures and heights of manometer

columns. It is important to note that all of the thermocouples

and sensors have a precision of 0.1 C and were calibrated before

they are attached to the test section. Also the hot water rotameter

calibrated in different temperate of hot water. An ordinary ther-

mometer measured the temperature of ambient. A plain explana-

tion about our experimental apparatus was presented in recent

experimental investigation done by Authors [21].

3. Preparation of nanofluid

In order to prepare the nanofluid by dispersing the nanoparti-

cles in a base fluid, special mixing and stabilization methods of

the nanoparticles are required. In the present study three effective

methods were used to stabilize the suspension against sedimenta-

tion of nanoparticles. These methods are: change the pH value of

the nanofluid, addition of surfactants or surface activators, and

use of ultrasonic vibration. In this work, distilled water was used

as liquid medium. The desired volume concentrations used in this

study are 0.01 (1.0%), 0.015 (1.5%) and 0.02 (2.0%). Nanoparticles

with average diameters of 10, 20, 30, and 50 nm are provided by

(USnano Inc.–Nabond Inc.). An ultrasonic vibrator with magneticstirrer was used for approximately 3 h in order to break down

agglomeration of the nanoparticles. Cetyl Trimethyl Ammonium

Bromide (CTAB) surfactants were used to ensure better stability

and proper dispersion without affecting nanofluid’s thermophysi-

cal properties since the surfactant concentrations used in the

experiments are very low (e.g., volume percentage around 0.01%)

[23]. In addition after measuring the pH, nanofluid pour into the

apparatus immediately and tests performed after about 4 h that

nanofluid flows at its maximum flow rate. It must be note that dur-

ing experiments, no sedimentation was observed even at low flow

rate. Also the values of pH of nanofluid measured for all nanofluids

at the beginning and at the end of tests. The pH values were be-

tween 5.62 and 7 for all nanofluids. Further stability is achieved

by keeping the pH value away from the iso-electric point (IEP)which is the point with zero zeta potential (and hence maximum

attraction between the particles). The pH values used in present

study were between 5.62 and 7 (IEP of TiO2 is 2.9 [25]). A minimum

of 2.7 l of each concentrations were prepared and it was observed

that the suspensions were stable for several hours (days).

In this experimental study a transmission electron microscope

(TEM) was used to approximate the size of the primary nanoparti-

cles. Fig. 2 was shown that the primary shape of nanoparticles is

approximately spherical. This method is commonly used by a wide

range of researchers [7,9–11,23,26,27].

As noted above in order to reaching a proper stability, it re-

quires to repeating mechanical mixing and ultrasonic sonication.

After 24 h no sedimentation was observed in any samples of nano-

fluid. In addition it should be mentioned, the sedimentation of nanoparticles is less important for turbulent flow regime due to

522 A.A. Abbasian Arani, J. Amani / Experimental Thermal and Fluid Science 44 (2013) 520–533



Fig. 1. Schematic diagram of the experimental apparatus.

Fig. 2. TEM image of dispersed TiO2 nanoparticles with an average diameter of (a) 10 nm, (b) 20 nm, (c) 30 nm, (d) 50 nm.




the higher imposed shear which breaks down the possible agglom-

erated particles, therefore, turbulent flow regime in the present

study helps to provide a stable solution during the experiments.

This view point was presented by Nasiri et al. [28]. Also to prevent

possible sedimentation, for each test a newnanofluid was prepared

and immediately used.

4. Data analysis

4.1. Density and specific heat capacitance

The effective density of the nanofluid is given by:

qnf ¼ uq p þ ð1 uÞq f ð1Þ

The heat capacitance is defined as:

c p;nf ¼uðqc pÞ p þ ð1 uÞðqc pÞ f

qnf ð2Þ

4.2. Thermal conductivity of nanofluid

It must be mentioned that during our studies, a lake of experi-

mental results about thermophysical properties variation by the

diameter of nanoparticles or temperature observed. According to

our studies several theoretical correlations existed but only one

empirical correlation about thermal conductivity and viscosity of

TiO2–water nanofluid considered the effects of nanoparticles diam-

eter and temperature. Corcione correlation [29] was used for deter-

mination of nanofluid effective thermal conductivity versus

nanofluid temperature, particles mean diameter, volume fraction

of nanofluid, particles Reynolds number and thermal conductivity

of nanoparticles and base fluid as follows:

knf

k f ¼ 1 þ 4:4 Re0:4

p Pr0:66 f

T

T fr

10k p

k f

0:03

u0:66 ð3Þ

where T fr is the freezing point of the base liquid (about 273.16 K).

Reynolds is the nanoparticle Reynolds number, defined as:

Re p ¼q f uBd pl f

¼2q f kBT

pl2 f d p

ð4Þ

kB is Boltzmann’s constant (1.38066 1023 J/K). This correlation is

applicable for nanoparticles diameter between 10 nm and 150 nm,

volume concentration between 0.2% and 9% and nanofluid temper-

ature between 294 K and 324 K.

Corcione correlation [29] used for the nanofluid effective ther-

mal conductivity, is derived from a wide variety of experimental

data relative to nanofluids consisting of Al2O3, CuO, TiO2 and Cunanoparticles with a diameter in the range from 10 nm to

150 nm, suspended in water or ethylene glycol (EG). Above empir-

ical correlation is produced by way of regression analysis, with a

1.86% standard deviation. It should be noted that the traditional

Maxwell theory largely fails when applied to nanofluids. The Max-

well equation presents either under-estimate or over-estimate the

value of knf , according as the nanoparticle diameter is small or

large, respectively.

4.3. Dynamic viscosity of nanofluid

Other correlation of Corcione [29] used to calculate dynamic

viscosity of nanofluid. It is applicable for nanoparticles diameter

from 25 to 200 nm, volume concentration of 0.01–7.1% and tem-perature from 293 to 333 K.

lnf l f

¼ 1

1 34:87 d pd f

0:3

u1:03

ð5Þ

where d f defined as the equivalent diameter of a molecule of base

fluid:

d f ¼ 6M N pq f 0

!1=3

¼ 6 0:018015286:022 10

23 p 998:26

1=3

¼ 3:85 1010 m ð6Þ

M is the molecular weight of the base fluid, N is the Avogadro num-

ber (6.022 1023 mol1), and q f 0 is the mass density of the base

fluid at temperature 293 K. As previously mentioned a lack of data

about thermophysical properties versus diameter was seen. There-

fore, Corcione correlation with a probable higher standard deviation

of the error (greater than 1.84%) used to calculate the dynamic vis-

cosity of nanofluid with nanoparticles with diameters of 10 and

20 nm. This empirical correlation is better than uses of other corre-

lation that are independent of particle diameter. The dynamic vis-

cosity used only for calculation Reynolds number of flows.

It is observed that, the relation of nanofluid dynamic viscosity

and dynamic viscosity of base fluid increases with decreasing

nanoparticles diameter and increasing nanoparticles volume con-

centration. Also it is seen this relation is independent of tempera-

ture. But the dynamic viscosity of nanofluid varies with

temperature. Thus, in order to consider the effect of temperature

variation of nanofluid in the tests, the viscosity of the base fluid as-

sumes to vary with temperature. In this study, thermophysical

properties of water and TiO2 calculated by several empirical corre-

lation. This correlation created by curves fitting to experimental

data as follows.

It must be noted that Corcione correlation for dynamic viscosity

is derived from a wide selection of experimental data available in

the literature. The best-fit of the selected data enumerated above

results in the following mean empirical correlation with a 1.84%standard deviation of error. As observed earlier for the Maxwell

theory, also the Brinkman equation largely fails when applied to

nanofluids, with a percentage error that increases as the nanopar-

ticle diameter decreases.

It is worth to note that only a few investigations have been pre-

sented in literature on viscosity. Nanofluid behaviour is always

Newtonian. Chen et al. [30] and Chandrasekar et al. [31] observed

a Newtonian behaviour in TiO2–ethylene glycol and Al2O3–water

nanofluid, respectively. Longo and Zilio [32] observed a Newtonian

behaviour in all the investigated ranges of temperature and parti-

cle volume fraction, (1–6% particle volume fraction and from 1 to

40 C). Rubio-Hernández et al. [33] studied the viscosity of dilute

suspensions of several metal oxides (SiO2, Al2O3 and TiO2) at differ-

ent pH values and reported that these non-Newtonian effects havenot been observed. Fedele et al. [34] conducted an experimental

study and found that TiO2–water nanofluid have a Newtonian

behaviour. Alphonse et al. [35] studied on viscosity of TiO2–water

nanofluids. They found a Newtonian behaviour in the shear rate

range of 1–100 s1. Chen et al. [36] reported a Newtonian behav-

iour at room temperature for particle volume fraction less than

1.5%. Bobbo et al. [37] performed an experimental study on viscos-

ity of TiO2–water nanofluid and found a Newtonian behaviour at

atmospheric pressure and temperatures ranging between 283.2 K

and 353.2 K.

Other authors found a non-Newtonian behaviour of nanofluids.

As an example Tseng and Lin [38] considered TiO2–water nanofluid

ranging between 5% and 12% volume fraction and found pseudo-

plastic flow behaviour. From above literature review one can seemost of investigators reported a Newtonian behaviour.




4.4. Properties of base fluid and solid phase

White [24] proposed a correlation to calculate the viscosity of

water at different temperature. In this study, we change that corre-

lation and get a new one with maximum deviation error of 1.27%

(half of maximum deviation error of White correlation).

lnl f

0:001792

¼ 1:24 6:44 273:15

T

þ 7:68 273:15

T 2

ð7Þ

A correlation with R2 = 99.99% obtained by curve fitting on data of

White [24] about the thermal conductivity of water:

k f ¼ 1:549404 þ 0:01553952 T 3:65967 105 T2

þ 2:9401 108 T3 ð8Þ

The density and specific heat capacity of water were calculated by

below correlations. These correlations obtained by curve fitting on

Bejan’s data [39].

q f ¼ 764:475639 þ 19:251515 T 0:07714568 T2

þ 1:364893 10

4

T

3

9:339158 10

8

T

4

;R2 ¼ 99:99% ð9Þ

c p; f ¼ 198531:690492 2894:853934 T þ 17:2363068 T2

0:05126994 T3 þ 7:616133 105 T4 4:517821 108 T5;

R2 ¼ 99:95% ð10Þ

All of the four above correlations are valid over 273.156 T

(K)6 373. These correlations are independent of pressure. Accord-

ing to Kreith and Goswami [40] data’s, at the pressure near atmo-

spheric pressure, these properties do not varies significantly.

The thermal conductivity of TiO2 calculated by following corre-

lation over 273 6 T (K) 6 350. This correlation obtained by curve

fitting on the presented data by Powell et al. [41].

k p ¼ 100 ð0:1813 4:768 104T þ 5:089 107

T2Þ;

R2 ¼ 100% ð11Þ

The specific heat capacity for different types of TiO2 was calculated

by following correlation obtained by curve fitting on the data of

Smith et al. [42]. The molecular weight of TiO2 is 79.8988 gr/mol.

Rutile :c p ¼ 58:4528þ 3:02195T 3:02923 103 T2; 269:356T6339:82K

Anatase :c p ¼ 30:09536þ3:12709T 3:36810103 T2; 269:46T6340:53K

( ð12Þ

The density of both types of TiO2 are 4250 kg/m3 (Rutile) [43] and

3840 kg/m3 (Anatase) [44].

4.5. Nusselt number

The heat transfer rate to nanofluid (from hot water) is defined

as:

_Q nf ¼ _mnf c p;nf ðT out T inÞnf ð13Þ

The heat transfer rate of hot water is defined as:

_Q w ¼ _mwc p;wðT in T out Þw ð14Þ

The average heat transfer rate is calculated by:

_Q m ¼_Q w þ _Q nf

2 ð15Þ

The convective heat transfer coefficient and Nusselt number fornanofluid were calculated from the following equations:

hnf ¼_Q m

AðT wall T nf ;mÞ ð16Þ

Nunf ¼hnf D

knf ð17Þ

A p is the heat transfer surface and T wall is average of temperature of

tube wall. In this study, the energy differences between nanofluidand hot water are defined as:

j _Q w _Q nf j

_Q m6 10% ð18Þ

And it was below 10% in this study. It must mentioned that Yang

et al. [4] reported about 25%, Duangthongsuk and Wongwises [10]

reported maximum 3%, Wongcharee and Eiamsa-ard [26] reported

maximum value about 5%, Zamzamian et al. [20] reported up to

25%, for the difference between the heat transfer rate to nanofluid

and available heat transfer rate.

4.6. Pressure drop

The pressure drop of the nanofluid is calculated from followingequation:

D p ¼ ðqHg q0Þ gh sinð48:5Þ ð19Þ

The parameter q0 is the mass density of water (not nanofluid) at

ambient temperature. The physical properties of the nanofluid

and hot water were calculated from water and nanoparticles char-

acteristics at mean inlet and outlet bulk temperature.

4.7. Uncertainty

The uncertainties of pressure drop and Nusselt number are de-

fined as follows:

dðD pÞD p

¼ dhh

2

þ dðsinðhÞÞsinðhÞ

2" #0:5

ð20Þ

dðNunf Þ

Nunf ¼

d _Q m_Q m

!2

þ dL

L

2

þ dDT

DT

224

350:5

ð21Þ

The values of uncertainties calculated in both low and high Rey-

nolds numbers. The maximum uncertainty of pressure drop at the

nanoparticle volume fraction of 0.01 and nanoparticle size of

50 nm are about 0.20% and 3.6% for highest and lowest Reynolds

number respectively. The maximum uncertainties of Nusselt num-

ber at lowest and highest Reynolds number are about 3% and 4.7%

for nanoparticle volume fraction 0. 01. The maximum uncertainty

of Reynolds number is 0.6%.The uncertainty in measurement of Nusselt number by Anoop

et al. [9], were to be around 2.45% in experimental investigation

of diameter effect of Al2O3-Nanofluid. Their study was carried out

for alumina–water with average particle sizes of 45 nm and

150 nm and particle concentrations of 1 wt.%, 2 wt.%, 4 wt.% and

6 wt.%. In an experimental study, Wen and Ding [3] focused on

the entrance region under the laminar flow conditions, for Al 2O3

nanoparticles of various concentrations and constant heat flux

boundary condition. The uncertainty of the Nusselt numbers mea-

surements were within 3% under the conditions of cited work.

Fotukian and Nasr Esfahany [15], in an experimental study, were

reported 4% for the uncertainty in Nusselt number measurement.

They conducted an experimental investigation in the turbulent

flow convective heat transfer and pressure drop of dilute Al 2O3–water nanofluids inside a circular tube. The uncertainty of the




Nusselt number and pressure drop were around 5% and 6% respec-

tively in experimental work that was done by Duangthongsuk and

Wongwises [45]. Duangthongsuk and Wongwises presented an

experimental study on the heat transfer and fluid flow of TiO2–

water nanofluids at a low concentration flowing in a horizontal

concentric tube-in-tube heat exchanger under a turbulent flow con-

dition. In another work by Duangthongsuk and Wongwises [10], for

TiO2

–water nanofluids under turbulent flowcondition, they reported

the uncertainty of the Nusselt number and pressure drop around 5%

and 6% respectively. He et al. [5] conducted an experimental study

on the fluid flow and heat transfer behaviour of the TiO2–water

nanofluids flowing upwards in a straight pipe under both laminar

and turbulence/transition conditions. They reported an uncertainty

of 3% for Nusselt number under above condition. One can see the

uncertainty in measurements of Nusselt number and pressure drop

in current experimental study are within an acceptable range.

5. Validation

In order to validate and estimate the accuracy of the experimen-

tal results, values of Nusselt number and friction factors for dis-

tilled water are compared with existing correlation. Values of

Nusselt numbers compared with values of Gnielinski equation

[46] and Petukhov equation [47].

Gnielinski equation:

Nu ¼ ð f =2ÞðRe 1000ÞPr

1 þ 12:7ð f =2Þ0:5ðPr2=3 1Þ

; 2300 < Re < 5 106;

0:5 < Pr < 2000 f ¼ ð1:58lnðReÞ 3:82Þ2

ð22Þ

Petukhov equation:

Nu ¼ ð f =8ÞRePr

1:07 þ 12:7ð f =8Þ0:5ðPr2=3 1Þ; 104 < Re

< 5 106; 0:5 < Pr < 200 ð23Þ

f ¼ ð1:82 logðReÞ 1:64Þ2

The friction factor can be calculated from the Colebrook equation

[48] as follows:

1

f 12

¼ 2:0 log 2:51

Re f 12

þe=D3:7

! ð24Þ

where e is the roughness of the copper tube and equals to

0.002 mm. The values of the pressure drop of base fluid in desire

Reynolds numbers calculated by the fitted curve to the experimen-

tal results of distilled water for hot water temperature at 60 C and

about 11 LPM flow rate. This correlation expressed as follows:

D p f ¼ 0:200304 þ 5:150343 105Re þ 6:856936 109

Re2;

R2 ¼ 99:98% ð25Þ

The results for Nusselt number with uncertainties presented in

Fig. 3 for hot water flow rate of 4.5 LPM and 10.8 LPM. It is observed

that our experiments have good accuracy. The maximum difference

between our experiment and Petukhov [47] equation are 5.18%

while maximum difference between experiments and Gnielinski

[46] equation is 11.93%. It must be noted that Wen and Ding [3] re-

ported maximum 30% difference between the results of experi-

ments and Shah equation. Kulkarni et al. [6] reported a maximum

±10% difference between their results and Dittus–Boelter equation

in turbulent flow.

Fig. 4 shows compatible results of friction factors between our

experiments on distilled water and Colebrook equation at various

hot water temperature and flow rate. Comparison between our re-sults shows very good agreement with Colebrook correlation.

6. Results and discussion

The experiments were carried out using TiO2–water nanofluid,

with particles of average diameter of 10, 20, 30 and 50 nm and

the following ranges of governing parameters: the Reynolds num-ber from 8000 to 55,000, the particle volume fraction from 0% to

2%. The results and discussion presented hereafter focus on the ef-

fects of particle volume concentration, Reynolds number and par-

ticle size diameter on the flow and heat transfer behaviour of the

nanofluid in the fully developed turbulent regime.

6.1. Heat transfer studies

Fig. 5 presents the mean Nusselt number of different nanopar-

ticle size at various volume concentrations. For u = 0.01, the Nus-

selt number increases for all Reynolds numbers when the d p

changes from 50 to 20 nm. For u = 0.015, the Nusselt numbers of

nanofluid with d p = 20 nm are greater than d p = 50 nm at all Rey-nolds numbers. For Reynolds > 32,000, by changing the diameter

Fig. 3. Mean Nusselt number with uncertainties for hot water flow rate of 4.5 LPM

and 10.8 LPM.

Fig. 4. Comparison of obtained friction factor from experiments on distilled water

and Colebrook equation.




from 50 to 30 nm and from 30 to 20 nm, higher Nusselt number

obtains. But for Reynolds > 24,000 by decreasing the diameter from

20 to 10 nm, the average Nusselt number decreases, meanwhile for

Reynolds > 34,000, nanofluid with d p = 10 nm has a greater Nusselt

number compare to d p = 50 nm.

At u = 0.02 for Reynolds > 26,000, higher Nusselt number ob-

serves by changing d p from 50 to 30 nm. This means that by chang-

ing the diameter from 30 to 20 nm, the Nusselt number increases

at approximately all Reynolds numbers. For Reynolds > 26,000,

the Nusselt number at d p = 10 nm are lower than those obtained

for 20 nm. However nanofluid containing nanoparticles with

d p = 10 nm have a greater Nusselt number relative to nanofluid

contains nanoparticles with d p = 50 nm for all experiments. Forlower Reynolds numbers by consideration of uncertainties, cannot

state anything.

In the consequent, at enough high volume concentrations of

nanoparticles, especially at higher Reynolds numbers, the values

of Nusselt number increase by changing the diameter of nanopar-

ticles diameter from 50 to 30 nm or from 30 to 20 nm. By more de-

creases the diameter of nanoparticles from 20 to 10 nm, lower

Nusselt number obtained. Thus the best diameter of nanoparticles

for TiO2 in order to get a higher heat transfer rate is 20 nm.

Values of maximum and minimum increment in Nusselt num-

ber of nanofluid compared to results of distilled water are shown

in Table 1 for different volume concentration and diameter of

nanoparticles. It is observed that the Nusselt number for all nano-

fluids increases by increasing volume concentration. All nanofluids

have a higher Nusselt number compared to distilled water. Bothminimum and maximum Nusselt numbers for u = 0.02 are higher

than the minimum and the maximum Nusselt number for

u = 0.015. The same trend exist for u = 0.015 and 0.01. Therefore

by increasing the volume concentration from 0.01 to 0.02, the Nus-

selt number increases.

As shown in Fig. 5, the Nusselt number increases with increas-

ing Reynolds number. Also it can be clearly seen that the Nusselt

number of the nanofluid is higher than that of the base fluid

(water) at a given Reynolds number. The results are agreed with

those obtained from Pak and Cho [2], He et al. [5] and Xuan and

Li [49] and. The possible reason for this enhancement may be

due to the following phenomena, the medium (fluid) with sus-

pended nanoparticles increases the thermal conductivity of the

mixture (nanofluid), and a large energy exchange process resulting

Fig. 5. Mean Nusselt numbers for (a) u = 0.01, (b) u = 0.015, (c) u = 0.02 with distilled water data.

Table 1

Maximum and minimum increment (%) of average Nusselt number compared to

distilled water.

vol.% 0.01 0.015 0.02

Nanoparticles diameter

(nm)

Min. Max. Min. Max. Min. Max.

10 29.18 44.96 39.68 62.26 62.94 82.44

20 35.31 60.87 49.89 78.46 67.66 98.87

30 27.10 44.54 41.37 59.17 56.84 82.47

50 22.76 40.57 36.28 62.42 48.35 67.01




from the chaotic movement of nanoparticles [50]. The reasons for

such enhancement in Nusselt number may be attribute to a large

number of phenomena such as mixing effects of particles near

the wall, thermal conductivity enhancement, Brownian motion of

particles, particle shape, particle migration and re-arrangement,

reduction of boundary layer thickness and delay in boundary layer

development as claimed by previous research works [3,51]. From

Fig. 5 it may be inferred that the enhancement in the heat transfer

coefficient is much higher compared to the enhancement in ther-

mal conductivity. This conclusion has been referred by Anoop

et al. [9] and Farajollahi et al. [13]. Anoop et al. [9] reported that

in their experimental study for 45 nm based nanofluid the

enhancement in heat transfer coefficient is around 25% whereas

the thermal conductivity for the same has increased only by 6%.

Similarly for 150 nm based nanofluids the heat transfer coefficient

enhancement is around 11%, whereas the thermal conductivity in-

crease was around 4% only.

Buongiorno [27] presented a relation between heat transfer

enhancement and Reynolds number and volume concentration.

He believed that the heat transfer enhancement of nanofluid in tur-

bulent flow relate to the reduction of viscosity and consequent

thinning of laminar sublayer. He explained that laminar sublayer

is a resistance against heat transfer and its thickness is propor-

tional to the viscosity of sublayer. Heat transfer enhancement by

nanoparticles in laminar sublayer is due to decrease in laminar

sublayer viscosity. Hence, with increasing Reynolds number as

well as nanofluid volume concentration, laminar sublayer gets

thinner and convective heat transfer coefficient increases

considerably.

The results of this study show that particle size can seriously af-

fect the Nusselt number enhancement. The movement velocity of

larger particles was much lower than that of smaller particles, thus

reducing the probability of collision. Also, at a same volume con-

centration, smaller particle size directly correlated with greater

number of nanoparticle and greater surface area of solid–liquid

interface. It helped to the enhancement of thermal conductivity re-

sult in enhancement of Nusselt number. Therefore, particle size af-fected not only the suspension state, better stability, but also the

thermal conductivity of nanofluid and Nusselt number. Using these

experimental data, the Nusselt number of nanofluid for TiO2–water

nanofluid can be expressed in terms of volume concentration,

Prantel number, Reynolds number and particle size.

The effects of particle concentration and nanofluid Reynolds

number, and particle size may be explained by the macroscopic

theory for the forced convective heat transfer. This theory states

that the convective heat transfer coefficient, can be approximately

formulate by h = k f /dt , inwhich k f and dt are the thermal conductiv-

ity and the thickness of thermal boundary layer, respectively. One

can see that both an increase in k f and a decrease in dt increase the

convective heat transfer coefficient. It is obviously presented that

an increase in Reynolds number leads to a decrease in the bound-ary layer thickness and an increase in the thermal conduction. Also

an addition of nanoparticles to base fluid increases the thermal

conduction and the enhancement increases with increasing parti-

cle concentration for a given particle size. The increase of the ther-

mal conduction should increase the convective heat transfer

coefficient. However, the increase in particle concentration also in-

creases the fluid viscosity, which should result in an increase in the

boundary layer thickness hence a decrease in the convective heat

transfer coefficient. As shown clearly in this study, addition of

nanoparticles enhances the convective heat transfer. These results

show that the positive effect of the thermal conduction enhance-

ment overcome the negative effect of the viscosity increase under

the conditions of this work. As can be seen, particle size has a mar-

ginal effect (compared to Reynolds number and volume concentra-tion) on the convective heat transfer under the conditions of this

work. In must be noted that nanofluids containing larger particles

have a lower thermal conductivity and a higher viscosity, both of

which should have led to a lower convective heat transfer coeffi-

cient. A possible reason for the marginal effect on the result may

be due to the particle migration mechanism [52]. According to this

opinion, large particles tend to migrate to the central part of the

pipe, which could lead to a particle depletion region with low vis-

cosity at the wall hence a decrease in the boundary layer thickness.

Also, small particles tend to be uniformly distributed over the pipe

cross-section due to the Brownian motion. Hence, for a given aver-

age particle concentration, the wall region could have a higher sol-

ids concentration and hence a higher viscosity when the flowing

nanofluids contain smaller particles. The combination of the above

two opposite mentioned effects could have been responsible for

the observed marginal effect of particle size under the conditions

of this work. It must be stated that, the proposed particle migration

mechanism is a hypothesis; further experimental study is needed

in order to verification and confirmation this conclusion.

6.2. Pressure drop studies

Fig. 6 depicts the values of the pressure drop of nanofluid for

different nanoparticles diameter. It is observed that by increasing

the Reynolds number, the D pnf increases. At a volume fraction of

0.01 and Reynolds > 18,000, D pnf increases by decreasing the diam-

eter of nanoparticles from 50 to 10 nm. Also an enhancement of

D pnf observes by change the diameter from 50 to 30 nm, 30 to

20 nm, 20 to 10 nm and Reynolds > 42,000. For lower Reynolds

numbers, because of uncertainties, cannot mention specific trend.

Although enhancement in theD pnf observed by changing the diam-

eter from 50 to 20 nm or 30 to 10 nm at enough high Reynolds

number. But for Reynolds < 14,000, all nanofluids have same pres-

sure drop.

Atu = 0.015 and Reynolds > 18,000, the D pnf relative to d p = 10 -

nm is higher than those obtained for d p = 30 and 50 nm. Also an

enhancement of D pnf observes by decreases d p from 50 till 10 nmand Reynolds > 34,000. Obvious enhancement in D pnf observed

by changing the diameter from 50 to 20 nm or 50 to 10 nm for a

wider range of Reynolds number. But for Reynolds < 14,000, all

nanofluids have same pressure drop.

At u = 0.02 and Reynolds > 18,000, the D pnf increases by

decreasing the diameter of nanoparticles from any diameter to

10 nm. Also an enhancement of D pnf observes by changing the

diameter from 50 to 20 nm and Reynolds > 26,000. For Rey-

nolds > 34,000 by decreasing the diameter of nanoparticles from

50 to30 nm, 30 to 20nm and from 20to 10nm, the D pnf increases.

Generally, D pnf changes by changing the diameter for Rey-

nolds > 12,000, while for a lower Reynolds number all nanofluid

have a similar pressure drop.

At low volume concentration, the change of nanoparticles diam-eter in nanofluid has not effected on the D pnf . The pump recoups

the pressure drops of nanofluid. Therefore, at large time of its func-

tion, higher energy consumes for nanofluid with nanoparticles

with diameters of 10 nm, especially at higher Reynolds numbers.

While its Nusselt number for enough high Reynolds numbers is

lower than the Nusselt number of nanofluid with 20 nm nanopar-

ticle diameter size. Thus decreases the diameter of nanoparticles

has not benefited always.

Anoop et al. [9] expressed that the results for 4 wt.% show that

nanofluid containing 45 nm nanoparticles has a higher convective

heat transfer coefficient compare with 150 nm. In the current

study, the Nusselt number increases by decreasing the nanoparti-

cles diameter from 30 or 50 to 20 nm at enough high Reynolds

numbers. But by more decreases in nanoparticles mean diameter,Nusselt number could be decreases compared with 20 nm.




It must be noted that the pressure drop is dependent on density

and viscosity of the fluid. With an increase in the nanoparticle vol-

ume concentration in the nanofluids the density and viscosity in-

creases and hence they cause an increased pressure drop as

shown in Fig. 6. With careful statistical analysis we have mini-

mized deviations between the empirical correlation and the data

obtained from the experiment. It is important to notice that that

pressure drop and friction factor vary weakly with viscosity but

strongly with density.

f nf ¼ 0:73Re0:32nf /

0:15 d pd f

0:02

; R2 ¼ 0:89% ð26Þ

These results are consistent with the results of Pak and Cho [2], and

Williams et al. [53]. Xuan and Li [49] presented that the dilute

nanofluid have no extra penalty of pump power. Our experiment

clearly showed that an extra pressure drop for dilute nanofluid.

6.3. Comparison of results with proposed correlations

There are a few correlations for Nusselt number of TiO2–water

nanofluid in literature. Nusselt number of fully developed turbu-

lent flow for TiO2–water proposed by Pak and Cho [2], and Maiga

et al. [54] and Dittus–Boelter are as follows, respectively:

Nu ¼ 0:023Re0:23Pr0:4 ð27Þ

Nu ¼ 0:021Re0:8Pr0:5 ð28Þ

Nu ¼ 0:085Re0:71Pr0:35 ð29Þ

Nusselt number proposed by Pak and Cho, Maiga et al. and Dittus–

Boelter are a function of Reynolds number and Prandtl number

only. However, in their correlations any dependence on the particle

volumetric concentration and or particle size diameter was not

considered.

Xuan and Li [49] presented a correlation in which Nusselt num-

ber was a function of concentration, particle size diameter

(through a particle Peclet number), Reynolds number and Prandtl

number as:

Nu ¼ 0:0059ð1:0 þ 7:6286u0:6886Pe0:001 p ÞRe0:9238

nf Pr0:4nf ð30Þ

Sajadi and Kazemi [18] noticed that increasing the nanoparticles

concentration had no influence on the heat transfer enhancement

in turbulent flow regime in the range of concentrations studied.

Therefore, their proposed Nusselt number was not a function of

concentration as:

Nu ¼ 0:067Re0:71Pr0:35 þ 0:0005Re ð31Þ

In the present investigation, a new correlation was derived by care-

ful analyzing of the data obtained for all volume concentration of

nanofluids. This correlation is a function of Reynolds number, Pra-

ndtl numbers, nanoparticles volume concentration and particle sizediameter as follow:

Fig. 6. Pressure drop of nanofluids for (a) u = 0.01, (b) u = 0.015, (c) u = 0.02.




Nunf ¼ 0:006Re0:86nf Prnf u

0:35 d p;c d f

0:1

; R2 ¼ 0:94%;

d f ¼ 0:386 nm u ¼ 1%; 1:5%; 2% ð32Þ

where

d p;c ¼ 90 þ 18:667d p 0:75d2 p þ 0:00833d

3 p;

d p ¼ 10; 20; 30; 50ðnmÞ ð33Þ

Proposed correlation is obtained by curve fitting all the experimen-

tal data for the nanofluids. Comparisons between the experimental

Nusselt number and those calculated by the proposed correlation

are shown in Fig. 7. This figure show good correspondence between

the experimental values and the calculated values by the above

equation. One can clearly see that the majority of the data falls

within ±6% of the proposed equation. The authors would like to

mention that this equation can be used for predicting the Nusselt

number of nanofluids with a volume concentration of 0–2% and a

Reynolds number range between 8000 and 55,000. In addition, it

is very important to note that this equation is only established with

respect to the data for TiO2–water nanofluid.

Fig 8 shows the results of Sajadi and Kazemi [18] and current

experiments for volume concentration of 0.002 and

5000 < Re < 30,000. It is obvious that both results show the same

values for Nusselt number at different Reynolds number. Correla-

tion of Sajadi et al. can be used for predicting the heat transfer

coefficient of nanofluids with a volume concentration of 60.25%

and a Reynolds number range between 5000 and 30,000. It is very

important to note that our correlation and Sajadi et al. were only

established with respect to the data of TiO2–water nanofluids.

Fig. 7. Comparisons of the empirical (propose) correlation (lines), Eq. (32), with the experimental data (symbols) (a) u = 0.01, (b) u = 0.015, (c) u = 0.02.

Fig. 8. Results of current experiments and Sajadi and Kazemi [18].




Sajadi and Kazemi [18] presented a comparison between the

experimental data and the proposed correlations for 0.2% volume

fraction of TiO2 dispersed in water. From this comparison, it is

clearly observed that except Maiga et al. [54] correlation, which

overestimates the Nusselt number, the other correlations underes-

timate the Nusselt number of nanofluids. This behaviour was ob-

served for all volume concentration of nanofluids investigated in

their work.

6.4. Thermal performance factor

The thermal performance factor is defined as follows [17,26]:

g ¼ ðNunf =Nu f Þ=ð f nf = f f Þ1=3

ð34Þ

Figs. 9–11 shows the thermal performance factor obtained with the

use of nanoparticles with water and various volume concentrations

of nanofluid (1%, 1.5% and 2%). One can seen that the thermal per-

formance factor for all the cases considered are greater than unity

which indicates that the heat transfer enhancement is possible by

using of nanofluid without huge penalty in pumping power. In this

study we obtained 1.6 for thermal performance factor at 1% volume

concentration for particle size diameter of 20 nm. At 1% volumeconcentration it varies between 1.35 and 1.6. Maximum thermal

performance factor obtained at Reynolds number equal to 9000

and 49,000. Same trend are exist for other volume concentrations.

At 1.5% it varies between 1.4 and 1.75. At 2% it varies between 1.6

and 1.9.

The main reason for presenting the thermal performance factor

is due to the fact the nanoparticles presented in the base liquid in-

crease the thermal conductivity and the viscosity of the base liquid

at the same time, and increase with increasing the particle concen-

trations. The increasing of the thermal conductivity leads to an

enhancement in the heat transfer performance, whereas the

increasing of the viscosity of the fluid leads to an increase in the

boundary layer thickness, which results in a decrease in the heat

transfer enhancement. As a result, for the volume concentration

studied in this work, the effect of thermal enhancement may over-

come the effect of the increasing of the viscosity. These results are

same as large number investigations that reported in literature

suchas He etal. [5], Xuan and Li [49], Nguyen et al. [55]. Moreover,

there are a few investigations that believe that the nanoparticles at

higher volume concentration may become combined together,

which caused the size became bigger and leads to a decrease in

the heat transfer performance factor. According to this study, the

present results are found to be different from those obtained from

other researchers, such as Pak and Cho [2]. As discussed above, it is

difficult to explain this difference in behaviour. One can be attrib-

uted to several factors, such as particle source, particle size, parti-

cle shape, particle preparation, and even solution chemistry (e.g.

pH value). Hence, more experimental works and theoretical study

are needed in order to explain exact heat transfer behaviour of

nanofluids for applying them in practical applications.

7. Conclusion

It is seen that the Nusselt number does not increase by decreas-

ing the diameter of nanoparticles generally. But pressure drop in-

creases significantly at high Reynolds number. Based on the

values of Reynolds number and the nanoparticle volume fraction,

change the diameter of nanoparticles could affect the Nusselt num-

ber and pressure drop of nanofluid. The Nusselt number increases

by enhancing the Reynolds number and nanoparticle volume frac-tion. By increasing the Reynolds number, the D pnf increases too.

Fig. 9. Variation of thermal performance factor with Reynolds number for 1%volume concentration and 10, 20, 30 and 50 nm particle size diameter.

Fig. 10. Variation of thermal performance factor with Reynolds number for 1.5%

volume concentration and 10, 20, 30 and 50 nm particle size diameter.

Fig. 11. Variation of thermal performance factor with Reynolds number for 2%

volume concentration and 10, 20, 30 and 50 nm particle size diameter.




Generally, D pnf changes by changing the diameter for Reynolds

greater than about 12,000, while for a lower Reynolds number all

nanofluid have a similar pressure drop. For cases that the diameter

of nanoparticles has a small effect on the Nusselt number, other

parameter expressed such as stabilization, pressure drop, accessi-

ble, the cost of preparation and so on must be considered. The re-

sults show that the best diameter of TiO2 nanoparticles to get a

higher heat transfer rate is 20 nm.

Based onto the obtained results, the following conclusions can

be drawn:

(a) It was observed that all nanofluids, with 10 nm, 20 nm,

30 nm and 50 nm particles size diameter showed higher

Nusselt number than the base fluid.

(b) It was further observed that the nanofluid with 20 nm parti-

cles size diameter shows higher thermal performance factor

than that other particles size diameter.

(c) With increase in Reynolds number and volume concentra-

tion the average Nusselt number was increased.

(d) A new experimental correlation was suggested to bring out

the effects of influencing parameters, Reynolds number, vol-

ume concentration and particle size diameter, on convective

heat transfer in the developing region while using nanofl-

uids. The majority of the data falls within ±6% of the pro-

posed equation. These equations are valid in the range of

Reynolds number between 9000 and 49,000 and particle vol-

ume concentrations in the range of 0 and 2.0 vol.%.

(e) It was observed that the pressure drop of nanofluid has not

significant increase compared to distillated water.

(f) Over the range investigated, the maximum thermal perfor-

mance factor of 1.9 is found with the simultaneous use of

the TiO2–water nanofluid with 0.02% volume, Reynolds

number of 47,000 and nanoparticle diameter size of 20 nm.

Acknowledgements

The authors would like to thank the referees for their valuable

comments. The authors are grateful to University of Kashan for

supporting this work by Grant No. 55806. They would also like

to thank the Iranian Nanotechnology Development Committee

for their financial support.

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