2

International Journal of Heat and Mass Transfer 54 (2011) 4376–4388

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Numerical investigation of effective parameters in convective heat transferof nanofluids flowing under a laminar flow regime

Ehsan Ebrahimnia-Bajestan a,⇑, Hamid Niazmand a, Weerapun Duangthongsuk b, Somchai Wongwises c,d

a Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iranb Department of Mechanical Engineering, South-East Asia University, Bangkok, Thailandc Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE), Department of Mechanical Engineering,King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailandd The Royal Institute of Thailand, Academy of Science, Sanam Sueapa, Dusit, Bangkok 10300, Thailand.

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 December 2010Received in revised form 29 April 2011Accepted 29 April 2011Available online 27 May 2011

Keywords:NanofluidsHeat transfer performancePressure dropNumerical studyThermal conductivity

0017-9310/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2011.05.006

⇑ Corresponding author. Tel.: +98 915 300 6795; faE-mail address: [email protected] (E.

This article presents a numerical investigation on heat transfer performance and pressure drop of nano-fluids flows through a straight circular pipe in a laminar flow regime and constant heat flux boundarycondition. Al2O3, CuO, carbon nanotube (CNT) and titanate nanotube (TNT) nanoparticles dispersed inwater and ethylene glycol/water with particle concentrations ranging between 0 and 6 vol.% were usedas working fluids for simulating the heat transfer and flow behaviours of nanofluids. The proposed modelhas been validated with the available experimental data and correlations. The effects of particle concen-trations, particle diameter, particles Brownian motions, Reynolds number, type of the nanoparticles andbase fluid on the heat transfer coefficient and pressure drop of nanofluids were determined and discussedin details. The results indicated that the particle volume concentration, Brownian motion and aspect ratioof nanoparticles similar to flow Reynolds number increase the heat transfer coefficient, while the nano-particle diameter has an opposite effect on the heat transfer coefficient. Finally, the present study pro-vides some considerations for the appropriate choice of the nanofluids for practical applications.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Common heat transfer fluids such as oil, water and ethyleneglycol have inherently poor thermal conductivity compared tomost solids. This problem is the primary obstacle to the highcompactness, light in weight and effectiveness of heat exchangers.In order to enhance the thermal conductivity of conventional heattransfer fluids, it has been tried to develop a new type of modernheat transfer fluid by suspending ultrafine solid particles in basefluids. In 1993, Masuda et al. [1] studied the heat transfer perfor-mance of liquids with solid nanoparticles suspension. However,the term of ‘‘nanofluid’’ was first named by Choi [2] in 1995, andsuccessively gained popularity. Because of the extensively greaterthermal conductivity and heat transfer performance of the nanofl-uids as compared to the base fluids, they are expected to be ideallysuited for practical applications.

Since a decade ago, research publications related to the use ofnanofluids as working fluids have been reported both numericallyand experimentally. There are also some review papers thatelaborate on the current stage in the thermal behaviours,

ll rights reserved.

x: +98 511 876 3304.Ebrahimnia-Bajestan).

thermophysical properties and flow characteristics of nanofluids[3–6]. However, this article is aimed at reviewing only the novelliterature considering convective heat transfer of nanofluids witha numerical approach. These studies are briefly described asfollows.

Mirmasoumi and Behzadmehr [7] reported the effect of nano-particle diameter on convective heat transfer performance ofAl2O3/water nanofluid flowing under a fully developed laminarflow regime numerically. In their study, a two-phase mixture mod-el was used. The results demonstrated that the heat transfer coef-ficient of the nanofluid dramatically increases with decreasing thediameter of nanoparticle. Moreover, the results also indicated thatnanoparticle diameter has no significant effect on the skin frictioncoefficient.

Kalteh et al. [8] numerically studied forced convective heattransfer of Cu/water nanofluid inside an isothermally heatedmicrochannel under a laminar flow regime. An Eulerian two-fluidmodel was used to simulate the heat transfer characteristic ofthe nanofluid. The results indicated that the heat transfer perfor-mance increases with increasing Reynolds number as well asparticle volume fraction. On the contrary, heat transfer enhance-ment increases with decreasing nanoparticle diameter. Finally,the results also showed that the pressure drop of nanofluids isslightly higher than that of base fluids.

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E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388 4377

Mirmasoumi and Behzadmehr [9] investigated the laminarmixed convection heat transfer of Al2O3/water nanofluid flowingthrough a horizontal tube numerically. A two-phase mixture mod-el was used to describe the hydrodynamic and thermal behaviourof the nanofluid. The numerical results indicated that in the fullydeveloped region the particle concentration has insignificant ef-fects on the hydrodynamic parameters, while it has important ef-fects on the thermal parameters. Moreover, the results showedthat nanoparticle concentration is higher at the bottom of the testtube and at the near wall region.

Akbarinia [10] and Akbarinia and Behzadmehr [11] numericallyinvestigated the fully developed laminar mixed convection ofAl2O3/water nanofluid flowing through a horizontal curved tube.In their studies, three-dimensional elliptic governing equationswere used. The effects of the buoyancy force, centrifugal forceand particle concentration on the heat transfer performance werepresented. The results showed that the particle concentration hasno direct effect on the secondary flow, axial velocity and skin fric-tion coefficient. However, when the buoyancy force is more impor-tant than the centrifugal force, the effect of particle concentrationon the entire fluid temperature can affect the hydrodynamicparameters. Moreover, the results also indicated that the buoyancyforce decreases the Nusselt number whereas the particle concen-tration has a positive effect on the heat transfer enhancementand on the skin friction reduction.

Izadi et al. [12] studied the hydrodynamic and thermal behav-iours of an Al2O3/water nanofluid flowing through an annulusunder a laminar flow regime. In their study, a single-phase modelwas used for nanofluid simulation. The results indicated that theparticle volume concentration has no significant effect on thedimensionless axial velocity, but affects the temperature fieldand increases the heat transfer coefficient.

He et al. [13] numerically studied the convective heat transferof a nanofluid with TiO2 nanoparticles dispersed in water underlaminar flow conditions. A single-phase model and combined Eulerand Lagrange methods were used to investigate the effects of vol-ume concentration, Reynolds number and aggregate size on theconvective heat transfer and flow behaviour of the nanofluid. Theirresults indicated that the nanofluid significantly enhances the Nus-selt number, especially in the entrance region. Moreover, thenumerical results were consistent with experimental data.

Bianco et al. [14] investigated the heat transfer performance ofan Al2O3/water nanofluid flowing through a circular tube under alaminar flow regime numerically. A single-phase model and two-phase model were used to determine the heat transfer coefficientof the nanofluid. The results demonstrated that the heat transferperformance increases with increasing Reynolds number as wellas particle volume concentration. Moreover, differences in theaverage heat transfer coefficient between the single-phase andtwo-phase models were observed as approximately 11%.

Kumar et al. [15] used a single-phase thermal dispersion modelto numerically investigate the thermal properties and flow fieldof a Cu/water nanofluid in a thermally driven cavity. The resultsindicated that the Grashof number, particle volume fraction andparticle shape factor augment the average Nusselt number ofnanofluids.

Talebi et al. [16] presented the numerical formulation to evalu-ate the laminar mixed convection heat transfer of Cu/water nano-fluid flowing through a square lid-driven cavity. They found that, ata given Reynolds number, the particle concentration affects thethermal behaviour and flow characteristic at larger Rayleigh num-bers. Moreover, the effect of particle concentration decreased withincreasing Reynolds number.

Shahi et al. [17] reported a numerical investigation to simulatethe heat transfer performance of Cu/water nanofluid flowingthrough a square cavity under a laminar flow regime. Their results

indicated that the average Nusselt number of the nanofluid in-creases with increasing particle concentration. In contrast, the re-sults also showed that the bulk temperature of the nanofluiddecreases with increasing particle concentration.

Akbarinia and Laur [18] presented the laminar mixed convec-tion heat transfer of Al2O3/water nanofluid flows in a circularcurved tube numerically. A two-phase mixture model and thecontrol-volume technique were used to investigate the effect ofparticle diameter on the hydrodynamic and thermal parameters.Their results indicated that the Nusselt number and secondary flowdecrease with increasing the particle diameter and uniform distri-bution of nanoparticles is observed.

Zeinali Heris et al. [19] numerically investigated the convectiveheat transfer of nanofluid in a circular tube with constant walltemperature, employing a dispersion model. Their results showedthat decreasing nanoparticle size and increasing nanoparticle con-centration augment the heat transfer coefficient.

Raisi et al. [20] carried out a numerical study on laminar con-vective heat transfer of Cu/water nanofluid inside a microchannelwith slip and no slip boundary conditions. They investigated the ef-fect of different parameters such as Reynolds number, particle con-centration, and slip velocity coefficient on the nanofluid heattransfer characteristics. The results indicated that the particle con-centration and slip velocity coefficient have significant effects onthe heat transfer rate at high Reynolds numbers.

Ghasemi and Aminossadati [21] investigated the natural con-vective heat transfer of CuO/water nanofluid inside an inclinedenclosure with top and bottom wall at different temperatures.The effects of Rayleigh number, inclination angle, and particle con-centration on heat transfer performance were studied. The resultsshowed that the flow pattern, temperature field and heat transferrate are affected by inclination angle at high Rayleigh numbers.Furthermore, it was found that the heat transfer rate is maximisedat specific particle concentration and inclination angle.

Zhou et al. [22] presented the lattice Boltzman method (LBmethod) to study the microscale characteristics of the multicom-ponent flow of nanofluids. In this method, the computation domainwas separated into fine mesh and coarse mesh regions, respec-tively. The multicomponent LB method was used in the fine meshregion and the single-component LB method was applied in thecoarse mesh region. The results indicated that the present modelcan be used to predict the microscopic characteristics of thenanofluid and the computational efficiency can be significantlyimproved.

Although numerous papers are currently available on thenumerical study of laminar convective heat transfer of nanofluids,there is no comprehensive study on different effective parametersin this field. The effect of several parameters such as nanoparticleshape, based fluid type and nanoparticle material are not consid-ered in literature. On the other hand, naturally the increase in heattransfer performance due to the nanofluids is accompanied byseveral undesirable effects such as an increase in pressure drop.Therefore, it needs to find the suitable nanofluid for optimum oper-ation. No significant attention is paid to find some criteria for thechoice of appropriate nanofluids in different heat transfer applica-tions. In the present study a modified single-phase model for pre-dicting the heat transfer performance of nanofluids is proposedand a home-made FORTRAN computer program is developed. Themodel has been validated against the measured data of Kim et al.[23] and the predicted values from Shah and London [24] for thebase fluid. The effects of particle concentration, mean particlediameter, Reynolds number, Brownian motion, nanoparticle mate-rial and shape, and type of base fluid on the heat transfer perfor-mance of nanofluids are then investigated in detail. Finally, someguidelines related to choice of the appropriate nanofluid for partic-ular applications are provided.

4378 E. Ebrahimnia-Bajestan et al. / International Journal of Heat and Mass Transfer 54 (2011) 4376–4388

2. Mathematical modelling

Normally, two different approaches can be used in predictingthe heat transfer performance of nanofluids. One is the two-phasemodel, where solid particles are treated as a solid phase in the basefluid, and the other is the single-phase model, where the presenceof the nanoparticles is accounted for by introducing the effectivethermophysical properties for the nanofluid. A single-phase modelis simpler to implement and requires less computational time, andtherefore, adopted here to describe the heat transfer characteristicsof nanofluids flowing through a straight circular tube under con-stant wall heat flux and laminar flow regime, as shown in Fig. 1.On the basis of this model, the governing equations are as follows.

For continuity equation:ZZqe~V � d~A ¼ 0: ð1Þ

For momentum equation:Z8qe@~V@t

d8 þZZ

~Vqe~V � d~A ¼ �

ZZp~n � d~Aþ

ZZle~r~V � d~A ð2Þ

For energy equation:Z8ðqCpÞe

@T@t

d8 þZZðqCpÞeT~V � d~A ¼

ZZke~rT � d~A ð3Þ

where ~V , p, T, t, ", ~A and~n are the velocity vector, pressure, temper-ature, time, volume, cross-sectional area vector and normal unitvector, respectively. The effective thermophysical properties ofthe nanofluid indicated by the subscript e are density (q), thermalconductivity (k), dynamic viscosity (l), and heat capacity (Cp). Theseeffective properties are modelled as temperature dependent vari-ables using available correlations and experimental data as follows.

Density:

qeð/; TÞ ¼ ð1� /Þqf ðTÞ þ /qp ð4Þ

Heat capacity:

Cp;eð/; TÞ ¼ð1� /ÞðqðTÞCpðTÞÞf þ /ðqpCpÞp

ð1� /Þqf ðTÞ þ /qpð5Þ

where / is the volume fraction of the nanoparticles, and the sub-scripts p and f indicate the nanoparticle and base fluid, respectively.

Regarding the dynamic viscosity and thermal conductivity ofnanofluids two different methods have been considered. In the firstmethod, available measured data of these properties in static con-dition are used. However, in the second method, available modelsfor dynamic viscosity and thermal conductivity of nanofluids,where different effects such as base fluid type, Brownian motions,volume concentration, and nanoparticle diameters are also in-cluded are employed. Clearly, these models are designed to accu-rately predict the heat transfer coefficient.

In the present study, the measured data of Kim et al. [23] is usedto develop the following correlations for predicting the effective

Flow

L =

q = co

x

Fig. 1. Flow geometry and num

thermal conductivity and viscosity of the nanofluids according tothe first method.

le ¼ �0:0001953þ 0:0475745T

� 0:42561T2

for 20 �C 6 T 6 80 �C ð6Þ

ke ¼ 0:65þ 4:864� 10�7T3 for 22 �C 6 T 6 52 �C ð7Þ

where T is the temperature in Celsius. However, it should be men-tioned that above correlations are valid only for Al2O3/water nano-fluid containing 3 vol.% of suspended particles.

As for the second method, the Vajjha et al.’s [25] model is takenfor viscosity with two parameters A and B, which are determinedaccording to the experimental data of Kim et al. [23].

le ¼ lf ðTÞA expðB/Þ ð8Þ

This correlation applies for 20 �C 6 T 6 90 �C and 1% 6 / 6 10%,with A = 0.9 and B = 10.0359.

For thermal conductivity, the model presented by Koo and Kle-instreuer [26] and modified by Vajjha and Das [27] is employed.The model consists of static thermal conductivity based on theMaxwell’s theory and dynamic thermal conductivity to includeBrownian motion of nanoparticles. This model is expressed asfollows:

ke ¼kp þ 2kf � 2ðkf � kpÞ/kp þ 2kf þ ðkf � kpÞ/

� �kf þ ð5� 104b/qf Cp;f Þ

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijðT þ 273:15Þ

qpdp

sf ðT;/Þ ð9Þ

f ðT;/Þ ¼ ð2:8217� 10�2/þ 3:917� 10�3Þ ðT þ 273:15ÞðT0 þ 273:15Þ

þ ð�3:0669� 10�2/� 3:91123� 10�3Þ ð10Þ

b ¼ 8:4407ð100/Þ�1:07304 ð11Þ

where j is the Boltzmann constant (1.381 � 10�23 J/K), dp is thenanoparticle diameter (m), and T is the temperature (�C). T0 = 0 �Cis the reference temperature. The correlation is valid for25 �C 6 T 6 90 �C and the volume fractions between 1% and 10%for Al2O3 nanofluids [27]. It should be mentioned that all thermo-physical properties of the base fluid (lf, kf, Cp,f and qf) are consid-ered as functions of temperature. For water as the base fluid,density, heat capacity and thermal conductivity are obtained fromthe curve-fits applied to available data [28], while for dynamic vis-cosity the following correlation is employed [29]:

lwater ¼ 0:00002414� 10½247:8=ðTþ133Þ� ð12Þ

The above methods for effective viscosity (Eqs. (6) and (8)) havebeen compared with measured data of Kim et al. [23] for 3.0 vol.%Al2O3/water nanofluids, where reasonable agreements areobserved (Fig. 2). Similarly, the temperature variations of thermal

2 m

D= 4.57 mm

D

nst.

erical grid distributions.


conductivity according to Eqs. (7) and (9) have been comparedwith the measured data of Kim et al. [23] as shown in Fig. 3. Itcan be seen that Eq. (9) over predicts the thermal conductivity ascompared to the measured data, however it can predict the heattransfer coefficient more accurately as compared to Eq. (7) as willbe discussed later.

3. Solution methodology

In order to evaluate the heat transfer coefficient of nanofluidsnumerically, the following assumptions are required.

As for boundary conditions for velocity filed, a uniform velocityprofile is assumed at the inlet, while zero gradients are applied toall hydrodynamic variables at the outlet, with no-slip condition at

Temp10 20 30 40

Visc

osity

(Pa.

s)

.0002

.0004

.0006

.0008

.0010

.0012

.0014

Fig. 2. Comparison of the predicted viscosity usi

Tempe

10 20 30

Ther

mal

con

duct

ivity

(W/m

K)

.60

.65

.70

.75

.80

.85

.90

Fig. 3. Comparison of the predicted thermal conductiv

walls. For the thermal field, constant heat flux of 60 W (2089.56 W/m2) and the inlet temperature of 22 �C are employed correspond-ing to the data of Kim et al. [23], while constant temperature gra-dient is applied at the outlet.

In order to simulate the nanofluid flow, pipe geometry with4.57 mm in diameter and 2 m long has been adopted accordingto the flow geometry in the experimental work of Kim et al. [23]as shown in Fig. 1. The problem under investigation is steady, how-ever, in the numerical scheme the steady solution is obtainedthrough sufficient integrations in time. The governing equationsare solved numerically in a body-fitted coordinate system using acontrol-volume technique. The numerical solution is based on aprojection-type method which solves the flow field in two steps.Firstly, an intermediate velocity field is obtained using the avail-able pressure field. Secondly, velocity and pressure corrections

erature (oC)50 60 70 80 90

Measured data of Kim et al. [23]Eq. (6) Eq. (8)

ng Eqs. (6) and (8) with the measured data.

rature (oC)

40 50 60 70

Measured data of Kim et al. [23]Eq. (7) Eq. (9)

ity using Eqs. (7) and (9) with the measured data.


are calculated from a Poisson equation designed to satisfy the con-tinuity equation. The numerical scheme was originally developedby Chorin [30] and improved further by Dwyer [31] as well as Ren-ksizbulut and Niazmand [32].

Moreover, extensive computations have been performed toidentify the number of grid points that produce reasonably gridindependent results. In Fig. 4 the grid resolution effects on the axialvariations of the centreline velocity (nondimensionalized with theinlet velocity) and the heat transfer coefficient for just four differ-ent mesh distributions are presented. It is clear that the grid sys-tem of 41 � 50 � 150 points in respective directions of radial,azimuthal, and axial adequately resolve the velocity and thermalfields with reasonable accuracy. Uniform grid spacing is used inthe azimuthal direction, while the expansion ratios of 1.15 and1.02 are employed in the radial and axial directions.

0.0 .5

Dim

ensi

onle

ss v

eloc

ity

1.0

1.2

1.4

1.6

1.8

2.0(a)

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

500

1000

1500

2000

2500(b)

Fig. 4. Grid resolution effects on the axial variations of (a) dimensionless centreline velonumber of 1460.

4. Model validation

For validating the present numerical scheme, the axial varia-tions of the local Nusselt number have been compared with theexperimental data of Kim et al. [23] and the results of Shah andLondon [24] as shown in Fig. 5. A laminar water flow in a straightcircular pipe geometry, as mentioned above, has been consideredunder the constant heat flux condition of 60 W (2089.56 W/m2)at Reynolds number of 1620. The Shah and London [24] equa-tion for the axial variations of the local Nusselt number isexpressed as:

NuðxÞ¼3:302x�1=3

� �1; x�6 0:000051:302x�1=3

� �0:5; 0:00005< x� <0:0015

4:264þ8:68ð103x�Þ�0:506 expð�41x�Þ; x�>0:001

8><>:

ð13Þ

x (m)1.0 1.5 2.0

21 x 30 x 70 41 x 50 x 150 51 x 50 x 170 61 x 50 x 190

r θ x

x (m)1.0 1.5 2.0

21 x 30 x 70 41 x 50 x 150 51 x 50 x 170 61 x 50 x 190

r θ x

city and (b) heat transfer coefficient for 6.0 vol.% Al2O3/water nanofluid at Reynolds


where x� ¼ x=DRe Pr. Excellent agreements between the results can be

observed in Fig. 5.For the validation of the effective nanofluid properties models,

the convective heat transfer of nanofluid in a straight pipe has beenconsidered. Fig. 6 shows the axial variations of heat transfer coef-ficient of Al2O3/water nanofluid containing 3.0 vol.% of nanoparti-cles for Reynolds number of 1460. The results indicate that thesecond method (Eqs. (8) and (9)) agrees better with the measureddata of Kim et al. [23] as compared to the first method (Eqs. (6) and(7)). This implies that the changes in thermal conductivity of nano-fluids at static condition cannot justify the enhancement in heattransfer coefficient of nanofluids and a model, which adjusts thethermal conductivity to accurately estimate the heat transfer coef-ficient, is required.

x

0.0 .5

Nus

selt

num

ber

0

5

10

15

20

25

30

Fig. 5. Comparison of the axial variations of the Nusselt number w

0.0 .5

Hea

t tra

nsfe

r co

effic

ient

(W

/m2 K

)

400

600

800

1000

1200

1400

1600

1800

2000

Fig. 6. Comparison of the local heat transfer coefficient with measured d

Other numerical scheme validations for nanofluids can be foundin Ebrahimnia-Bajestan et al. [33], which are not repeated here forconciseness.

5. Results and discussion

As shown in Fig. 6, the second method of nanofluid propertiesmodels predicts the heat transfer coefficient more accurately thanthe first method. In addition, the second method is more generalthan the first method, which is only valid for 3.0 vol.% Al2O3/water.Therefore, the second method has been employed for the evalua-tions of the effective thermal conductivity and viscosity in allnumerical computations reported here. Moreover, the effects of

(m)

1.0 1.5 2.0

Measured data of Kim et al. [23]Present model

Shah and London [24]

ith available data in literature at Reynolds number of 1620.

x (m)1.0 1.5 2.0

Measured data of Kim et al. [23]Present model (Using Eqs. 6 & 7)Present model (Using Eqs. 8 & 9)

ata of 3.0 vol.% Al2O3/water nanofluid at Reynolds number of 1460.


several parameters on the convective heat transfer characteristicsof nanofluids will be examined in detail.

5.1. The effect of nanoparticle concentration

Fig. 7 shows the effect of particle volume concentration on theheat transfer coefficient along the pipe for Reynolds number of1460 and heat flux of 2089.56 W/m2. The results indicate thatthe heat transfer coefficient of nanofluid increases with increasingparticle volume concentration. According to Eq. (9), nanofluidswith higher particle concentrations have higher static and dynamicthermal conductivities, which in turn increase the heat transfercoefficient. For example, in the case of 6.0 vol.%, the local heattransfer coefficient is about 22% larger than pure water at theend of the pipe.

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

2000

Re = 1460Particle type : Al2O3

Fig. 7. Axial variations of heat transfer coefficient for different particle volum

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

2000


2.dp =

6.0

Fig. 8. Axial variations of heat transfer coefficient for different particle diameter

5.2. The effect of nanoparticle diameter

The effect of nanoparticle diameter on the heat transfer perfor-mance of nanofluid for Reynolds number of 1460 and heat flux of2089.56 W/m2 is shown in Fig. 8. The results show that the nano-fluid with smaller nanoparticle diameter slightly increases the heattransfer coefficient as compared to the larger particle diameter,especially at lower volume concentrations. In general, accordingto Eq. (9) the nanoparticle diameter has a negative effect on thethermal conductivity and consequently on the heat transfercoefficient.

5.3. The effect of Reynolds number

Fig. 9 presents the effect of Reynolds number on the heattransfer coefficient along the pipe for Al2O3/water nanofluid with

x (m)

1.0 1.5 2.0

water2.0 vol.%4.0 vol.%6.0 vol.%

e concentrations of Al2O3/water nanofluid at Reynolds number of 1460.

x (m)1.0 1.5 2.0

0 vol.% 2.0 vol.%6.0 vol.%

20 nm dp = 100 nm

vol.%

s and concentrations of Al2O3/water nanofluid at Reynolds number of 1460.


particle diameter of 20 nm. The results indicate that the heat trans-fer coefficient of nanofluid increases with increasing Reynoldsnumber. This is due to the fact that higher Reynolds numbers leadto higher velocity and temperature gradients at the pipe wall.

5.4. The effect of Brownian motion of nanoparticles

According to Eq. (9), the second term is related to the dynamicthermal conductivity and reflects the Brownian motion effects onthe thermal characteristics of nanofluids. In order to study the ef-fects of Brownian motion on the heat transfer performance ofnanofluids, Eq. (9) without the dynamic thermal conductivity termis used to simulate the convective heat transfer. It means that theclassical two-phase model of Maxwell is employed and compared

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

2000

Re = 5Re = 1Re = 1

φ = 0 vol.

Fig. 9. Axial variations of heat transfer coefficient for different Reynol

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

2000

2200

with Brownian effectwithout Brownian effe

φ = 2.0 vol.%


Fig. 10. Effects of Brownian motion on the local heat transfer coefficient as a function

with the new nanofluid thermal conductivity model. Fig. 10 com-pares the axial variations of the heat transfer coefficient of Al2O3/water nanofluid with and without Brownian motion effects onthermal conductivity model for various particle concentrations atReynolds number of 1460 and particle diameter of 20 nm. It isclearly seen that the Brownian motion has significant effects onthe heat transfer coefficient of the nanofluids.

5.5. The effect of nanoparticle material

The nanoparticle material affects the nanofluid properties andconsequently is an important factor in heat transfer performance.In order to study the effect of nanoparticle material, the CuO/waternanofluid is selected to compare with the results of the Al2O3/

x (m)1.0 1.5 2.0

dp = 20 nmParticle type : Al2O3

00 000 460

Re = 500 Re = 1000 Re = 1460

% φ = 4.0 vol.%

ds numbers and particle concentrations of Al2O3/water nanofluid.

x (m)1.0 1.5 2.0

with Brownian effectwithout Brownian effect ct

φ = 6.0 vol.%

of particle concentration for Al2O3/water nanofluid at Reynolds number of 1460.


water nanofluid. For the viscosity of the CuO/water nanofluid, Eq.(8) is employed, where constants A = 0.9197 and B = 22.8539 areobtained following Vajjha et al. [25]. The thermal conductivity ofCuO/water is evaluated based on Eqs. (9) and (10), however, theparameter b is determined from [27] as expressed below, whichis valid for 25 �C 6 T 6 90 �C and 1% 6 / 6 6%.

b ¼ 9:881ð100/Þ�0:9446 ð14Þ

As shown in Fig. 11, CuO/water nanofluids give higher convec-tive heat transfer coefficients than the Al2O3/water nanofluids.For example, the heat transfer coefficient of 4.0 vol.% CuO/waternanofluids is greater than that of the 6.0 vol.% Al2O3/water nanofl-uids. This is because of the fact that the thermal conductivity ofCuO nanoparticles is much larger than the thermal conductivityof Al2O3 nanoparticles.

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

600

800

1000

1200

1400

1600

1800

2000

dp = 20 nmRe = 1460

CuO2.0 vo4.0 vo6.0 vo

Fig. 11. Effects of particle type and particle concentration on the local heat trans

0.0 .5

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

2000

W604.4.

dp = 40 nm Re = 1460

Fig. 12. Axial variations of heat transfer coefficient for different base fl

5.6. The effect of base fluid properties

Another important factor in the heat transfer characteristics ofnanofluids is the type of base fluid. In addition to water, a commonbase fluid consists of 60% ethylene glycol and 40% water (60% EG/water) by mass has also been considered. This kind of heat transferfluid is common in cold regions of the world because of its lowfreezing point. The thermophysical properties of 60% EG/water asfunctions of temperature are obtained from [34] as follows:

q60%EG=water ¼ �2:475� 10�3T2 � 0:35T þ 1090:93 ð15Þ

Cp;60%EG=water ¼ 4:248T þ 3042:74 ð16Þ

k60%EG=water ¼ �3:196� 10�6T2 þ 7:54� 10�4T þ 0:34 ð17Þ

x (m)1.0 1.5 2.0

Al2O3l.%l.%l.%

2.0 vol.%4.0 vol.%6.0 vol.%

fer coefficient at Reynolds number of 1460 and particle diameter of 20 nm.

x (m)1.0 1.5 2.0

ater%EG/Water

0 vol.% (Al2O3 - Water nanofluid) 0 vol.% (Al2O3 - 60%EG/Water nanofluid)

uids at Reynolds number of 1460 and particle diameter of 20 nm.

Table 1Properties of CNT/water and TNT/water nanofluids.

Nanofluids Nanoparticles aspect ratio Nanoparticles concentration (vol.%) Viscosity (Pa s) Thermal conductivity (W/m K)k = a + bT + cT2

a b c

CNT/water >100 0.0384 0.00308 51.88156 �0.35487 6.14 � 10�4

TNT/water �10 0.6 0.0015 0.42548 6.4 � 10�4 0

x (m)0.0 .5 1.0 1.5 2.0

Hea

t tra

nsfe

r coe

ffici

ent (

W/m

2 K)

400

600

800

1000

1200

1400

1600

1800

20000.0384 vol.% (CNT-Water)0.6 vol.% (TNT-Water)2.0 vol.% (Al2O3-Water)4.0 vol.% (Al2O3-Water)4.0 vol.% (CuO-Water)

Re = 1460

Fig. 13. Effects of particle shape on the local heat transfer coefficient at Reynolds number of 1460.

Table 2Different nanofluids flow conditions simulated in the present study and theircorresponding temperature increase, pressure drop, and pumping power.

Type ofworking fluids

Re dp (nm) /(vol.%)

DT(�C)

DP(Pa)

Pumppower (W)

Al2O3/60% EG/water 1460 20 4 0.56 43240 1.3860% EG/water 1460 – – 0.68 26240 0.69CNT/water 1460 Lp/dp > 100 0.038 0.9 9625 0.16CuO/water 1460 20 6 1.05 8838 0.12CuO/water 1460 20 4 1.52 3830 0.04TNT/water 1460 dp = 10, Lp = 100 0.6 1.8 2241 0.017Al2O3/water 1460 100 6 2.05 2020 0.014


l60%EG=water ¼ 0:001 exp3135:6

T þ 273:15� 8:9367

� �ð18Þ

These correlations are valid for 0 �C 6 T 6 97 �C.According to Vajjha and Das [27], Eqs. (8)–(11) are still applica-

ble for the evaluation of viscosity and thermal conductivity of 60%EG/water base nanofluids.

In Fig. 12, the heat transfer coefficients of Al2O3 nanoparticles inboth water and 60% EG/water base fluids are compared. The resultsindicate that the heat transfer characteristics of nanofluids arestrongly influenced by the type of the base fluid.

Al2O3/water 1460 40 6 2.06 2020 0.014Al2O3/water 1460 20 6 2.08 2020 0.014CuO/water 1460 20 2 2.18 1670 0.011Al2O3/water 1460 40 4 2.39 1416 0.008Al2O3/water 1460 20 4 2.39 1417 0.008Al2O3/water 1460 20 3 2.52 1188 0.007Water 1620 – – 2.6 974 0.005Al2O3/water 1460 20 2 2.72 996 0.005Al2O3/water 1460 100 2 2.72 995 0.005Al2O3/water 1460 40 2 2.73 995 0.005Water 1460 – – 2.78 869 0.004Al2O3/water 1000 20 4 3.44 936 0.004Water 1000 – – 4.08 572 0.002Al2O3/water 500 20 4 6.91 438 0.0009Water 500 – – 8.19 266 0.0004

5.7. The effect of nanoparticle shape

It has been shown that nanofluids containing nanoparticleswith a higher aspect ratio have better thermal properties [35,36].For example, the cylindrical nanoparticles give higher thermal con-ductivity and heat transfer coefficient than the spherical nanopar-ticles. To study the effect of nanoparticle shape, two kinds ofcylindrical nanoparticles, which are CNT and TNT are used andthen compared with the nanofluids with spherical nanoparticles.He et al. [35] studied the heat transfer performance of CNT/waternanofluid containing 0.1 wt.% (0.0384 vol.%) and TNT/water nano-fluid containing 2.5 wt.% (0.6 vol.%) numerically and experimen-tally. They indicated that, at a given temperature, the shearviscosity of both nanofluids decreases with increasing shear rate,exhibiting a shear thinning behaviour. Moreover, the shear viscos-ity approaches a constant minimum value at higher shear rate. Themeasured viscosity did not show an important change versus sharerate, more than the shear rates of 200 1/s and 500 1/s for the CNT/

water and TNT/water nanofluids, respectively. They simulated theconvective heat transfer of nanofluids as both Newtonian andnon-Newtonian fluids. Their results showed that the heat transfercoefficients based on the non-Newtonian model agree well withthe measured data. Furthermore, they indicated that, when the


nanofluid is considered as Newtonian with the constant minimumvalue of viscosity, the heat transfer coefficient has also reasonableagreement with the result of non-Newtonian model.

In the present work, the constant minimum value of viscositypresented by He et al. [35] was adopted as the effective viscosity.Similarly, the thermal conductivity of nanofluids as a function oftemperature is taken from [35] as listed in Table 1.

Fig. 13 presents the comparison of axial heat transfer coeffi-cients for nanoparticles with different aspect ratios at Reynoldsnumber of 1460. The results show that the heat transfer coefficientof the CNT/water nanofluid is significantly greater than that of theother nanofluids, which can be attributed to its large aspect ratio(>100) as listed in Table 1. In addition to the nanoparticle shape,the higher thermal conductivity of CNTs compared with Al2O3

and CuO is the reason of substantial thermal characteristicsenhancement of CNT/water nanofluids, even at low concentrations.

Particle volume 0 1 2 3

Δ T (o C

)

2.2

2.4

2.6

ΔTΔP

ParticleRe = 14dP = 20

Fig. 14. Temperature differences and pressure drops for different particle volume concenof 20 nm.

Particle volume0 1 2 3

Δ T (o C

)

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

ΔTΔP

ParticleRe = 1dP = 2

Fig. 15. Temperature differences and pressure drops for different particle volume conceof 20 nm.

On the other hand, because of the low aspect ratio of TNT (�10)and its lower thermal conductivity as compared with Al2O3, CuOand CNT, the heat transfer coefficient of TNT/water nanofluid islower than those. Yet, it should be mentioned that the concentra-tion of TNT is lower than Al2O3, CuO. The TNT/water nanofluid con-taining 0.6 vol.% nanoparticle shows approximately the same heattransfer coefficient as that of Al2O3/water nanofluid containing2 vol.%, which also indicates the considerable effect of nanoparticleshape on the heat transfer characteristics of nanofluids.

Thus far, several influential parameters on the heat transfer ofnanofluids are investigated; yet the important question is whichnanofluid is more appropriate for a specific application. In this arti-cle, considering a constant wall heat flux condition, two importantfactors are considered as the criteria for the choice of proper nano-fluids. These factors are pressure drop and temperature differencealong the pipe. For a constant wall heat flux condition with a given

fraction (%)4 5 6

Δ P (P

a)

1000

1200

1400

1600

1800

2000 type : Al2O360 nm

trations of Al2O3/water nanofluid at Reynolds number of 1460 and particle diameter

fraction (%)4 5 6

Δ P (P

a)

2000

4000

6000

8000 type : CuO

4600 nm

ntrations of CuO/water nanofluid at Reynolds number of 1460 and particle diameter


amount of heat transfer to the fluid, the lower temperature differ-ence along the pipe can be considered as an advantage in someapplications. On the other hand, lower pressure drop reduces thepumping cost.

In the view of these two criteria, all cases simulated in the pres-ent study are listed in Table 2, which have been sorted by pressuredrop. It can be concluded from the table that almost all cases withlower pressure drops have higher temperature differences, whichalso implies that nanofluids should be selected according to theapplication requirements.

From Table 2 it is observed that considerable pressure drop areassociated with high particle concentration of nanofluids, whilemuch less pressure drop has been reported in numerical studiesof [37,38] for similar flow conditions. It must be emphasised thatthe viscosity model, le ¼ lf ð1� /Þ�2:5, which has been used inthese studies produces much lower values for viscosity as com-pared to the present experimental data [23] and consequentlyleads to relatively lower pressure drops. However, the applied vis-cosity model in the present study (Eq. (8)) represents the experi-mental data with reasonable accuracy and therefore, theresulting pressure drops are higher.

Another related issue to the pressure drop is the relative in-crease in viscosity with respect to thermal conductivity as thenanoparticle concentration increases. In general, the advantage ofthe nanofluids for the heat transfer applications is directly relatedto the amount of the thermal conductivity increase, leading to theheat transfer enhancement, to the amount of the viscosity increaseassociated with higher pressure drops. For the nanofluids used inthe present study, the viscosity of the base fluid increases fasterthan its thermal conductivity as nanoparticle concentration in-creases, and therefore, the heat transfer enhancements come atthe expense of relatively considerable pressure drop.

Considering Table 2, the temperature increase along the pipeand the pressure drop behave in an opposite manner. In Figs. 14and 15 these parameters are plotted versus the particle volumefraction to see if an optimum nanoparticle concentration for a spe-cific application can be identified. Fig. 14 shows the Al2O3 nanopar-ticles in water with particle diameter of 20 nm and Reynoldsnumber of 1460. From this figure, the optimum choice for theAl2O3/water nanofluid is the volume fraction of about 4 vol.%,which has more reasonable temperature increase and pressuredrop. Similarly, Fig. 15 indicates that for the case of the CuO/waternanofluid with particle diameter of 20 nm and Reynolds number of1460, the proper choice is the volume fraction of about 3.7 vol.%.

Another limitation for nanofluids applications is the toxicity ofnanoparticles. Clearly, the green nanofluids with no environmen-tal, health and safety dangers are desirable. There are some studieson toxicity of nanoparticles considered in this article, Al2O3 [39],CuO [40], CNT [41,42] and TiO2 [40]. Among them, the high toxicityof CuO nanoparticles has been reported [40]. Moreover, Bottiniet al. [42] indicated that CNTs nanofluids can be very toxic at highparticle concentrations.

In addition, the economical justification is one of the importantconsiderations in nanofluid selection. In the present study, CNT/water nanofluid with a low concentration of 0.038 vol.% but highheat transfer coefficient seems to be a low cost nanofluid as com-pared with the others. Finally, the chemical reaction of nanofluidswith the pipe wall is a consideration, especially in the case of sur-factants, which may affect the nanofluids applications.

6. Conclusions

The laminar convective heat transfer performance and pressuredrop of different nanofluids flowing in a straight circular pipe un-der a constant heat flux condition were numerically investigated.The effects of particle concentration, Reynolds number, Brownian

motion, particle diameter, particle shape, particle material andtype of base fluid on the heat transfer performance of nanofluidsare examined in details. Major findings can be summarised asfollows:

– The predicted heat transfer coefficients based on the thermo-physical properties of nanofluids in a static condition are lowerthan the experimental data. This means that the static thermalconductivity increase is not the only reason of convective heattransfer enhancement of nanofluids.

– A thermal conductivity model which considers the effect ofBrownian motion of nanoparticles predicts the heat transfercoefficient of nanofluids more accurately as compared to themodels based on the pure static conditions of the nanofluids.

– The particle volume concentration, Brownian motion and aspectratio of nanoparticles similar to the flow Reynolds numberincrease the heat transfer coefficient of nanofluids, while theparticle diameter has an opposite effect. Moreover, the heattransfer characteristics of nanofluids are strongly influencedby the type of both base fluid and nanoparticle.

– There are several parameters to select the proper nanofluids forconvective heat transfer of nanofluids in pipes. These parame-ters are the amount of heat transfer enhancement, pump power,stability, cost, toxicity and chemical corrosion of pipe wall. Also,there are some other restrictions in the special applicationssuch as low freezing temperature nanofluids as the anti-refrig-erant fluids in cold region.

Acknowledgements

The authors wish to thank Ferdowsi University of Mashhad(Iran), South-East Asia University (Thailand), King Mongkut’s Uni-versity of Technology Thonburi (Thailand) for the valuable supportin the present study. The fourth author would like to acknowledgethe Thailand Research Fund and the National Research UniversityProject for financial supporting.

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