Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall...

7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou

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Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubeswith imposed wall temperature boundary conditions

Sbastien Ferrouillat a,, Andr Bontemps a, Joo-Paulo Ribeiro b, Jean-Antoine Gruss b, Olivier Soriano b

a Universit Joseph Fourier, LEGI, BP 53X, 38041 Grenoble cedex, Franceb CEA/LITEN/DTS/LETH, 17, Avenue des martyrs, 38052 Grenoble cedex, France

a r t i c l e i n f o

Article history:

Received 6 October 2009

Received in revised form 25 August 2010

Accepted 18 January 2011

Available online 18 February 2011

Keywords:

Nanofluid

Convective heat transfer

Imposed wall temperature

a b s t r a c t

The convective heat transfer of SiO2/water colloidal suspensions (534 wt.%) is investigated experimen-

tally in a flow loop with a horizontal tube test section whose wall temperature is imposed. Experiments

were performed at different inlet temperatures (20, 50, 70 C) in cooling and/or heating conditions at var-

ious flow rates (200 < Re < 10,000). The Reynolds and Nusselt numbers were deduced by using thermal

conductivity and viscosity values measured with the same temperature conditions as those in the tests.

Results indicate that the heat transfer coefficient values are increased from 10% to 60% compared to those

of pure water. They also show that the general trend of standard correlations is respected. The problem of

suspension stability at the highest temperatures is discussed. In order to evaluate the benefits provided

by the enhanced properties of the nanofluids studied, an energetic performance evaluation criterion (PEC)

is defined. This PEC decreases as the nanoparticle concentration is increased. This process is also dis-

cussed in this paper.

2011 Elsevier Inc. All rights reserved.

1. Introduction

The development of high-performance thermal systems has

been stimulated in many fields of new technologies. Conventional

heat transfer devices have to be substantially improved to answer

the needs of systems from the microscale to large power plants. In

this perspective, convective heat transfer can be enhanced in sev-

eral ways, by using either active or passive techniques. In the latter

case, it is made possible by changing the structure of the heat ex-

changer or the properties of the heat exchange surface. However

another possibility is to modify the fluid itself by enhancing its

thermal conductivity. Various techniques have been used to in-

crease the thermal conductivity of base fluids by introducing solid

particles whose conductivity is generally higher than that of liq-

uids. A new class of fluids called nanofluids have recently beendeveloped and tested. As a result, we are seeing an increasing

amount of published work on the subject. Nanofluids are colloids

made of a base fluid and nanoparticles (1100 nm). A substantial

increase in the thermal conductivities of nanofluids containing a

small amount of metallic or non-metallic nanoparticles has been

reported. In addition, some authors have measured an increase of

heat transfer coefficients compared to pure liquids beyond the

mere thermal-conductivity effect. However, many results found

in published literature are not consistent with others or with stan-

dard correlations. Several reasons have been put forward to explainthese discrepancies. In an attempt to explain this type of

behaviour, a range of experiments has been defined: measure-

ments of thermophysical properties of nanofluids, measurements

of pressure drop in channels, measurements of heat transfer coef-

ficients with different boundary conditions, stability of colloidal

suspensions.

2. Selected bibliography

To characterise heat transfer in forced-convection, the heat

transfer coefficient is one of the parameters to be determined. It

takes into account the fluid thermal conductivity either directly

or indirectly using the Nusselt number. Thus, a first assessment

of the heat transfer potential of a nanofluid involves considering

its thermal conductivity. Up to now, most of research has been

published in this area because thermal conductivity is probably

easier to measure than heat transfer coefficients. Consequently,

thermal conductivity results have been used extensively to esti-

mate nanofluid heat transfer enhancement rates. Nevertheless,

while increases in effective thermal conductivity as well as

changes in density, specific heat, and viscosity are important indi-

cations of improved heat transfer behaviour of nanofluids, the net

benefit of nanofluids as heat transfer fluids is determined through

the heat transfer coefficient. Thus, it is essential to directly mea-

sure this coefficient under flow conditions typical of specific appli-

cations and, until now, there has been limited experimental work

0142-727X/$ - see front matter 2011 Elsevier Inc. All rights reserved.doi:10.1016/j.ijheatfluidflow.2011.01.003

Corresponding author.

E-mail address: [email protected] (S. Ferrouillat).

International Journal of Heat and Fluid Flow 32 (2011) 424439

Contents lists available at ScienceDirect

International Journal of Heat and Fluid Flow

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 / i j h f f
http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003http://www.sciencedirect.com/science/journal/0142727Xhttp://www.elsevier.com/locate/ijhffhttp://www.elsevier.com/locate/ijhffhttp://www.sciencedirect.com/science/journal/0142727Xhttp://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003


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reported in published literature, as shown in Table 1. The nanofluid

types, testing parameters and a summary of results are listed in

this table. Many research groups have found that heat transfer

enhancement exceeds thermal conductivity enhancement in lami-

nar flow (Chen et al., 2008; Faulkner et al., 2004; Hwang et al.,

2009; Jung et al., 2009; Lai et al., 2008; Lee and Choi, 1996; Lee

et al., 2005; Li and Xuan, 2002; Rea et al., 2009; Wen and Ding,

2004; Xuan and Li, 2003; Zeinali Heris et al., 2006a,b, 2007). This

finding indicates that the presence of nanoparticles in the flow

influences the heat transfer beyond what would be expected from

increased thermal conductivity alone. Some authors have attrib-

uted this added effect to particle-fluid interactions.

First, it must be remarked that due to the particle size, it has

generally been considered that the two-phase solidliquid flow

does not lead to specific flow patterns.

The effect of particle volume concentrations have been studied

by several research groups. In laminar flow, at particle volume con-

centrations below 2%, there is a limited Reynolds effect on heat

transfer enhancement. For particle volume concentrations above

2%, the heat transfer enhancement augments with the Reynolds

number. This trend is consistent with the increase of thermal con-

ductivity with increased particle volume concentration. However,

it has been noticed that heat transfer enhancement is more sub-

stantial than thermal conductivity enhancement.

Nevertheless, two groups found that the heat transfer enhance-

ment either is much lower than the effective thermal conductivity

enhancement (graphite nanofluids, Yang et al., 2005) or is not sig-

nificant (nano-diamond nanofluid or ethylene based titanium

nanofluid, Ding et al. (2007)).

Amongst all nanofluids tested, Carbon Nano Tube (CNT) solu-

tions seem to provide the highest heat transfer enhancement

(Faulkner et al., 2004; Ding et al., 2006) compared to other nano-

particles (Al2O3, CuO, TiO2, graphite, etc.). This enhancement can

be related to several potential reasons: improved thermal conduc-

tivity, shear-induced enhancement in flow, reduced boundary

layer, particle re-arrangement, and high aspect ratio of CNTs.

Indeed, particle shape or aspect ratio should be an important fac-

tor. Studies with nearly spherical nanoparticles (aspect ratio

around 1) (Li and Xuan, 2002; Wen and Ding, 2004; Xuan and Li,

2003) show an increase of the convective heat transfer coefficient

up to 60%. Results cited previously on CNT nanofluids, which are

characterised by an aspect ratio above 100, show a heat transfer

enhancement of up to 350% at Re = 800 for 0.5 wt.% nanoparticle

concentration. However, graphite nanofluids results cited previ-

ously (Yang et al., 2005), with an aspect ratio lower than 0.02,

showed a much lower increase of the convective heat transfer coef-

ficient with respect to the effective thermal conductivity. Thus, the

available experimental data seem to show that the particle shape

and the aspect ratio are significant parameters which affect the

thermal performance of nanofluids. However, is yet to be examined

in-depth.

Heat transfer results in turbulent flow are available from few

groups (He et al., 2007; Kulkarni et al., 2008; Li and Xuan, 2002;

Nguyen et al., 2007; Pak and Cho, 1998; Sommers and Yerkes,

2009; Williams et al., 2008; Xuan and Li, 2003; Yu et al., 2009).

Some of them (He et al., 2007; Kulkarni et al., 2008; Li and Xuan,

2002; Nguyen et al., 2007; Xuan and Li, 2003) reported heat trans-

fer enhancement for turbulent flow higher than predicted by the

pure fluid correlation (DittusBoelter), even when the measured

nanofluid properties were used in defining the dimensionless

groups in the correlation. However, these same researchers show

that turbulent friction factors in their nanofluids can be predicted

by the traditional friction factor correlations for pure fluids if the

measured nanofluid viscosity is used. Moreover, it has been shown

that the heat transfer enhancement increases with increased parti-

cle volume concentration. The heat transfer enhancement is the

highest for Cu particles, (Table 1), followed by Al2O3 particles

and then TiO2 particles at the same concentration levels. When

taking into account thermal conductivity, it is not surprising that

the Cuwater nanofluid shows the highest heat transfer enhance-

ment. However, the thermal conductivity enhancements of

Al2O3 and TiO2 in water are similar although the heat transfer

enhancement of Al2O3 in water is higher than that of TiO2 in water.

Nevertheless, two groups found that the heat transfer coefficient of

Nomenclature

At thermocouple cross section areaCp specific heat capacityd tube diameterdh hydraulic diameterD thermocouple diameter

f fanning friction factorh heat transfer coefficientht heat transfer coefficient near the thermocouplek thermal conductivityl thermocouple lengthL tube length_m mass flow rate

Nu Nusselt numberP perimeter of the thermocouplePe Peclet numberPr Prandtl number_Q heat flow rate

Rw thermal resistance of the copper tube wallRe Reynolds numberS heat exchange area

Sp cross section areaU overall heat transfer coefficient

Greek symbolsb shape factor

DP pressure dropDTlm log mean temperature differencee absolute roughnessu nanofluid volume fractionuw nanofluid mass fraction

l dynamic viscosityK Darcy coefficientq densityw particle sphericity

Subscriptsb bulke externalexp experimentalf base fluidi internalin inletnf nanofluidout outlets nanoparticlest thermocouplew wall

S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 425


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nanofluids (Al2O3 and TiO2 in water and SiC in water) was lower

than for pure water for constant average velocity in turbulent flow

(Pak and Cho, 1998; Yu et al., 2009).

Recently, Williams et al. (2008) and Rea et al. (2009) studied

turbulent convective heat transfer behaviour of Al2O3 and ZrO2nanoparticle dispersions in water. They demonstrated that if the

measured temperatures dependent on the thermal conductiv-

ity and viscosity of the nanofluids are used in calculating the

Reynolds, Prandlt, and Nusselt numbers, the existing correlations

(DittusBoelter and Blasius/MacAdams) accurately reproduce the

experimental convective heat transfer and viscous pressure loss

behaviour in tubes. This finding indicates that no abnormal heat

transfer enhancement was observed when nanofluid propertieswere accurately taken into account.

At present, there is too little data to establish the heat transfer

enhancement trend with laminar or turbulent flow as a function of

particle type and/or size. The thermal conductivity enhancement

seems to increase with particle size, but more experiments are re-

quired to establish this type of trend with regard to heat transfer

enhancement. Some authors show a heat transfer coefficient

enhancement with particle size (Kulkarni et al., 2008) and some

others show that for a given flow Reynolds number and particle

concentration, the convective heat transfer coefficient does not

seem to be sensitive to the average particle size (He et al., 2007 ).

Moreover, as nanofluids are usually moderately concentrated

suspensions of anisotropic objects, they can be non-Newtonian

materials with a thermodependent rheology. Therefore, it is funda-mental that a thermo-rheo-structural study of these materials be

conducted. As a conclusion of this scientific work, it seems clear

that there is a general lack of characterisation concerning the ther-

mal properties of nanofluids.

Few studies have been conducted which carefully examine

nanofluid stability (Sommers and Yerkes, 2009; Bontemps et al.,

2008a,b). Discoloration of the nanofluid has been observed after

being cycled at high flow rates and increased temperatures for long

periods of time. This may be the result of nano-abrasion occurring

in the loop. The authors suppose that the optical change was due to

trace contaminants. Nanofluid stability must be taken into account

in defining new nanofluids for heat transfer purposes.

3. Nanofluid characterisation

What is called nanofluid is generally a dilute suspension of

nanoparticles (volume fraction 65%). To extend the field of the

present study and to possibly relate our results to those obtained

with rheological fluids the decision was made to vary the nanopar-

ticle concentration beyond the 5% value.

The nanofluids used were colloidal suspensions of SiO2 nano-

particles in water (Fig. 1). They were prepared from a commercial

solution (Ludox

TMA colloidal silica from SigmaAldrich) with a

mass fraction of 34%. Three mass fractions were used: 34%, and

after dilution in demineralised water, 16% and 5%. They correspond

to volume fractions of 18.93%, 7.95%, and 2.3% respectively. Thephysical properties of SiO2 particles are shown in Table 2.

Table 1

Bibliography on experimental forced convective heat transfer with nanofluids.

Ref. Nanofluid Re Nunf/Nuf

Lee and Choi (1996) Metallic nanoparticle suspension Laminar +100%

Pak and Cho (1998) Al2O3water TiO2water 3 vol.% Turbulent 3% to 12% for constant average velocity

Li and Xuan (2002) Cuwater 2 vol.% 80023,000 +60%

Xuan and Li (2003) Cuwater 0.32 v ol.% Laminar and

turbulent

+30%

Wen and Ding (2004) Al2O3water 0.21.6% 6502050 Nu > Nu Shah especially near the entranceFaulkner et al. (2004) MW CNT (aspect ratio > 100) 1.1

4.4 vol.%

217 +48% to +221% with high volume concentration

Yang et al. (2005) Graphite 22.5 wt.% 5110 Nunf/Nuf < knf/kf (aspect ratio l/d = 0.02)

Lee et al. (2005) Agwater 2.5 wt.% 10002000 +17% to +25%

Ding et al. (2006) CNTwater (aspect ratio > 100) 0.1

1 wt.%

8001200 +350%

Zeinali Heris et al.

(2006a)

CuOwater 0.23 v ol.% 6502050 Enhancement of a with U and Pe


(2006b)

Al2O3water CuOwater 0.2 3 vol.% 6502500 Enhancement ofa with u and Pe. Al2O3 shows more enhancement than CuO


(2007)

Al2O3water 0.2-2.5 v ol.% 7002050 Enhancement of a with u and Pe

Nguyen et al. (2007) Al2O3water 16.8 vol.% 300015,500 +40% enhancement ofa with diameter decreases and U increasesDing et al. (2007) Nano-diamond 0.1 wt.% ethylene-

based titanium 24 wt.%

135 No significant enhancement

Chen et al. (2008) Titanate nanotubewater (aspect

ratio = 10) 0.52.5 wt.%

1700 a increases with aspect ratio (nanoparticle shape) increase

Williams et al. (2008) Al2O3water 0.93.6 vol.% ZrO2

water 0.20.9 vol.%

900063,000 No abnormal heat transfer enhancement using measured properties of the

nanofluid

Rea et al. (2009) Al2O3water 0.66.0 vol.% ZrO2

water 0.323.5 vol.%

Laminar No abnormal heat transfer enhancement using measured properties of the

nanofluid

He et al. (2007) TiO2water 0.242 v ol.% 8006000 Enhancement of a with u for a given Re and particle size but no abnormal heattransfer enhancement with particle size increase

Lai et al. (2008) Al2O3water 0.51.0 v ol.% Laminar Enhancement of a with u and volume flow rateKulkarni et al. (2008) SiO2ethylene glycol/water 2

10 vol.%

300012,000 +16% enhancement ofa with 10 vol.%, 20nm particle diameter at Re = 10000enhancement ofa with particle size increase

Jung et al. (2009) Al2O3water 0.61.8 v ol.% 5300 +32% enhancement of a with 1.8 vol.% without major friction lossSommers and Yerkes

(2009)

Al2O3propanol 0.53 wt.% 18002800 Small but significant enhancement for 1 wt.%

Yu et al. (2009) Silicon carbidewater 3.7vol.% 330010,000 +5060% for a given Re, but 7% for constant average velocity

Hwang et al. (2009) Al2O3water 0.010.3 v ol.% 550800 +8% at 0.3 v ol.%

426 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439


4/16

It is essential to use the correct thermal and physical properties

of nanofluids, since all correlations depend on these properties. The

thermal and physical properties of interest are discussed below.

3.1. Density

The density of the nanofluid is evaluated according to the stan-

dard formula:q 1uqf uqs 1where u is the volume fraction of the nanofluid, qf the density ofthe base fluid, and s is the density of the nanoparticles.

3.2. Specific heat

The formula for the specific heat of a mixture is given by:

Cp 1uwCpf uwCps 2where uw is the mass fraction of the nanofluid, Cpf the specific heatcapacity of the base fluid, and Cps the specific heat capacity of the

nanoparticles.

3.3. Thermal conductivity

Currently, there are no reliable theories to determine the effec-

tive conductivity of a flowing nanofluid. However, there exist

numerous theoretical studies for particle-fluid mixtures based on the

pioneering work of Maxwells effective medium theory (Maxwell,

1881). These studies are essentially concerned by relatively large

particles (down to micrometric sizes). The effective thermal con-

ductivity k for a mixture with spherical particles is given by

k kfks 2kf 2 kf ks

u

ks 2kf kf ks

u3

u is the volume fraction of the nanofluid, kf the thermal conductiv-

ity of the base fluid, and ks is the thermal conductivity of thenanoparticles.

Hamilton and Crosser (1962), proposed a model for non-spher-

ical particles by introducing a shape factor b given by b = 3/w,where w is the particle sphericity, defined as the ratio of the sur-face area of a sphere with the same volume as that of the particle

and the surface area of the particle. The conductivity is expressed

as follows:

k kfks

b

1

kf

b

1

kf

ks u

ks b 1kf kf ks

u 4The Maxwell formula corresponds to sphericity equals one. Sev-

eral authors have proposed other models to take into account

either the effects of the interface between the nanoparticle and

the base fluid or several micro-convection phenomena. They will

not be evoked here.

The available experimental data on conductivity from different

research groups vary widely, and the proposed theories to explain

such dispersion vary from one author to the other. It seems that the

different preparation methods and the different measurement

techniques of each research group contribute to this dispersion.

Due to these problems, the thermal conductivity of our nanofluids

was measured using two techniques: The first by using the hot

wire classical transient method with an industrial instrument(Kd2 Pro) and the second by using a steady-sate method in a coax-

ial cylinder cell (Glory et al., 2008). The results from this instru-

ment were validated by using demineralised water. The values

obtained (shown in Fig. 2) were found to be close to the Maxwell

theory in accordance with the molecular dynamics simulation of

heat flow in a well-dispersed nanofluid (Evans et al., 2006). For

the analysis of our experiments we used the conductivity values

obtained from measurements.

3.4. Dynamic viscosity

The viscosity of nanofluids was measured using a MCR300 An-

ton PAAR rheometer as a function of temperature for the three

mass fractions. The results obtained were compared with currenttheories.

The limiting case for dilute suspensions of small, rigid, spherical

particles was treated by Einstein (1906), and extended to ellipsoi-

dal particles. The viscosity is given by:

l lf1 Bu 5

where B depends on the ratio of the revolution ellipsoid axes and is

equal to 2.5 for spherical particles.

Measurements revealed that all the tested fluids have a dy-

namic viscosity nearly constant from shear rates varying from

100 to 1000 s1. However, Einsteins formula does not allow us

to predict the experimental values.

Results obtained as a function of temperature are given in Fig. 3

for a shear rate of 1000 s

1

which is a mean value in ourexperiments.

4. Experimental set-up and data reduction

4.1. Experimental set-up

4.1.1. Test loop and test section

A test loop was constructed to measure pressure loss and con-

vective heat transfer coefficients with fixed wall temperature

boundary conditions. The experimental apparatus is shown sche-

matically in Fig. 4.

A 1 l copper vessel equipped with drain valves was used as

the nanofluid reservoir. After injection in the reservoir tank,

the nanofluid, with specified concentration, was circulated usinga gear pump (Micropump, Ismatec, 0200 l h1). Assuming that

Fig. 1. SEM picture of SiO2 nanoparticles used (34 wt%)

Table 2

Physical properties of SiO2 particles.

Nanoparticles Meandiameter

(nm)

Density(kgm3)

Thermal conductivityat 25 C (Wm1 K)

Specificheat at

25 C

(J/kg K)

SiO2 22 2200 1.38 740



5/16

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

20 30 40 50 60 70 80

Temperature (C)

Thermalconductiv

ity(W/(m.K

)

SiO2 5%w SSSiO2 16%w SSSiO2 34%w SSSiO2 5%w THWSiO2 34%w THWWaterMaxwell 5%wMaxwell 16%wMaxwell 34%w

Fig. 2. Thermal conductivity versus temperature(SS: Steady State Method, THW: Transient Hot Wire Method).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 20 30 40 50 60 70

Temperature (C)

Viscosity(cP)

SiO2/Water 5%w

SiO2/Water 16%w

SiO2/Water 34%w before destabilizing

SiO2/Water 34%w after destabilizing

Fig. 3. Viscosity versus temperature for SiO2/water nanofluids.

Pump

Gearpump

Nanofluid

reservoir

Test sectionP

T

P Mixer

TPump

AcquisitionSystem

T T

Sewer

heat

exchanger

Heated bath

T

Coriolis

flow

TT T

T T T T

pH meter

Heated bath

Tap water

Fig. 4. Schematic diagram of the experimental loop.



6/16

nanofluids are considered as homogeneous fluids, the flow rate

was measured by a Coriolis flow meter (Micro Motion ELITE,CFM10) that was calibrated with 0.1% accuracy over the range

of 080kg h1. The pressure drop was measured directly by

three differential strain-gauge pressure transducers operating

over a range of 01620 kPa with uncertainty within 0.075% f.s.,

as calibrated by the manufacturer (Rosemount). A pH meter (Eu-

tech Instruments) was inserted downstream of the test section

to follow the nanofluid pH change with a maximum accuracy

of 0.01.

The test section (Fig. 5) consisted of a 0.5 m long tube-in-tube

heat exchanger, the tested nanofluid flowing into the 4 mm diam-

eter and 1 mm thick inner copper tube (CuA1) and heating or cool-

ing water flowing into a 10 mm diameter and 1 mm thick stainless

steel annular tube. The test section was preceded by a 0.5 m (125

diameters) adiabatic section.The nanofluid was circulated inside the inner tube (primary

loop) with a temperature varying between 15 and 90 C. To ob-

serve the potential influence of the transverse temperature gradi-

ent, the water temperature was varied within the same range

allowing us to change the temperature difference between the

fluid and the wall. The fluid could be heated or cooled thanks to

various valves in the experimental loop, and then the gradient

direction could be modified. After passing through the test section,

the nanofluid entered a heat exchanger in which water was used as

a cooling or heating fluid depending on nanofluid heating or cool-

ing tests. For both primary and secondary loops, temperature was

controlled using two thermostatic baths (Polystat 37, Fischer Sci-

entific) and a second heat exchanger.

The entire test section was insulated with polyurethane foam

(Armaflex) in order to minimize heat losses.

A simplified test section of identical dimensions in which

only inlet and outlet fluid temperatures were measured, was alsoused in order to estimate the influence of thermocouple

insertions on heat transfer (Section 4.1.2) and on pressure losses

(Section 5.1).

4.1.2. Temperature measurements in the test section

Two (K-type) thermocouples were inserted into the flow at the

inlet and outlet of the test section for measuring bulk tempera-

tures of nanofluid. In order to increase the outlet temperature

accuracy for laminar flow, a static mixer was inserted down-

stream of the test section. To record the temperature at the

outer surface of the copper tube and the bulk temperature, four

(K-type) thermocouples were brazed on the inner tube wall and

four (K-type) thermocouples were inserted into the inner tube

at equally spaced 10 cm distances. The thermocouples werecalibrated before tests and had a maximum accuracy of 0.1 C.

All the data were recorded by an Agilent 34970 A data acquisition

unit.

To determine inner wall temperature, the thermal resistance

due to conduction through the tube (Fig. 5) was taken into account

(Eq. (8)). To determine inner flow bulk temperature we added a

corrective term by writing an energy balance between forced con-

vective flow perpendicular to the thermocouple and conduction in

the thermocouple between its extremity and the wall. The thermo-

couple is considered as a fin of constant area, and if the heat loss

from its end is negligible, the temperature at the fin tip is given

by the equation (Kaka et al., 1985):

T

TbTw Tb

1

cosh dl 6

4 mm6 mm10 mm12 mm

Copper

Copper

Stainless steel

Stainless steel

TWall (K-type thermocouple)

TBulk (K-type thermocouple)

Fig. 5. Schematic diagram of the test section with thermocouple locations.



7/16

where d is given by:

d ffiffiffiffiffiffiffiffiffi

htP

ktAt

s7

Pis the perimeter of the thermocouple, kt is the average conductiv-

ity of the thermocouple (15 W m1 K1) and At, its cross section

area.

The heat transfer coefficient ht is calculated from the followingcorrelation developed by Churchill and Bernstein (1977):

NuD 0:3 0:62Re1=2D Pr

1=3

1 0:4=Pr2=3h i1=4 1 ReD282000

5=8" #4=58

where NuD = htD/kt, with D being the thermocouple diameter. This

formula holds for all values of ReD and Pr, provided the Peclet num-

ber PeD = ReD Pr is greater than 0.2. As thermocouple temperatures

are close to bulk temperatures, physical properties in dimensionless

numbers are evaluated at Tb.

4.2. Data reduction

The heat flow rate _Q was determined from the mass flow rate _m

and the inlet and outlet temperatures of the fluid:

_Q _mCpTin Tout 9The internal heat transfer coefficient hi between the nanofluid

and the wall was derived from the following expression of the heat

flow rate:

_Q 11hi

Rw

S Twe Tbi 10

where S is the heat exchange area (m2), Twe the average external

wall temperature of the four K-type thermocouples brazed on the

inner tube (K), Tbi the average internal bulk temperature of the four

K-type thermocouples inserted into the inner tube (K), and Rw is thethermal resistance of the copper tube wall (m K W1).

This thermal resistance Rw is given by:

Rw di2kw

lndedi

11

where di and de are respectively the inner and outer diameters of

the inner tube (m),

kw is the thermal conductivity of the inner tube (W m1 K1).

The internal heat transfer coefficient hi (W m2 K1) can thus be

calculated from

hi S Twe Tbi _Q

Rw 1

12

Once the experimental heat transfer coefficient hi is deter-

mined, the experimental Nusselt number must be compared with

the value obtained experimentally with pure water, which is the

base fluid. This comparison is done by plotting the ratio of the Nus-

selt number measured with the nanofluid Nunf and the Nusselt

number measured with pure water Nuf. In each case, the Reynolds

number was deduced from the mass flow rate measurement by:

Re 4 _mpdil

13

where l is the measured fluid dynamic viscosity taken at averagebulk temperature. Knowing the exact value of viscosity is crucial

because incorrect determination of the Reynolds number can cause

a shift in the curves and lead to misinterpretation of the Nunf/Nufratio.

Using three differential strain-gauge pressure transducers, the

pressure drop measurement enables the Darcy coefficient to be de-

duced with the following expression:

Kexp 2DPdhL

qS2pi_m2

14

where the Darcy coefficient is 4 times larger than the fanning

friction factor f. The maximum relative uncertainties of the Rey-nolds number and Darcy coefficient were estimated and are respec-

tively less than 1.9% and 4.3%. The maximum relative uncertainty of

the Nusselt number is highly dependent on the Reynolds number.

For example, this uncertainty is between 78% and 5% for a Reynolds

number between 100 and 12,000. Details of uncertainty calcula-

tions are given in Appendix A.

5. Results and discussion

5.1. Pressure drop

5.1.1. Preliminary tests

To be confident in the experimental loop and its instrumenta-

tion, the pressure drop of pure demineralised water flowingthrough the entire length of the copper tube was measured. Several

measurement conditions were studied as shown in Table 3. Fig. 6

shows experimental results in isothermal, heating and cooling

conditions at several temperature levels (20 C, 50 C, 70 C). In

the heating and cooling conditions, the temperature of one fluid

was 20 C, the other being at 50 or 70 C. These results were

compared with classical relationships.

In laminar flow regime (Re < 2300), the following Poiseuille

equation is used in the calculations:

K 64Re

15

In turbulent flow regime, the Blasius equation is used:

K 0:316Re0:25 16In heat transfer conditions, the Poiseuille and the Blasius laws

are followed provided that the experimental Darcy coefficient is

modified by using a corrective factor as indicated by Petukhov

(1970):

K Kexp lw=l m 17

where lw is the viscosity of the fluid near the wall and l is the vis-cosity of the bulk temperature.

The m exponent was experimentally found to be equal to the

following:

for heating conditions, m = 0.58 for laminar flow and

m = 0.25 in turbulent flow;

for cooling conditions, m = 0.50 for laminar flow and

m = 0.25 for turbulent flow.

Table 3

Measurement conditions.

Reference Measurement

conditions

Inlet internal

temperature (C)

Inlet external

temperature (C)

1 Isothermal 20 20

2 Isothermal 50 50

3 Isothermal 70 70

4 Heating 20 50

5 Heating 20 70

6 Cooling 50 20

7 Cooling 70 20



8/16


9/16

Fig. 8 shows the Darcy coefficient for water and several nano-

fluids versus the Reynolds number. As for demineralised pure

water, using the measured viscosities, nanofluid results correlate

quite well with Poiseuilles law for Re < 1000. Then, Poiseuilles

law underpredicts the measurements for 1000 < Re < 2300 be-

cause of inserted thermocouples. Finally, for Re > 2300, the Cole-

brook correlation seems to concord with experimental results

better than the Blasius law. It should be noted that the greatest

difference between experimental results and the Blasius law or

Colebrook correlation is observed for some results with the

34 wt.% nanofluid. These differences with the Blasius law or

Colebrook correlation are respectively slightly higher than 25%and 10%.

5.2. Heat transfer coefficient

5.2.1. Preliminary tests

As for pressure drop analyses, in order to be confident in the

experimental loop and its instrumentation, the heat transfer

coefficient of pure demineralised water was measured. Several

measurement conditions were studied, as shown in Table 3.

Fig. 9 shows the measured Nusselt number versus the predicted

Nusselt number calculated with the classical correlation of

Gnielinski valid for Re > 2300 in transition and turbulent regime

in heating and cooling conditions (measured conditions 4, 5, 6

and 7) (Gnielinski, 1976):

Nu K=8Re 1000Pr1 12:7

ffiffiffiffiffiffiffiffiffiffiffiffiffiK=8p Pr2=3 1 Pr

Prw

0:111 dh

L

2=3" #19

In this formula, the Darcy coefficient is given by K = (1.82log10-Re 1.64)2, where Re is the Reynolds number, Pr and Prw are the

Prandtl numbers calculated at the water bulk temperature and at

the inner wall temperature respectively, L is the tube length and

dh the hydraulic diameter. The bulk temperature is an average be-

tween the inlet and outlet fluid temperatures.

It can be seen that experimental data correspond well with the

predictions of the correlation to within 20%. It can be noted that

20% is also the Gnielinski range of validity.

0.01

0.1

1

10

10000100010010

Reynolds number

Darcycoefficient

Poiseuille

Blasius

Colebrook 20 m

SiO2/Water 5%w (heating and cooling)



Water (heating and cooling)

Fig. 8. Darcy coefficient as a function of the Reynolds number for several measurement conditions with water and nanofluids.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90

Predicted Nuf

MeasuredNuf

20%

-20%

Water heating (4)

Water heating (5)

Water cooling (6)

Water cooling (7)

Fig. 9. Tube averaged Nusselt number for water tests.



10/16

5.2.2. Results with nanofluids

Figs. 1012 present the Nusselt number versus the Reynolds

number for the three mass fraction nanofluids and pure deminer-

alised water for both heating and cooling conditions.

Significant enhancement of the nanofluid Nusselt number com-

pared to the base fluid in the turbulent regime with nanofluid con-

centration can be observed. There is a strong particle concentration

influence in that the larger the mass fraction, the higher theenhancement is.

Considering Fig. 10, these results can be divided into three

parts. A first part, for Re > 1000, shows that the heat transfer is con-

trolled by turbulence regime flow. As previously observed on pres-

sure drop results, heat transfer results seem to show turbulent flow

regime development below the classical value (Re = 2300) due to

thermocouples inserted in the test section.

A second part, for 200 < Re < 1000, characterises the heat trans-

fer controlled by laminar regime flow.

A third part for Re < 200 shows a probable longitudinal con-

duction effect which implies a Nusselt number decrease (Bontemps,

2005). Indeed, the elementary theory of heat exchangers assumes

that heat is transferred locally from the hot to the cold fluid

through an interposed solid wall which only acts as a thermal

resistance, while conduction along the wall is neglected. In real

equipment, however, heat transfer is actually a multi-dimensional

conjugate problem, in which heat conduction may play a rolenot only in the direction orthogonal to the walls (transverse

conduction), but also in that parallel to them (longitudinal

conduction). As it can be observed in Fig. 10, a strong scattering

of data occurs for Re < 1000. The uncertainty on measured values

was calculated (see Appendix A) and relative errors vary from

78% to 5% from low to high Reynolds numbers. In Fig. 10, an

example of uncertainty for low Reynolds numbers is given. For

high Reynolds numbers, uncertainty is of the order of magnitude

of point sizes.

1

10

100

10000010000100010010

Reynolds number

Nusseltnumber



SiO2/Water 34%w (heatind and cooling)

Water (heating and cooling)

200

Part 3 Part 2 Part 1

Fig. 10. Nusselt number versus Reynolds number.

0

10

20

30

40

50

60

70

80

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Reynolds number

Nusseltnumber

Water (heating 4)

SiO2/Water 5%w (heating 4)



Water (heating 5)




Fig. 11. Nusselt number versus Reynolds number for heating condition.



11/16

Taking into account the measurement accuracy, it is difficult

to know whether or not some heat transfer intensification/dete-

rioration occurs in laminar regime. For the following analyses,

results below Re < 1000 will not be considered. In Figs. 11 and

12, results in linear scales for heating and cooling conditions

are indicated respectively. It is clearly seen that in turbulent re-

gime and compared to pure water, heat transfer enhancement

occurs when using nanofluids. In order to quantify the possible

intensification of the heat transfer coefficient due to nanofluids

compared to that of the base fluid (pure demineralised water),

the ratio Nunf/Nuf versus the Reynolds number is given in

Fig. 13 (heating and cooling conditions 4, 5, 6 and 7). For

Re > 1000, whatever the measurement conditions, significant

heat transfer enhancement with nanofluid concentration up to+50% with 34 wt.% nanofluid can be observed.

The temperature gradient direction effect (comparison of heat-

ing and cooling condition) must be analysed with caution. Heating

and cooling conditions were not realized at the same bulk temper-

ature. Nevertheless, in most cases, the cooling condition seems to

lead to equal or better heat transfer performance characteristics

than the heating condition.

To compare theses results with the prediction of classical corre-

lation, Fig. 14 shows the experimental ratio Nunf/Nuf versus the

predicted ratio Nunf/Nuf calculated with the classical correlation

of Gnielinski valid for Re > 2300 in transition and turbulent regime.

It can be observed that heat transfer performance characteristics

for all nanofluids concentrations are predicted by the Gnielinski

correlation within 20% if the nanofluid mixture properties are ta-

ken into account.

5.3. Nanofluid stability

We have seen in the selected bibliography that heat transfer

enhancement in various nanofluids has been attributed to different

0

10

20

30

40

50

60

70

80

90

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Reynolds number

Nusseltnum

ber Water (cooling 6)

SiO2/Water 5%w (cooling 6)



Water (cooling 7)




Fig. 12. Nusselt number versus Reynolds number for cooling condition.

0%

20%

40%

60%

80%

100%

120%

140%

160%

0 2000 4000 6000 8000 10000 12000 14000

Reynolds number

Nunf/Nuf

5%w heating (4) 5%w heating (5) 5%w cooling (6) 5%w cooling (7)

16%w heating (4) 16%w heating (5) 16%w cooling (6) 16%w cool ing (7)

34%w heating (4) 34%w heating (5) 34%w cooling (6) 34%w cool ing (7)

Fig. 13. Nunf/Nuf versus Reynolds number.



12/16

mechanisms. There have recently been further discussions thatpoint to particle coatings on heat transfer surfaces as being impor-

tant (Yu et al., 2009) and nanofluid discoloration (Sommers and

Yerkes, 2009).

Studying the thermal performance of the nanofluid at the Rey-

nolds number was difficult due to the increase in fluid viscosity

and the limitations imposed by the pump. However, in order to

collect results at higher Reynolds number for 34 wt.% nanofluids,

some tests were carried out by increasing the nanofluid inlet tem-

perature to higher than 80 C to reduce the apparent viscosity of

the nanofluid. These measurement conditions show the 34 wt.%

nanofluid to be destabilized, leading to a modification of hydraulic

performance. Fig. 15 shows the Darcy coefficient increase after the

nanofluid destabilization, by 1.5 in laminar flow and 3.0 in turbu-

lent flow. According to Ludox product information, most Ludoxapplications involve the use of sols at room temperature, thereby

minimizing concentration by evaporation. Higher temperaturesnot only increase the loss of water by evaporation but also the

movement of the colloidal particles in suspension and the dissoci-

ation of electrolytes present in the system and surfactants avoiding

particle agglomeration. Each of these factors contributes to gela-

tion or formation of silica aggregates.

To validate the hypothesis of the formation of silica aggregates,

after emptying the test section, other tests with pure deminera-

lised water were conducted. Fig. 16 also shows an increase of the

Darcy coefficient after nanofluid destabilizing. These results seem

to indicate that 34 wt.% nanofluid destabilization leads to a coating

of the test surface.

Another test for assessing fluid stability involved analysing fluid

samples after different periods of time and at different tempera-

ture conditions. The 34 wt.% nanofluid was stored in two differentsealed glass beakers for two weeks. The first one was heated to

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Predicted Nunf/Nuf

MeasuredNunf/Nuf

5%w heating (4 and 5)

5%w cooling (6 and 7)





20%

-20%

Fig. 14. Measured (Nunf/Nuf) versus predicted (Nunf/Nuf).

0.01

0.1

1

10

10000100010010

Reynolds number

Darc

ycoefficient

Poiseuille

Blasius

Colebrook 20 m

Before destabilizing

After destabilizing

Fig. 15. Darcy coefficient evolution after 34%w nanofluid destabilizing.



13/16

88 C for 24 h, the second was left at room temperature. It was

observed that the heated nanofluid showed some particleaggregates with sediment on the beaker bottom confirming the

temperature effect. This type of effect was already observed with

Al2O3 nanoparticles in water by Lee and Mudawar (2007), who

observed sedimentation in long-term use and by Nguyen et al.

(2008), who found a critical temperature beyond which the

particle suspension properties seem to be drastically altered.

Moreover, viscosity measurements of the 34 wt.% nanofluid

after destabilization show a decrease which confirms a formation

of silica aggregates which lead to sedimentation and thus to

coating. By interpolation, we deduce from Fig. 3 a new concen-

tration at roughly 31 wt.%. With this new mass concentration,

we deduce the other new thermal and physical properties of

nanofluids.

From results after nanofluid destabilization presented in Fig. 16,we have estimated a new hydraulic diameter of the test section in

laminar flow regime thanks the following equation deduced from

Eqs. (13) and (14):

dh 128Lp :lm:

qDPexp

14

20

The new hydraulic diameter is roughly 3.5 mm instead of

4.0 mm.

The results after destabilization presented in the Fig. 15 were

modified to take into account the new thermal and physical

properties and hydraulic diameter. The new results are presented

in Fig. 17. It can be observed that in laminar flow regime, the re-

sults follow Poiseuille classical laws up toRe < 1000. But for

1000 < Re < 2300, the Poiseuille law underpredicts the measure-

ments. This deviation may also be associated with the presence

of the four (K-type) thermocouples inserted into the inner tube.

For Re> 2300, the Blasius law underpredicts the Darcycoefficient measurement. It should be noted that the Colebrook

0.01

0.1

1

10

10000100010010Reynolds number

Darcycoefficie

nt

Poiseuille

Blasius

Colebrook 20 m

1 before destabilizing

1 after destabilizing

4 before destabilizing

4 after destabilizing

7 before destabilizing7 after destabilizing

Fig. 16. Darcy coefficient evolution after 34%w nanofluid destabilizing with pure demineralised water.

0.01

0.1

1

10

10000100010010

Reynolds number

Darcy

coefficient

PoiseuilleBlasiusColebrook 20 mColebrook 250 m7 before destabilizing7 after destabilizing7 after destabilizing with new properties and hydraulic diameter

Fig. 17. Darcy coefficient evolution after 34%w nanofluid destabilizing with new physical properties and hydraulic diameter.



14/16

correlation with e = 250 lm absolute roughness seems to concordbetter with the results. This absolute roughness corresponds well

with the estimation of the new hydraulic diameter. Nevertheless,

the above explanation requires further experimental validation

through copper tube roughness measurements, for instance.

5.4. Energetic performance evaluation criterion (PEC)

In general, the results on SiO2/water nanofluids are apparently

attractive in terms of their thermal performance. Nevertheless,

an important point must be discussed. Indeed, the strong increase

of dynamic (and kinematic) viscosity of nanofluids inevitably in-

volves an increase of the pressure losses inside the system. Conse-

quently, even if a heat transfer enhancement is observed, the

required power for the pumping is increased compared to the base

fluid. This is the reason why a significant increase of viscosity may

lead to an unfavourable energetic balance. There are several ways

to characterise the energetic or thermal performance of a fluid

flowing in a specific device (Colburn, AP, 1933) (Sahiti et al.,

2006). We can use the PEC (performance evaluation criterion) de-

fined below and based on an energetic global approach.

It is defined as the ratio of heat transferred to the required

pumping power in the test section:

PEC _m CpTout Tin_v DP 21

where_

m is the mass flow rate (kg/s),_v the volumic flow rate

(m3/s), Tin and Tout the tube inlet and outlet temperatures and DP

the pressure drop (Pa).

Fig. 18 shows the evolution of this energetic criterion with the

Reynolds number in the case of water and of the SiO2/water nano-

fluids. We can notice that all measurements lead to PEC values be-

neath those corresponding to the case of water, which means that

the energy budget is unfavourable.

For specific applications in which the energetic cost is not

important, the use of such nanofluids could be relevant.

6. Conclusions

As seen in the literature survey, heat transfer coefficient

enhancement was generally observed in using nanofluids. However,in a recent experiment it was shown that by using measured

thermophysical properties, the heat transfer in forced convection

experiments with nanofluids was quite similar to that of conven-

tional fluids (Williams et al., 2008). To find possible effects in con-

vection to interpret the literature data we performed experiments

with several conditions: mass fraction varying from a small value

corresponding to that of a nanofluid to a high value, different wall

boundary conditions, imposed flux and, as described in this paper,

imposed temperature.

In this paper, the convective heat transfer of colloidal suspen-

sion of SiO2 nanoparticles in water was studied experimentally.

The flow regime was varied from laminar to turbulent and constant

wall temperature was considered as a thermal boundary condition.

Both flow cooling and flow heating were studied. Results have

shown that with the presence of nanoparticles, heat transfer of

the resulting nanofluid significantly increases compared to the

base fluid (water) in turbulent regime. Such an enhancement has

been found more pronounced with the increase of particle concen-

tration. The Nusselt number increases from 10% to about 50% when

volume concentration varies from 2.3% to 18.93%.

It is shown that, if the measured thermal and physical proper-

ties of the nanofluid were taken into account to calculate the

dimensionless numbers, the existing correlations reproduce the

convective heat transfer and pressure loss behaviour in tubes with-

in the correlations range of validity. Therefore, the merits of nano-

fluids for heat transfer enhancement depend on the compromise

between thermal conductivity increase and viscosity increase. In

this objective, a Performance Evaluation Criterion (PEC) was de-

fined, which indicates that the global energy budget is not favour-able to the studied nanofluid.

Finally, this paper examines nanofluid destabilizing with high

temperature. A temperature influence on fluid stability was

observed.

Based on these results, the use of nanofluids seems to remain

suitable for applications in which an increase in pumping power

is not of great concern. Nevertheless, nanofluid stability must be

carefully studied for an industrial application.

Acknowledgments

This work was partially supported by the Programme Interdis-

ciplinaire Energie Microcond of the CNRS (National Scientific

Research Centre) and the Environment and Energy ManagementAgency (ADEME) under grant No. 0566C00.

1000

10000

100000

1000000

10000000

100000100001000100

Reynolds number

PEC

Water

SiO2/Water 5%w

SiO2/Water 16%w

SiO2/Water 34%w

Fig. 18. Evolution of the PEC versus Reynolds number in cooling condition (6).



15/16

The authors thank Olivier PONCELET from CEA L2T for his work

preparing nanofluids and Marco BONETTI from CEA IRAMIS for

thermal conductivity measurements.

Appendix A

The internal heat transfer coefficient is given by:

hi 1S TweTbi _Q

Rw

If Ui S TweTbi

_Q S TweTbi

_mCpTinTout; the uncertainty of the internal heat

transfer coefficient hi was determined using Moffats method:

dhi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

@hi@Ui

dUi

2 @hi

@RwdRw

2s

where @hi@Ui

1U2i

1Ui

Rw 2

hiUi

2and @hi

@Rw 1

Ui Rw

2 h

2i

In the same way, the uncertainty of Ui is written as:

where @Ui@ _m

Cp TinToutj j

TweTbi jj S Ui

_m

@Ui@S

_mCp Tin Toutj jTwe Tbijj S2

UiS

@Ui@Cp

_m Tin Toutj jTwe Tbijj S2

UiCp

@Ui@ Twe Tbi

_mCp Tin Toutj jTwe Tbijj 2S

UiTwe Tbijj

@Ui@ Tin Tout

_mCpTwe Tbijj S

UiTin Toutj j

The internal heat transfer area S is given by: S= pdiLThus, the uncertainty of S is written as:

dSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffi

@S

@diddi

2 @S

@LdL

2s

where @S@di

pL and @S@L

pdi

The thermal resistance of the copper tube wall Rw is given by:

Rw di2kCu

ln de

di

In the same way, the uncertainty of the thermal resistance Rc is

written as:

dRw ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

@Rw@di

ddi

2 @Rw

@dedde

2s

where @Rw@di

12kCu

ln dedi

1

and @Rw@de

12kCu

dide

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@CpdCp

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@ Twe Tbi d Twe Tbi 2

@Ui@ Tin Tout d Tin Tout

2s



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Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall...

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