pressure drop and convective heat transfer of water and nanofluids in

8/11/2019 Pressure Drop and Convective Heat Transfer of Water and Nanofluids In

1/9

Pressure drop and convective heat transfer of water and nanouids ina double-pipe helical heat exchanger

Zan Wu, Lei Wang, Bengt Sundn*

Department of Energy Sciences, Lund University, P.O. Box 118, Lund SE-22100, Sweden

h i g h l i g h t s

Pressure drop and heat transfer characteristics of alumina/water nanouids in helical heat exchangers were experimentally investigated.

An accurate correlation was developed for laminar ow in helically coiled tubes.

Secondary ow intensity mitigation due to nanouids may neutralize the benet from the thermal conductivity increase.

No anomalous heat transfer enhancement was found.

a r t i c l e i n f o

Article history:

Received 3 April 2013

Accepted 26 June 2013

Available online 16 July 2013

Keywords:

Nanouid

Pressure drop

Heat transferHelically coiled tube

Heat exchanger

Figure of merit

a b s t r a c t

Pressure drop and convective heat transfer characteristics of water and ve alumina/water nanouids of

weight concentrations from 0.78% wt. to 7.04% wt. were experimentally investigated for both laminar

ow and turbulent ow inside a double-pipe helically coiled heat exchanger. Effect of nanoparticles on

the critical Reynolds number is negligible. A new correlation was developed for laminar ow in helically

coiled tubes, which can predict the experimental heat transfer data very well. For turbulent ow, the

Seban and McLaughlin correlation can accurately predict the thermal behavior of water and nanouids

when nanouid properties are taken into account. For both laminar ow and turbulent ow, no

anomalous heat transfer enhancement was found. The heat transfer enhancement of the nanouids

compared to water is from 0.37% to 3.43% according to the constant ow velocity basis. Figure of merit

based on the constant Reynolds number can be misleading and should not be used for heat transfer

enhancement comparison. Additional possible effects of nanoparticles, e.g., Brownian motion, thermo-

phoresis and diffusiophoresis, on the convective heat transfer characteristics of the nanouids are

insignicant compared to the dominant thermophysical properties of the nanouids. No multiphase

phenomenon was found and the tested alumina nanouids can be treated as homogeneous uids.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

Helically coiled tubes and double-pipe helical heat exchangers

belong to the most common passive heat transfer enhancement

devices in many applications including nuclear reactors, food pro-cessing, electronics, air-conditioning, waste heat recovery, power

production, environmental engineering, manufacturing industry

and space applications, due to their high heat and mass transfer

coefcients, compact design, narrow residence time distributions

and ease of manufacture [1]. Therefore, knowledge about the

pressure drop and convective heat transfer characteristics in heli-

cally coiled tubes and helical heat exchangers are very important.

The ow eld in helically coiled tubes is affected by centrifugal

forces, which induce a secondary ow eld with a couple of

vortices in a cross-section of the tube. Theuid in the central part is

driven toward the outer wall by the centrifugal force, then returns

to the inner wall by owing back along the wall, as illustrated inMori and Nakayama[2].Compared with straight tubes, the above-

mentioned secondary ow in helical tubes enhances heat transfer

rates as it reduces the temperature gradient across the tube cross-

section, producing an additional convective heat transfer mecha-

nism perpendicular to the main ow.

Nanouids are engineered colloidal suspensions of nano-

particles of a base uid[3], which are more stable than micropar-

ticle colloids, with little particle setting, channel erosion and

clogging. In addition, nanouids also have novel properties that

make them potentially important in heat exchangers, nuclear re-

actors, electronics cooling, fuel cells, pharmaceutical processes,* Corresponding author. Tel.: 46 46 2228605; fax: 46 46 2224717.

E-mail address:[email protected](B. Sundn).

Contents lists available at SciVerse ScienceDirect

Applied Thermal Engineering

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 / a p t h e r m e n g

1359-4311/$e see front matter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051

Applied Thermal Engineering 60 (2013) 266e274
mailto:[email protected]://www.sciencedirect.com/science/journal/13594311http://www.elsevier.com/locate/apthermenghttp://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://dx.doi.org/10.1016/j.applthermaleng.2013.06.051http://www.elsevier.com/locate/apthermenghttp://www.sciencedirect.com/science/journal/13594311http://crossmark.dyndns.org/dialog/?doi=10.1016/j.applthermaleng.2013.06.051&domain=pdfmailto:[email protected]


2/9

food industry, etc. [4]. For example, nanouids generally provide

higher thermal conductivity compared to their base uids. Con-

centration, size, dispersion and stability of nanoparticles and uid

temperature affect the determination of the thermal conductivity

of nanouids [5]. Heat transfer characteristics of nanouids in

straight tubes have been extensively studied, as shown in reviews

of Dalkilic et al.[6], Huminic and Huminic[7]and Taylor et al. [8].

However, no agreement on anomalous heat transfer enhancementhas been achieved. Sergis and Hardalupas [9] stated statistically

that most of the previous studies indicated low heat transfer

enhancement; 11% of the sample showed deterioration of the heat

transfer coefcient and 3% indicated no enhancement at all. An

earlier study by Xuan and Li[10]stated anomalous enhancement.

Buongiorno [3]considered seven slip mechanisms which can pro-

duce a relative velocity between the nanoparticles and the base

uid, and concluded that only Brownian diffusion and thermo-

phoresis are important slip mechanisms. The abnormal heat

transfer enhancement was proposed to be related to the property

variation within the solid/liquid boundary layer due to the effect of

temperature gradient and thermophoresis. Timofeeva et al. [11]

also stated that the complexity and the controversy of nanouid

systems are related to the solid/liquid boundary layer betweennanoparticles and the base liquid, at which signicant surface area

of nanoparticles contributes to the uid properties, resulting in

three-phase systems (instead of traditional consideration of

nanouids as two-phase systems of solid and liquid). On the other

hand, Williams et al. [12]showed that existing correlations accu-

rately reproduced the turbulent convective heat transfer behavior

of nanouids in tubes by adopting the measured temperature- and

loading-dependent thermal conductivities and viscosities of the

nanouids in analysis and stated that the anomalous enhancement

could be an analysis artifact. Yu et al.[13]analyzed a large database

related to nanouids owing inside straight tubes and presented

that the turbulent heat transfer coefcients of nanouids can

be predicted quite accurately with the standard single-phase

equations.

So far, studies on heat transfer characteristics of nanouids in

helically coiled tubes or double-pipe helical heat exchangers are

scarce. Akhavan-Behabadi et al.[14]experimentally showed higher

Nusselt numbers of multi-walled carbon nanotube (MWCNT)/oil

nanouids compared to baseuid (oil) inside vertical helically coiled

tubes under uniform wall temperature condition for laminar ow.

Mukesh Kumar et al. [15] experimentally observed that the

maximum enhancement of the tube side heat transfer coefcientwas up to 24.6% foralumina/water nanouids based on the constant

Dean number. Mohammed and Narrein [16] and Narrein and

Mohammed [17] performed numerical investigations of effects of

different geometrical parameters and material, diameter and volume

concentration of nanoparticles on the hydraulic and thermal char-

acteristics in helically coiled tube heat exchangers under laminar

ow conditions. Sasmito et al. [18]conducted a numerical study of

laminar nanouidows (alumina/waterand copper/water) in coiled

square tubes, and stated that adding 1% nanouid (volumetric con-

centration) improved the heat transfer performance; however,

further addition tended to deteriorate heat transfer performance.

The purpose of this experimental study is to investigate and

evaluate the pressure drop and convective heat transfer perfor-

mance of water and g-Al2O3/water nanouids of different con-centrations in a double-pipe helically coiled heat exchanger, for

both laminar ow and turbulent ow.

2. Experiment

2.1. Experimental apparatus and method

A schematic illustration of the experimental setup is shown in

Fig. 1a. It consists of two loops, for the cold and hot uids,

respectively. The hot water or nanouid runs in the hot closed loop,

while cold water is forced in the cold open loop. Wateror nanouid

is heated in a 50-L reservoir by an imbedded electric heater of 6 kW

xed at the bottom of the reservoir. The heated uid is pumped

from the reservoir, and then it passes a control valve, enters the

Nomenclature

Ai inner surface area of the inner tube (m2)

Ao outer surface area of the inner tube (m2)

cp specic heat at constant pressure (J kg1 K1)

Dc coil diameter of curvature (m)

da

hydraulic diameter of the annulus (m)

di diameter of the inner tube (m)

dp particle diameter (m)De Dean number,Reb(di/Dc)

0.5

eA mean absolute deviation (%)

fapp apparent friction factor

h heat transfer coefcient (W m2 K1)ha annulus heat transfer coefcient (W m

2 K1)

k thermal conductivity (W m1 K1)

Kn Knudsen number

L length of the helical heat exchanger (m)

LMTD logarithmic mean temperature difference (K)

m mass ow rate (kg s1)

n number of turns

Nu Nusselt number,hdi/k

p pitch of helical coil (m)Pr Prandtl number,cpm/k

q heat ux (W m2)

r gure of meritRe Reynolds number,rudi/m

T temperature (K)u velocity (m s1)

w weight concentration

Greek symbols

DP pressure drop (Pa)

F volume concentration

l mean free path (m)

m dynamic viscosity (Pa s)

r density (kg m3)

sN standard deviation (%)

Subscripts

b bulk

c cold side

ci cold side inlet

co cold side outlet

exp experimental

f base uid

h hot side

hi hot side inlet

ho hot side outletn nanouid

p nanoparticles

pre predicted

Z. Wu et al. / Applied Thermal Engineering 60 (2013) 266e274 267


3/9

inner helically coiled tube of the helical heat exchanger, goes into a

rotameter, and returns to the reservoir. For the cold loop, water

ows through the pump from a water tank, passes a control

valve, enters the rotameter for volume ow rate measurement,

and then goes into the annulus counter-currently. Each loop has

two rotameters of small and large ranges for accurate ow rate

measurement. A differential pressure transducer with an accuracy

of0.075% of the set span was used to measure the pressure drop

across the inner tube. All rotameters were calibrated for water and

nanouids of different concentrations at different temperatures by

using a stopwatch and measuring cylinders. The inlet and outlet

temperatures of the inner tube and the annulus were measured by

four calibrated copper-constantan thermocouples with an accuracy

of 0.1 K, respectively. All temperature measurements were

Fig. 1. Schematic illustrations of (a) experimental rig, and (b) helically coiled tube.

Z. Wu et al. / Applied Thermal Engineering 60 (2013) 266e274268


4/9

recorded by a data logger. Uncertainties of the measurements were

listed inTable 1.

The double-pipe helically coiled heat exchanger considered was

constructed by copper tubes and standard copper connections. The

inner helically coiled tube, shown inFig. 1b, has an inner diameter

(di) of 13.28 mm. The outer surface of the inner tube was enhanced

by circular n arrays (not shown in Fig. 1b) with a n height of

3.2 mm. The ratio of the outer surface area (Ao) to the inner surface

area (Ai) of the inner tube is 4.83. The outer helically coiled tube has

an inner diameter of 26 mm. The approximate hydraulic diameter

of the annulus side (da) is 8 mm (n arrays not considered). The

number of turns (n) of the helical coils is4.5, and eachcoil has a coil

diameter of curvature (Dc, measured from the center of the inner

tube) of 254 mm. The pitch of the helical coil (p) is 34.5 mm. The

total length of the tested helical heat exchanger is 3.591 m.

The inlet temperature of the hot uid was maintained at

28.0 3.0 C. The inlet temperature of the cold uid was kept at

5.5 0.5 C. Test conditions were considered stableas the deviation

was below 0.15 K when the thermal equilibrium conditions were

achieved. For each test condition, four measurements were recor-

ded and averaged. Also, repeatability of the experiments was very

good, with a deviation less than 1.0%.

2.2. Nanouid preparation and properties

Untreated concentratedg-Al2O3/water nanouid with spherical

alumina nanoparticles of 40-nm mean diameter was purchased

from a commercial company (Nanophase Technologies Corpora-

tion, US). No surfactants were added in the nanouid. Different

amounts of concentrated nanouid were diluted in tap water to

obtain nanouids with low weight concentrations. The diluted

nanouid mixture was mechanically stirred for 0.5 h followed by

ultrasonic vibration for 4 h. The nal milk-like nanouid was very

stable and no particle setting was found, at least within two weeks.

Tap water was used as the base uid. To obtain weight concentra-

tions, a certain volume of the stable nanouid was weighed for

several times to obtain the average value. The density of tap waterused in weight concentration calculation was measured by a bal-

ance and a measuring cylinder at different temperatures. Five

nanouids with weight concentrations, 0.78% wt., 2.18% wt., 3.89%

wt., 5.68% wt. and 7.04% wt. were obtained and tested in the hot

loop. Volume concentration F of the nanouid can be obtained

from its weight concentrationw:

F wrf

1 wrpwrf(1)

The volume concentrations of the ve tested nanouids are

0.20%, 0.56%, 1.02%,1.50% and 1.88%, respectively. The density of the

nanouid was calculated by

rn 1 Frf Frp (2)

The specic heat of the nanouid was calculated by

rncpn 1 Frfcpf Frpcpp (3)

where cpn, cpfand cpp are specic heats of the nanouid, the base

uid and the particle, respectively. The effective dynamic viscosity

and thermal conductivity of nanouids can be calculated by exist-ing formulas that have been obtained for two-phase mixtures, i.e.,

the well-known Einstein equation [19] for dynamic viscosity and

the Maxwell model[20]for thermal conductivity. Maiga et al.[21]

and Williams et al. [12] proposed dynamic viscosity and thermal

conductivity equations based on limited experimental data for the

g-Al2O3/water nanouid. Table 2 lists these formulas and their

respective applicable ranges.Fig. 2illustrates the relative viscosity

and thermal conductivity ofg-Al2O3/water nanouids versus vol-

ume concentrations based on the formulas listed in Table 2. Both

dynamic viscosity and thermal conductivity increase with increase

in volume concentration of nanoparticles. The dynamic viscosity

calculated by the Einstein equation [19]is lower than that of the

other two equations. The equation of Williams et al. [12]gives the

highest viscosity and thermal conductivity values. The Maxwellequation [20] and the Maiga et al. equation [21] present similar

thermal conductivity behavior. In this study, the well-known Ein-

stein equation[19]and the Maxwell equation[20]were adopted to

analyze the experimental data. As shown by Drew and Passman

[22], Wen and Ding[23]and Zhang et al.[24]and others, the Ein-

stein equation [19] and the Maxwell model [20] are in good

agreement with the experimental results at low volume concen-

trations (F< 2.0%).

2.3. Data analysis

The apparent Darcy friction factor was calculated by the

following equation:

fapp 2$diL

DP

ru2 (4)

The heat ux q was averaged between the heat transferred by

the inner hot uidqh and the heat absorbed by the annulus cold

waterqc:

q

qhqc

2

cphmhThiTho cpcmcTcoTci

2

(5)

Table 1Uncertainties estimation for primary measurements and dependent quantities.

Primary measurements

Diameter 0.05 mm

Length 0.2 mm

Temperature 0.1 K

Inner tube ow rate, range: 30e540 L h1 2.0% at the lowest ow rate

Annulusow rate, range: 30e300 L h1 2.0% at the lowest ow rate

Pressure drop across the inner tube 1.5% at the lowest ow rate

Dependent quantities

Mass ow ratem, kg s1 2.0%

Heat uxq, W m2 2.8%

LMTD, K 1.5%

Apparent Darcy friction factor fapp 3.3%

Heat transfer coefcienth, W m2 K1 3.2%

Table 2

Several existing equations for effective dynamic viscosity and thermal conductivity

of nanouids.

Authors Equations

Einstein[19] Theoretical model for dilute non-interacting

suspensions of small, rigid, spherical particles,

F < 2%: mn mf1 2:5F

Maxwell[20] Effective medium theory, for dilute non-contact

suspensions of rigid spherical particles,

F < 2%: kn kfkp 2kf2Fkp kfkp2kfFkp kf

Maiga et al.[21] Least-square curve tting of three data sets

for g-Al2O3/water nanouid:

mn mf1 7:3F 123F2,

kn kf1 2:72F 4:97F2

Williams et al.[12] Experimental correlation based on its own

data forg-Al2O3/water nanouid:

mn mfTexp4:91F=0:2092F,

kn kfT1 4:5503F

Z. Wu et al. / Applied Thermal Engineering 60 (2013) 266e274 269


5/9

The deviation in energy balance between the hot loop and thecold loop is less than 1.0%. The logarithmic mean temperature

difference (LMTD) was determined by the following equation[25]

LMTD ThiTco ThoTci

lnThiTco=ThoTci (6)

Assuming no fouling resistance and ignoring the wall thermal

resistance due to the thin wall, large tube length and high thermal

conductivity of copper, the inner tube heat transfer coefcient h

was determined by

h 1

AihLMTD

q 1haAoi

(7)

The annulus thermal resistance in Eq. (7) was also neglected

because of the following reasons: (1) the annulus heat transfer

coefcient ha is relatively large due to the intensive turbulence

induced by the ns on the outer surface of the inner tube; (2) Ao/Ai4.83; (3) the volumetric ow rate on the annulus side was kept

relatively large during the experiments; (4) a small change inh was

noticed for a 20% change of the annulus ow rate during the ex-

periments. Thus, Eq.(7) can be simplied as

h q

Ai$LMTD (8)

Only the inner tube heat transfer coefcient was investigated

and evaluated in this study. Uncertainties of the dependent quan-

tities were listed inTable 1.

Before and after the nanouid tests, water experiments were

conducted in the same double-pipe helically coiled heat exchanger

to verify the nanouid stability, as shown in Fig. 3. The water

experimental data points before and after the nanouid tests show

very similar thermal behavior, indicating very small and negligible

deposition of nanoparticles during the nanouid tests.

3. Results and discussion

3.1. Pressure drop

The relationship between the apparent Darcy friction factor fappcalculated from Eq.(4)and the Reynolds numberRe for tap water is

illustrated inFig. 4. The apparent friction factor decreases withRe

whenRe6000. In this

study, a critical Reynolds number of approximately 6000 was

assumed, which agrees with the transition value of 6494 calculated

by the transition criterion in Ito[26]. The Ito equation[26]and the

Seban and McLaughlin equation[27]can predict the experimental

value relatively well for both laminar ow and turbulent ow,

respectively. The apparent Darcy friction factors for the ve nano-

uids are presented inFig. 5.Data of tap water is also included for

comparison. The transition from laminar ow to turbulentow forall the tested uids occurs almost at the same Reynolds number.

Therefore, the transitional velocity of the nanouids will be larger

than that of the base uid due to the larger viscosity of the former

compared to the latter. The nanoparticles may stabilize the ow in

helically coiled tubes. However, more data are needed to verify this

phenomenon. No obvious difference exists among the six tested

uids, especially in the laminar ow. During the turbulent ow, the

friction factor seems to increase with the nanoparticle concentra-

tion.Fig. 6a and b presents comparisons of the experimental fric-

tion factors with the predictive friction factors by the Ito equation

[26] and the Seban and McLaughlin equation [27] for laminar

ow and turbulent ow, respectively. Both equations can predict

the data points within a 30% error band. The Seban and

McLaughlin equation [27] tends to under-estimate the turbulentfriction factor, and this underestimated deviation increases with

Reynolds number and weight concentration of the nanoparticles.

3.2. Heat transfer in laminarow

Fig. 7demonstrates the relationship between Nub(Prb)0.4 and

the inner tube Dean number Deb (Reb(di/Dc)0.5) for laminar ow.

The subscript b indicates the average bulk temperature. All

Fig. 2. Rheological behavior of alumina nanouids at 20 C based on existing equations

in Table 2: (a) relative viscosity vs. volume concentration; (b) relative thermal con-

ductivity vs. volume concentration.

Fig. 3. Water experimental data before and after nano

uid tests.

Z. Wu et al. / Applied Thermal Engineering 60 (2013) 266e274270


6/9


7/9

McLaughlin [27] correlation can predict the thermal behavior of

water and nanouids very accurately, with a mean absolute error

and a standard deviation of 2.60% and 3.11%, respectively. Theexisting correlation can accurately reproduce the turbulent

convective heat transfer behavior of nanouids in helically coiled

tubes by adopting the properties of the nanouids in the analysis.

The nanouid density, specic heat, dynamic viscosity and thermal

conductivity were calculated by Eqs. (2) and (3), the Einstein

equation[19], and the Maxwell equation[20], respectively.

No abnormal heat transfer enhancement exists in our case

because of small nanoparticle/uid slip ow. The liquid around the

nanoparticles can be regarded as a continuum because the Knudsen

number, Kn, which is dened as the ratio of the water molecule

mean free path to the nanoparticle diameter (l/dp 0.3/40), is

relatively small. Nanoparticle rotation can be ignored due to the

very lowrotational Peclet number which was developed by Ahuja

[30]to evaluate particle rotation under the effect of shear stress.Buongiorno[3]stated that Brownian diffusion and thermophoresis

may become important as slip mechanisms. Thus, these two slip

mechanisms were checked. For a 40-nm alumina nanoparticle and

a temperature of 300 K, the magnitudes of the time a nanoparticle

needs to diffuse a length equal to its diameter for Brownian diffu-

sion and thermophoresis can be estimated to 104 and 101 s,

respectively, which are much longer than that for turbulent

transport, 107 s[3]. A temperature gradient of 104 K/m was esti-

mated in our case to calculate the thermophoretic velocity. Due to

the prepared homogeneous nanouid and negligible Brownian

diffusion and thermophoresis during experiments, diffusiophoresis

can also be ignored. Therefore, turbulent transport occurs without

any slip effects and nanoparticles move homogeneously with the

base uid. It is concluded that the tested nanouids can be treated

as homogeneous uids. Additional effects of nanoparticles, e.g.,

Brownian motion, thermophoresis and diffusiophoresis, on the

convective heat transfer characteristics of the nanouids are

negligible compared to the dominant thermophysical properties of

the nanouids.

3.4. Figure of merit

A gure of merit r hn/hffor the heat transfer coefcient ratio of

the nanouid over the base uid is adopted to compare the heat

transfer performance of the nanouid to that of the base uid, as

given inYu et al. [31]. Ifr> 1, the nanouid is benecial for the heat

transfer coefcient. Because water and the ve tested nanouids

can be accurately reproduced by Eq. (9) forthe laminar owand the

Seban and McLaughlin correlation [27]for the turbulent ow, the

gure of merit can be obtained based on Eq.(9)and the Seban and

McLaughlin correlation [27]. It shouldbe noted that the appropriate

property equations mentioned above in Section2.2should be used.

Different comparison bases can be used to obtain the gure of

merit, such as constant Reynolds number basis and constant ow

velocity basis[31]. However, the constant Reynolds number basis

can be misleading because the net result for the constant Reynoldsnumber comparison is a combination of the nanouid property

effect and the ow velocity effect. Due to the higher viscosity of the

nanouid, the ow velocity in the nanouid is generally higher

than that of the base uid at the same Reynolds number, which

provides an advantage for the nanouid over the base uid. If the

base uid is to be pumped at the same ow velocity as the nano-

uids, it may approach or exceed the thermal performance of the

nanouid. The result based on constant Reynolds number will be

more misleading at higher estimated or measured relative viscos-

ity. This misleading effect can be seen clearly in Fig. 10. Over 40%

Fig. 8. Comparison of Eq.(9) with two existing correlations.

Table 3

Description of three existing heat-transfer correlations.

Authors Correlations

Laminarow

Dravid et al.[28] Applicable range: 50< Deb< 2000, 5 < Prb< 175.

Nub 0:65ffiffiffiffiffiffiffiffiffi

Debp

0:76$Pr0:175bKalb and Seader[29] Applicable range: 80< Deb< 1200, 0.7< Prb< 5.

Nub 0:913$De0:476b $Pr

0:200b

Turbulentow

Seban and

McLaughlin[27]

Applicable range: 6000< Reb< 65,600, 2.9 < Prb

pressure drop and convective heat transfer of water and nanofluids in

Documents