Powder Technology 246 (2013) 82–92Contents lists available at SciVerse ScienceDirectPowder Technologyj ourna l homepage: www.e lsev ie r .com/ locate /powtec

Comparative study between metal oxide nanopowders on thermalcharacteristics of nanofluid flow through helical coils

M. Kahani, S. Zeinali Heris ⁎, S.M. MousaviChemical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran

Abbreviation: HCT, helical coiled tube.⁎ Corresponding author. Tel.: +98 511 8816840; fax:E-mail address: zeinali@ferdowsi.um.ac.ir (S. Zeinali

0032-5910/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.powtec.2013.05.010

a b s t r a c t

a r t i c l e i n f o Article history:Received 13 December 2012Received in revised form 23 February 2013Accepted 4 May 2013Available online 10 May 2013

Keywords:Metal oxide nanopowdersNanofluidHelical coilsThermal performance

Nanofluids and helical coils are two different techniques to enhance thermal performance of highly efficientheat exchangers. By combining these techniques together, energy efficiency of equipments could beincreased dramatically. The present study is an experimental comparison of heat transfer behavior betweenmetal oxide nanofluid flows through helical coiled tube with uniform heat flux boundary condition.Nanofluids with required volume concentration of 0.25–1.0% were prepared by dispersing specified amountsof Al2O3 (35 nm) and TiO2 (50 nm) nanoparticles and appropriate amount of surfactants in distilled water.The experiments covered a range of Reynolds number from 500 to 4500. Experimental results indicatedthat a considerable heat transfer enhancement is achieved by both nanofluids. In addition, because of greaterthermal conductivity and smaller size of Al2O3 nanoparticles compared to TiO2 nanoparticles, Al2O3/waternanofluid showed better heat transfer augmentation. Moreover, due to the curvature of the tube whenfluid flows inside helical coiled tube instead of straight one, convective heat transfer coefficient and thepressure drop of both nanofluids grew dramatically. Besides, experiments indicated that the effect of coilpitch spacing is to some extent weaker than the curvature ratio effect on the heat transfer rate. Finally, it wasstudied that the experimental and predicted results of Nusselt number and pressure drop held reasonableagreement.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

With the increasing heat transfer rate of the heat exchange equip-ment, a conventional process fluid with low thermal conductivity canno longer meet the requirements of high-intensity heat transfer. Thelow thermal property of the heat transfer fluid is a primary limitationto the development of high compactness and effectiveness of heat ex-changers. Nanofluid is defined as a conventional fluid with suspendedparticles at nanometer size (normally up to 100 nm). In the last twodecades a lot of researchers reported about this new engineeredfluid and most of the published papers emphasized that adding asmall amount of nanoparticles to a normal thermal fluid (water, oil,ethylene glycol,…etc.) can increase thermal conductivity and heattransfer properties [1].

On the one hand, nanofluids can be considered to be the nextgeneration heat transfer fluids as they offer exciting new possibilitiesto enhance heat transfer performance compared to pure liquids.Addition of nanoparticles into heat transfer fluids could have thepotential for heat transfer enhancement in pipe flow without payingthe penalty of increasing pumping power [2]. Compared to convention-al solid/liquid suspensions for heat transfer intensifications, nanofluids

+98 511 8805108.Heris).

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possess the following advantages: (a) high specific surface area andtherefore more heat transfer surface between particles and fluids;(b) high dispersion stability with predominant Brownian motion ofparticles; (c) reduced pumping power as compared to pure liquid toachieve equivalent heat transfer intensification; (d) reduced particleclogging as compared to conventional slurries, thus promoting systemminiaturization [3].

Preparation and application of nanoparticles and also the effects ofparticle size, particle volume fraction, temperature dependence,properties of base liquid and particle phase on effective thermal con-ductivity of nanofluid have been emphasized by several researchers[4–14]. Also, the importance of actual agglomerated particle size inthe nanofluid and its effect on the fluid properties have been consid-ered by Yang et al. [15]. Rea et al. [16] have studied laminar convec-tive heat transfer and viscous pressure loss for Al2O3/water andzirconia/water nanofluids flowing in a vertical heated tube whichshowed that the heat transfer coefficient was increased by thenanofluids. Also the measured pressure loss for the nanofluids wasmuch higher than pure water and the pressure loss of the 6.0 vol.%alumina nanofluid was approximately 7.2 times higher than that ofwater. Duangthongsuk and Wongwises [17] have investigatedexperimentally the forced convective heat transfer and flow charac-teristics of a nanofluid consisting of water and 0.2 vol.% TiO2nanoparticles. Their results indicated that use of a nanofluid hadhardly any penalty in pressure drop. Also, considerable enhancement

Nomenclature

A inner surface of tube (m2)b pitch of coil (m)Cp specific heat (J kg−1 K−1)d inside diameter of tube (m)D diameter of coil (m)De Dean numberf Fanning friction factorh e heat transfer coefficient (W m−2 K−1)He Helical coil numberk thermal conductivity (W m−1 K−1)L length of tube (m)_m mass flow rate (kg s−1)N number of coil turnsNu average Nusselt numberPr Prandtl numberRe Reynolds numberR2

adj. adjusted correlation coefficientT temperature (K)U average velocity (m s−1)

Greek lettersΔP axial pressure drop (Pa)η thermal performance factorρ density (kg m−3)μ dynamic viscosity (Pa s)λ curvature ratio (=D/d)φ nanoparticle volume fraction (%)

Subscriptsb bulkC coiled tubef base fluidnf nanofluidp particleS straight tubew wall

83M. Kahani et al. / Powder Technology 246 (2013) 82–92

for both the convective heat transfer coefficient and the Nusseltnumber of the TiO2/water nanofluid through a cylindrical minichannel under laminar flow and constant wall heat flux conditionshave been reported by Murshed et al. [18].

Zeinali Heris et al. [19,20] have considered the convective heattransfer of Al2O3/water and CuO/water nanofluids in circular tubesand observed that the heat transfer coefficient enhances by increasingthe concentration of nanoparticles in the nanofluids. It was obtainedfrom the experimental investigation of Nassan et al. [21] on the heattransfer characteristics of Al2O3/water and CuO/water nanofluidsthrough a square cross-section duct that CuO/water nanofluid givesbetter enhancement in heat transfer than Al2O3/water nanofluid.Hamed Mosavian et al. [22] have employed aqueous solutions ofmetallic and oxide nanoparticles to study the forced convective heattransfer under constant wall temperature. Their result revealed thatnanofluids that contain metal nanoparticles (Cu/water) show moreenhancements compared to oxide nanofluids (Al2O3/water and CuO/water). Also, they emphasized that there is an optimum concentra-tion for each nanofluid in which more enhancements are availablethat is related to viscosity by increasing particle concentration. ForAl2O3/water nanofluid with volume fraction of 7.5% of nanoparticles,45% increment in the average wall heat transfer coefficient has been

achieved by Palm et al. [23] for the same Reynolds numbers.

Conversely, Pak and Cho [24] have expressed that the convective heattransfer coefficient of Al2O3/water and TiO2/water nanofluids withconcentration of 3.0 vol.% was 12.0% smaller than that of pure water.

On the other hand, curved tubes have been used as one of the mosteffective heat transfer enhancement techniques and are themost widelyused tubes in several heat transfer applications [25]. The facts concerningthe working principle of curved tubes and reasons for its enhancedperformance are well established as mentioned [26]: (a) generation ofsecondary flow due to unbalanced centrifugal forces; (b) enhancedcross-sectional mixing; (c) reduction in axial dispersion; (d) improvedheat transfer coefficient; (e) improved mass transfer coefficient.

Dean [27] has done an earlier theoretical work on fluid motion in acurved pipe using a perturbation technique.He predicted the character-istics of the twin-vortex secondary flow and pointed out that thedynamic similarity of such a flow depends on a dimensionless parame-ter,De, called the Dean number, which is defined byDe = Re (d / D)1/2.The Dean number characterizes the intensity of the cross stream flowdriven by an imbalance between centrifugal and radial pressure gradi-ent induced forces.

Flow in curved tube is higher than that for straight tube at thesame flow rate and tube length. Many researchers have beenconducted regarding fluid flow in helical coiled tubes with circularcross-sections. The use of both active and passive techniques to en-hance the heat transfer rate was reported by Cengiz et al. [28]. Theyhave studied the effect of rotation of helical pipes on the heat transferrates and pressure drop for various air-flow rates. Their resultsshowed that although the rotation caused an increase in pressuredrop, the heat transfer rates were augmented.

Jamshidi et al. [29] have highlighted the significant effects of coildiameter and coil pitch on thermal performance of nanofluid in heli-cal coils. Akhavan-Behabadi et al. [30] have emphasized that utilizingvertical helical coiled tubes instead of straight ones enhances the heattransfer rate remarkably. Besides, nanofluid flows showed muchhigher Nusselt numbers compared to the base fluid flow. They usedmultiwall carbon nanotube in heat transfer oil to run their experi-ments and reported that the Nusselt numbers acquired for the heattransfer oil inside tested helical coils were 3 to 7 times higher thanthe values evaluated for the base fluid inside straight tubes with asimilar length of the coils. Hashemi et al. [31] have argued that apply-ing helical tubes instead of the straight tubes is a more effective wayto enhance the convective heat transfer coefficient compared to usingnanofluids instead of the pure liquid. Last but not the least, MukeshKumar et al. [32] have reported 55% and 26% enhancement in Nusseltnumber and friction factor, respectively for Al2O3/water nanofluidturbulent flow in helical coiled tube.

Due to the advantages of accommodating large heat transfer areawithin a small space, high heat transfer coefficient and small residencetime distribution, tube coils are extensively used in industries as heatexchangers and reactors. Moreover, nanofludics is an excellent way toenhance the heat transfer rate. So by combining these techniques to-gether, remarkable efficiency enhancement of heat transfer equipmentscan be obtained. In addition, oxide nanopowders are themost common-ly used particles because of their low prices and special properties.

In the present investigation, by designing the experimental setupwith constant heat flux boundary condition, the heat transfer perfor-mance and pressure loss of two metal oxide (Al2O3 and TiO2)nanofluids through helical coiled tubes in various concentrationsand in the ranges of flow rates that the flow remains laminar are in-vestigated and the increase of pure water heat transfer and pressuredrop which resulted from the adding of nanoparticles is evaluated.

2. Preparation and property of nanofluids

In this study, the water-based nanofluids of different nanoparticlesincluding Al2O3 and TiO2 have been employed. Thermophysical

Table 2Certificate of analysis (contents of elements) of nanopowders.

Al2O3 Ca V Cl Na Mn Co

99% 25 ppm 7 ppm 315 ppm 70 ppm 3 ppm 2 ppm

TiO2 Al Mg Si Ca S Nb

99% 17 ppm 65 ppm 120 ppm 75 ppm 130 ppm 80 ppm

84 M. Kahani et al. / Powder Technology 246 (2013) 82–92

characterizations of nanopowders and also equations which are used toevaluate the physical properties of distilled water are shown in Table 1.The purity of nanopowders which are used in this study was 99.0% andthe exact content of nanopowders is shown in Table 2. These 1.0% impu-rities can decrease the thermal conductivity of nanoparticles in compar-ison of 100% purified nanopowders considerably.

The nanofluid in 0.25, 0.5, 0.75 and 1.0 vol.% concentrations wasprepared. Fig. 1 shows that the TEM(transmission electronmicroscopy)images of nanoparticles dispersed in distilledwater and reveal that bothkinds of nanoparticles have a spherical shape.

There are several procedures to produce stable nanofluid. Amongthem, using a stabilizer, a dispersant, a surface activator and an ultra-sonic vibrator can be cited. Within these methods, surface modifica-tion attracts more attention because of its versatility, low cost andtechnological advantages [34]. Without using suitable surfactants,the tested nanofluids could be stabled for a maximum of 45 minwhile surfactant can improve stability of nanofluids dramatically. Inthis study, Cetyltrimethyl Ammonium Bromide (CTAB) and TritonX-100 were used as surfactant for TiO2 and Al2O3 nanoparticles,respectively. The required amounts of nanoparticles and optimumamounts of their related surfactant were mixed with distilled waterby a high-speed stirrer. Then, sonication was done continuously byultrasonic processor (Hielscher, UP400S) for at least thirty minutesto obtain a more stable and evenly dispersed nanoparticle suspension.

No settlement of nanoparticles was observed after 45 days for TiO2/water and after 48 h for Al2O3/water nanofluids. The settlement perioddifference between Al2O3/water and TiO2/water is due to larger surfacearea per mass of alumina than Titan oxide nanopowders. Al2O3nanopowders have very large surface areas relative to their mass(160 m2/g), which result in strong inter-particle interactions andinduce strong tendency of agglomeration, rapid sedimentation andconsequently limited mobility of nanoparticles in the aquaticenvironment than TiO2 nanopowders [35]. Besides, the larger surfacearea to mass requires more surfactant to cover all parts of the surfacewhich can increase the sedimentation rate of nanopowders.

The thermophysical properties of the prepared nanofluids werecalculated from water and nanoparticle characteristics at bulktemperature using the following equations for density, specific heatand viscosity [36–38].ρnf ¼ φ : ρs þ 1−φð Þ:ρw ð1ÞCpnf ¼ φ : ρp : Cpp� �þ 1−φð Þ : ρf : Cpf� �ρnf

ð2Þμnf ¼ μ f

1−φð Þ2:5 ð3ÞA detailed summary of all classical models for the prediction of the

thermal conductivity of nanofluids has been provided byMurshed et al.

Table 1Thermophysical characterizations of nanopowders and base fluid.Particle/base fluid Average diameter (nm) Purity

(%)Actu(kg/m

Al2O3 (γ) 35 99 3690TiO2 (rutile) 50 99 3900Distilled water⁎ ρ = 999.7968 + 0.0683 T − 0.01074 T2 + 0.0008214 T2.5

Cp = 4.2174 − 0.005618 T + 0.001299 T1.5 − 0.0001153μ ¼ 1557:8248þ19:4084 Tþ0:13604 T2−3:11608�10−4 T3

k = 0.56502 + 0.002636 T − 0.0001251 T1.5 − 1.51549 ×⁎ All temperatures in degrees Celsius [33].

[39]. Among existing models, the Wasp model is more suitable to pre-dict the thermal conductivity of spherical particles [40].

knfkf

¼ kp þ 2kf−2 kf−kp� � :φ

kp þ 2kf þ kf−kp� � :φ ð4Þ

3. Experimental setup and procedure

The experimental setup (Fig. 2) consists of test sections, coolingunit, pump, manometer, dampener, flow rate measuring unit and afluid reservoir. As shown in Table 3, three copper helical coiledtubes (HCT) with different geometries and a straight tube wereused in the test sections. In fabricating the coil, the straight tubewas first filled with shock-compacted fine-grain sand to minimizedistortion of the circular cross section. Winding was done manuallyover special cylindrical modules (Fig. 3) to form helical coils with de-sired geometries. Tubes were equipped with straight entry and exithydrodynamic lengths made of flexible plastic (nonconductive)pipes of the same inner diameter as the tubes. The entry length,about 30 tube diameters, was used as a hydrodynamic developmentlength, while the exit length was about 15 tube diameters. Bothlengths were attached tangentially to the tubes. To obtain a constantheat flux boundary condition, the electric resistance was utilizedaround the heat transfer section. The heat flux was set by adjustingthe electrical voltage with the help of an autotransformer and theconstant heat flux was allowed to continue till the steady state isobtained. Also, in order to minimize heat loss to the surroundings,all heat transfer sections were isolated by two thick layers of rockwool and fiberglass sheets as well.

Two (PT100-type) thermocouples were inserted into the calmingand mixing chambers of the flow at inlet and outlet of each test sec-tion for measuring the bulk temperatures of working fluids andother thermocouples from the same type were inserted through thelittle soldered tubes on the surface of the each test section at differentpoints over the tubes. The accuracy of the all thermocouples was ±0.1% of full scale. A differential U-tube manometer was fitted acrossthe test sections to measure the pressure drop along the tubes. More-over, to minimize the vibration of fluid flow, a flow dampener wasalso located before the test section. Besides, flow rate is measureddirectly from the time required to fill a glass vessel.

al density3)

Surface area to mass(m2/g)

CP(J/kg·K)

k(W/m·K)

>160 780 30.540 710 13.7− 2.30309 × 10−5 T3

T2 + 4.14964 × 10−6 T2.5

10-6 T2 − 0.00094129 T0.5

Fig. 1. TEM images of nanoparticles.

85M. Kahani et al. / Powder Technology 246 (2013) 82–92

After filling the reservoir tank with nanofluid, the pump and the

cooling heat exchanger were switched on. Then electric resistancewas turned on and the temperature of the test section started toincrease. Using bypass line the flow rate was adjusted. After thefluid passing the heated test section flowed through the coolingunit, it finally collects in the reservoir.

Experiments were conducted for straight tube and subsequentlyfor helical coils at different flow rates and volume concentrations ofnanofluids. Through initial tests it has been found that the systemneeds 30–35 min to reach the steady state condition and after thatthe readings could be taken. Each measurement was repeated atleast two times. The essential parameters that were measured includeelectric power inputs, flow rate, bulk temperatures (inlet and outlet),outer wall temperatures and pressure drops of working fluid alongthe coils.

Fig. 2. The schematic of ex

4. Data processing

Considering fluid passing through a tube with constant heat flux,the convective heat transfer coefficient and Nusselt number resultingfrom heat balance are as follows:

h expð Þ ¼ _m : Cp : Tb1−Tb2

� �A : Tw−Tbð ÞM ð5Þ

Nu expð Þ ¼ h expð Þ : dk ð6Þ

in which (Tw − Tb)M is the logarithmic mean temperature difference.

perimental apparatus.

Table 3Physical dimensions of helical coils and straight tube.

Tube d (mm) t (mm) L (mm) D (mm) λ b (mm) N

HCT-I 7 0.5 1318.8 140 20 24 3HCT-II 70 10 42 6HCT-III 70 10 24 6Straight tube –86 M. Kahani et al. / Powder Technology 246 (2013) 82–92

Also, three important dimension parameters in the nanofluid flow

through helical coils, including Reynolds number (Re), Prandtlnumber (Pr) and Helical number (He) are defined as follows:

Re ¼ ρ :U : d=μ ð7ÞPr ¼ μ : CP=k ð8ÞHe ¼ De 1þ b

2πD� �2� �1=2 ð9Þwhere U is the average velocity in the coiled tube.

The theoretical equations for predicting the Nusselt number of lami-nar flow through straight tube and HCT have been presented by Seiderand Tate [41] and Manlapaz and Churchill [42] in the following forms:

NuS ¼ 1:86 Re:Pr:dL� �1=3 μμw

� �0:14 ð10ÞNuC ¼ 48

11þ 51=111þ 1342

Pr:He2� �2

264 3753 þ 1:86 He1þ 1:15

Pr

" #3=28><>: 9>=>;1=3 ð11Þwhere μw in Eq. (3) is the viscosity of fluid at wall temperature.

Moreover, the pressure drop in the axial direction of straight tubecan be obtained from the following equation [43]:ΔPS ¼ 4f S L

d� ρU2

2 ð12Þwhere fS is the Fanning friction factor for straight tube. After replacingthe fS by fC and also L by LC (length of the coiled portion of the coil),Eq. (12) also can be used to evaluate the pressure drop of fluid flowthrough HCT. To predict the Fanning friction factor of straight andhelical coils the following correlations can be applied [44,45].

f S;Laminar ¼ 16=Re ð13Þ

Fig. 3. Helical coils with their special modules.

f S;Turbulent ¼ 0:079Re−1=4 ð14Þf Cf S

¼ 0:47136De1=4 ð15ÞAlso, the criterion for transition from laminar to turbulent flow in

curved pipes was established experimentally by Kubair et al. [46] andcan be represented by Rcri. = 12,730 / λ0.32. HCTs in this studyhave curvature ratios λ = 10 and 20, therefore the related criticalReynolds numbers are 6092 and 4880, respectively. So, in order totake a laminar flow inside the coils, all tests were done at Re b 4500.

5. Experimental uncertainty

Eq. (16) is a general relation for prediction of experimental errors [47]:

UPi ¼ XiP

∂P∂XiUXi

ð16Þin which Xi is themeasurable parameter, P is the calculated quantity frommeasurable parameter,UXi

is themeasuring error andUPi is themaximumerror of a parameter. The effect of all errors in calculation of goal functioncan be summarized as follows [48]:

MaxUP ¼ � X1P

∂P∂X1U1

� �2 þ X2P

∂P∂X2U2

� �2 þ…þ XiP

∂P∂XiUXi

� �2" #0:5:ð17Þ

The uncertainty of the experimental data may have resulted frommeasuring errors of parameters such as mass flow rate, inlet andoutlet temperature difference, the logarithmic mean temperaturedifference between surface and fluid and also thermal conductivityand specific heat of nanofluid. It can be calculated using Eq. (17) forthe Nusselt number:

MaxUNu ¼ � U _mð Þ2 þ UCp

� �2 þ U Tb1−Tb2ð Þ� �2 þ −U Tw−Tbð ÞM� �2 þ −Ukð Þ2� �0:5:ð18ÞFlow rates were measured directly from the time taken to fill a

glass vessel of known volume with 4.0% uncertainty in measurement.Also, the uncertainty of the temperature difference is calculated at0.74%. Wasp and Einstein relations (Eqs. (4) and (2)) that are usedin this study to predict thermal conductivity and specific heat ofnanofluid have the appropriate agreement with experimental studiesof spherical particles. By assuming 4.0% and 2.0% uncertainties forthermal conductivity and specific heat of nanofluids respectively,the maximum uncertainty of the Nusselt number calculated takinginto account the above considerations is obtained at 6.09%.

6. Results and discussion

6.1. Validation check

In order to validate and estimate the accuracy of the experimental re-sults, values of Nusselt number for distilled water are compared withexiting correlations for straight tube and HCTs. Fig. 4 shows the variationof theoretical values (Eqs. (10) and (11)) with experimental values forNusselt number. As it is seen from this figure, the deviation of the exper-imental data from the theoretical one is within −19% and +32%.

Moreover, to verify the validity of measured pressure drop throughthe tubes, a comparison between theoretical and empirical pressuredrops has been done. Fig. 5 depicts the variety of the theoretical valuesfor pressure drop (Eqs. (12)–(15)) along the test section versus mea-sured pressure drop. As it can be seen from Fig. 5, the deviation of the

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45

Theo

ritic

al N

u

Experimental Nu

HCT No.1

HCT No.2

HCT No.3

Straight tube -19%

+32%

Fig. 4. The comparison between theoretical and experimental Nusselt numbers ofdistilled water flow inside tubes.

Table 4The effects of surfactants on Nusselt number for 0.25 vol.% concentration of nanofluidflows through HCT-II.

Particle Re Nu

With surfactant Without surfactant Deviation (%)

Al2O3 4265 47.3 48.1 −1.69905 21.3 21.9 −2.82

TiO2 3915 46.2 46.7 −1.08862 21.1 21.3 −0.95

87M. Kahani et al. / Powder Technology 246 (2013) 82–92

experimental data from the theoretical one is within −27% and +19%.Accordingly, for both Nusselt number and pressure drop the experimen-tal results show reasonable agreement with the theoretical correlationswhich confirms the reliability and accuracy of the experimentalprocedure.

The experiments were performed for a wide range of (500–4500)Reynolds number and for various concentrations of Al2O3 and TiO2nanopowders (0.25–1.0 vol.% concentration) inside helical coiledtubes with different geometries and straight one. As shown in Table4, since the amount of surfactants which are used in the experimentsis not considerable, there are no noticeable effects on heat transferrate.

6.2. Heat transfer study

Fig. 6 demonstrates the heat transfer coefficient for nanofluidsthrough HCT-I versus Reynolds number for different concentrations.The results clearly show the enhancement of heat transfer coefficientfor both nanofluidswith nanoparticle concentrations aswell as Reynoldsnumber which is due to superior thermal conductivity of nanofluidcompared to water and also Brownianmotion of nanoparticles, particlemigration and reduction of boundary layer thickness as reported in pre-vious literatures [49–51]. In addition, at high flow rates, the dispersioneffects and chaotic movement of the nanoparticles intensify the mixingfluctuations, change the temperature profile to aflatter profile similar toturbulent flow and cause increase in heat transfer coefficient.

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Theo

ritic

al ΔP (kpa)

Experimental ΔP (kpa)

HCT-I

HCT-II

HCT-III

+19%

-27%

Fig. 5. The comparison between theoretical and experimental pressure drops ofdistilled water flow inside helical coiled tubes.

Moreover, the variation of Nusselt number of nanofluid flowsthrough HCT-III as a function of Reynolds number at different concen-trations is shown in Fig. 7. It can be understood from this figure thatthe Nusselt number of each nanofluid is greater than distilled waterand is intensified by increasing Reynolds number as well as thevolume fraction of nanoparticles.

Diffusion and relative movement of nanoparticles near tube walllead to rapid heat transfer from wall to nanofluid. It means that in-creasing the concentration of nanoparticles amplifies the mechanismsresponsible for enhanced heat transfer. Therefore, in general,nanofluids with higher volume concentrations have generally higherconvective heat transfer coefficients.

It is worth mentioning that when particle concentration increases,the viscosity of nanofluids intensifies, so the pressure drop throughHCTs increases too [52]. In another word, when volume concentrationof tested nanofluids is more than 1.0%, dramatic pressure losses willoccur through the tubes. So application of nanofluids in high concen-tration is not recommended and all experiments have been done fornanofluids with volume concentration of less than 1.0%.

Another evidence to confirm these results is presented in Fig. 8which illustrates the ratio of heat transfer coefficient of nanofluidsto that of distilled water inside HCT-II as a function of Reynolds num-ber. Al2O3/water nanofluid causes more enhancement of water heattransfer compared to TiO2/water. The maximum enhancement ratiois observed for 1.0% Al2O3/water and TiO2/water nanofluid flows atthe lowest Reynolds number which is equal to 45% and 27%, respec-tively. With increasing nanoparticle contents and Reynolds number,physical properties of nanofluids (Prandtl number) change too.Since in this figure the ratio of heat transfer is depicted only versusReynolds number, some nonlinearity and non-uniform trends areobserved over experimental data which is due to lack of consideringPrandtl number in this figure. In the last section of this article theeffect of Prandtl number on heat transfer rate will be considered.

For low Reynolds number the heat transfer coefficient is mainlyproportional to the fluid thermal conductivity. The other main effects

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

h (

Wm

-2K

-1 )

Re

HCT-I

Distilled water0.25% TiO20.25% Al2O30.5% TiO20.5% Al2O30.75% TiO20.75% Al2O31.0% TiO21.0% Al2O3

Fig. 6. Heat transfer coefficient versus Reynolds number and volume concentration forAl2O3/water and TiO2/water nanofluid flows inside HCT-I.

10

15

20

25

30

35

40

45

50

55

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Nu

Re

HCT-III

Distillated water0.25% TiO20.25% Al2O30.5% TiO20.5% Al2O30.75% TiO20.75% Al2O31.0% TiO21.0% Al2O3

Fig. 7. Nusselt number versus Reynolds number and volume concentration for Al2O3/water and TiO2/water nanofluid flows inside HCT-III.

88 M. Kahani et al. / Powder Technology 246 (2013) 82–92

of the nanopowders inside the fluid ‘considering the Brownianmotion and fluctuation of the nanoparticles’ change the flow struc-ture of the fluid to a semi turbulent regime with a flattened transversetemperature gradient in the bulk of the fluid [53], which leads to en-hance the nanofluid convective heat transfer. But at a higher Reynoldsor Helical numbers this mechanism is not dominant. In other words,at higher flow rate, the heat transfer coefficient has no considerabledependency to the thermal conductivity of the fluid. Therefore, theeffect of thermal conductivity becomes less pronounced. Since, inthe presence of nanopowders, the aforementioned heat transfer en-hancement ratio (Fig. 8) decreases for a higher Reynolds number [54].

In order to investigate the effects of geometrical parameters (cur-vature ratio and pitch spacing) of helical coils on heat transfer rate,Nusselt numbers of both nanofluids at 0.25–1.0 vol.% concentrationversus Reynolds numbers through helical coiled tubes are shown inFig. 9(a–d). As it can be seen from these figures, the highest Nusseltnumbers are observed for flow inside HCT-II which has the biggestpitch spacing and smallest curvature ratio among other helical coiledtubes. It means that the heat transfer rate marginally increases as thecurvature ratio decreases and pitch spacing increases. For instance, at0.25 vol.% fraction of Al2O3/water nanofluid while Reynolds numbervaries between 500 and 4000 the Nusselt number increases from13.9 to 46.9 for HCT-III and from 14.9 to 47.3 for HCT-II and from12.5 to 36.4 for HCT-I. The smaller curvature ratio leads to the morepowerful centrifugal forces which in turn causes more severe second-ary flow motions.

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500

h (n

f) / h

(wat

er)

Re

HCT-II 0.25% Al2O30.25% TiO20.5% Al2O30.5% TiO20.75% Al2O30.75% TiO21.0% Al2O31.0% TiO2

Fig. 8. The ratio of nanofluid heat transfer coefficient to that of distilled water versusReynolds number inside HCT-II.

Since the experimental data for all tested nanofluid flows throughHCT-II and HCT-III (same curvature ratio) are closer together in com-parison of HCT-I and HCT-III (same pitch spacing), it can be concludedthat the pitch spacing effect on the heat transfer rate is to some extentweaker than the curvature ratio effect. For example, for 0.5% TiO2/water nanofluid the enhancement of Nusselt number betweenHCT-II and HCT-III is 3.4% while this increment is 42.0% betweenHCT-III and HCT-I at Re = 1400. Also, the maximum achievableNusselt numbers are 52.5 and 49.8 for 1.0% Al2O3/water and 1.0%TiO2/water nanofluid, respectively at highest Reynolds number.

Considering Figs. 6, 7, 8 and 9(a–d), it is clear that Al2O3 nano-particles with 35 nm particle size present better enhancement of heattransfer rate in comparison with TiO2 (50 nm)/water nanofluids atthe same concentration and Reynolds number. For example, asshown in Fig. 7 at 0.75 vol.% fraction of nanofluid flow throughHCT-III while Reynolds number varies from 530 to 3410 and theNusselt number increases from 15.6 to 49.5 for Al2O3/water nanofluidand from 13.9 to 47.4 for TiO2/water nanofluid when Reynolds numberchanges from 530 to 3500. Two major reasons to support this kind oftrend are hidden in the thermal conductivity and average size ofnanoparticles. Since Al2O3 nanoparticles have higher thermal conduc-tivity compared to TiO2 nanoparticles, low enhancement of heat trans-fer rate for TiO2/water nanofluid is obtained in comparison with Al2O3/water nanofluids. In addition, the smaller size of Al2O3 nanoparticlescan intensify the Brownian motion of particles which led to more en-hancements on Nusselt number. In brief, the greater enhancementshown by Al2O3/water nanofluid compared to TiO2/water nanofluid isbecause of the combined effect of greater surface to volume ratio andthermal conductivity of Al2O3 nanoparticles compared to TiO2 particles.The same mechanism has been presented by Suresh et al. [55], ZeinaliHeris et al. [56] and Nassan et al. [21] for CuO/water and Al2O3/Waternanofluid flow in a straight circular duct with helical screw tape,straight circular tube and square cross-section duct, respectively.

6.3. Pressure drop results

Pressure drop along HCT-II versus Reynolds number for distilledwater and both nanofluids is shown in Fig. 10. Both nanofluids indi-cate a higher pressure drop compared with distilled water. The largersize of TiO2 nanoparticles leads to more increments of pressure dropin comparison with Al2O3/water nanofluid. For instance, by adding1.0 vol.% fraction of Al2O3 and TiO2 nanoparticles into water atRe = 2600, pressure drop in comparison to water can be increasedup to 89.4% and 97.7%, respectively.

Also, from Fig. 10 it is found that the pressure drop increases overparticle volume concentration due to the rise of working fluid viscos-ity and density as well as Reynolds number. As mentioned inEqs. (12)–(15), the larger the value of viscosity, the more growth inaxial pressure drop. In the interim, Brownian motion, dispersion,and fluctuation of nanoparticles especially near the wall of tubeslead to amplify the momentum exchange rates between the particles.This momentum exchange can considerably increase axial pressuredrop. The results compare well with other investigations [16,57].The maximum pressure drop is 17.43 and 17.25 kPa for TiO2/waterand Al2O3/water, respectively at the highest Reynolds number andvolume concentration.

6.4. Thermal performance evaluation

The thermal performance factor (η) can be defined as the ratio ofthe heat transfer coefficient (or Nusselt number) ratio to the frictionfactor (or pressure drop) ratio at the same pumping power:η ¼ h�=hSt;f

f �=f St;f� �n ð19Þ

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Nu

Re

(a) 0.25%

Al2O3, HCT-I

TiO2, HCT-I

Al2O3, HCT-II

TiO2, HCT-II

Al2O3, HCT-III

TiO2, HCT-III10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Nu

Re

(b) 0.5%

Al2O3, HCT-I

TiO2, HCT-I

Al2O3, HCT-II

TiO2, HCT-II

Al2O3, HCT-III

TiO2, HCT-III

10

15

20

25

30

35

40

45

50

55

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Nu

Re

(c) 0.75%

Al2O3, HCT-I

TiO2, HCT-I

Al2O3, HCT-II

TiO2, HCT-II

Al2O3, HCT-III

TiO2, HCT-III10

15

20

25

30

35

40

45

50

55

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Nu

Re

(d) 1.0%

Al2O3, HCT-I

TiO2, HCT-I

Al2O3, HCT-II

TiO2, HCT-II

Al2O3, HCT-III

TiO2, HCT-III

Fig. 9. Nusselt number results versus Reynolds number of helical coils at (a) 0.25, (b) 0.5, (c) 0.75, and (d) 1.0 vol.% concentrations of both nanofluids. 89M. Kahani et al. / Powder Technology 246 (2013) 82–92

where n is the value index. h⁎ and f⁎ represent the Nusselt number andpressure drop of the flow resulted by applying enhanced heat transfertechniques, respectively. The larger the values of the thermal perfor-mance factor, the more suitable the enhancement heat transfertechnique. The value index (n) has experienced different values in pre-vious literatures. Usui et al. [58] and Suresh et al. [55] have consideredn = 0.1666 for laminar flow while Hashemi et al. [31] have taken n =1.0. Wongcharee et al. [59] have used thermal performance factor withn = 1/3 for turbulent flow and the same value of n has been used byAbbasian Arani and Amani [60] in their experiments.

0

2

4

6

8

10

12

14

16

18

0 500 1000 1500 2000 2500 3000 3500 4000 4500

ΔP (kPa)Re

HCT-II

Distiiled water0.25% TiO20.25% Al2O30.5% TiO20.5% Al2O30.75% TiO20.75% Al2O31.0% TiO21.0% Al2O3

Fig. 10. Experimental pressure drop of nanofluid flows through HCT-II versus Reynoldsnumber.

In order to investigate the influence of both coiled tubes andnanofluid techniques on thermal performance of the equipments,the following equation was used in this study:η ¼ NuC;nf =NuSt;fΔpC;nf =ΔpSt;f� �0:1666 ð20Þwhere NuC,nf and NuSt,f are the Nusselt number for nanofluid flow inhelical tubes and for distilled water flow in straight tube, respectively.Besides, ΔpC,nf and ΔpSt,f represent the pressure drop for nanofluidflows in helical coils and for distilled water flow in straight tube,respectively.

The variation of thermal performance factor with Reynoldsnumber for 1.0 vol.% concentration of Al2O3/water and TiO2/waternanofluids through helical coiled tubes is illustrated in Fig. 11.

The thermal performance factor for all helical coils is greater thanunity. It means that using both of the heat transfer enhancementtechniques studied in this investigation is a good choice in practicalapplication. Also, HCT-II shows the best thermal performanceamong other helical tubes. For example, at the lowest Reynolds num-ber the thermal performance factor for Al2O3/water nanofluidsthrough HCT-II is 11.7% and 25.3% greater than the flows insideHCT-III and HCT-I, respectively. As mentioned before, small curvatureratio and large pitch spacing of HCT-II intensify centrifugal forcesand secondary flow which lead to more enhancement of thermalperformance.

In addition, Al2O3/water nanofluid through helical coils showsbetter performance than TiO2/water nanofluids. For instance, thermalperformance factor of Al2O3/water nanofluid flow in HCT-I changes

1.5

2

2.5

3

3.5

4

0 500 1000 1500 2000 2500 3000 3500 4000

ηRe

1.0% Vol. Nanofluid

Al2O3, HCT-IIITiO2 , HCT-IIIAl2O3, HCT-IITiO2 , HCT-IIAl2O3, HCT-ITiO2 , HCT-I

Fig. 11. Variation of thermal performance factor with Reynolds number for 1.0 vol.%concentration of nanofluid flows inside helical tubes.

90 M. Kahani et al. / Powder Technology 246 (2013) 82–92

between 2.11 and 3.09 while this variation for TiO2/water nanofluidsis between 1.71 and 2.88. Besides, the maximum thermal perfor-mance factor is 3.82 and obtained for 1.0 vol.% concentration ofAl2O3/water nanofluid through HCT-II at Re = 1865.

10

20

30

40

50

60

Pred

icte

d N

u

(a)+15%

-15%

6.5. Estimation of Nusselt number and pressure drop

Fig. 12 depicts the ratio of the experimental Nusselt number to theresults obtained from Manlapaz–Churchill equation versus Reynoldsnumber for nanofluid flows through HCT-I. From this figure it canbe noticed that Manlapaz–Churchill equation fails to predict theNusselt number of Al2O3/water and TiO2/water nanofluids. Othermechanisms besides thermal conductivity increase such as Brownianmotion and particle migration can be responsible for heat transferenhancement too and these two main factors are not considered inthe common theoretical equations.

In order to incorporate the effect of pitch in the empirical correla-tion for the Nusselt number and pressure drop through helical coils,Helical number is employed instead of the Reynolds number. WhenReynolds number varies from 500 to 4500, the Helical numberchanges between 157 and 1420 for HCT-II and III and also variesfrom 111 to 1005 for HCT-I.

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 1000 2000 3000 4000

Nu

(exp

) / N

u (th

)

HCT-I

0.25% TiO2 0.25% Al2O30.5% TiO2 0.5% Al2O30.75% TiO2 0.75% Al2O31.0% TiO2 1.0% Al2O3

Re

Fig. 12. The ratio of experimental Nusselt number to Manlapaz–Churchill equation forAl2O3/water and TiO2/water nanofluids versus Reynolds number through HCT-I.

Using the present empirical data, the following correlations arederived to predict the Nusselt number of nanofluid flows inside thehelical coils using least square method of regression analysis.

For TiO2/water nanofluid:NuC ¼ 0:5He0:522Pr0:613φ0:0815 R2

adj: ¼ 95:0% : ð21ÞFor Al2O3/water nanofluid:

NuC ¼ 0:7068He0:514Pr0:563φ0:112 R2adj: ¼ 96:4% ð22Þ

the applicable ranges are (i) 0.25% ≤ φ ≤ 1.0%, (ii) 5.89 ≤ Pr ≤ 8.95and (iii) 115.3 ≤ He ≤ 1311.4.

As shown in Fig. 13(a,b), the deviation between the predictedNusselt number and experimental Nusselt number is found to be inthe range of between +15% to −15% for TiO2/water and +18% to−25% for Al2O3/water nanofluid.

Besides, a correlation is developed by using least square method ofregression analysis to predict pressure drop through helical coiledtubes as follows:ΔpC ¼ 5:584He1:36φ0:446dp0:163 R 2

adj: ¼ 95:8% ð23Þthis correlation is valid for metal oxide (spherical shape nanoparticles)/water nanofluid flows in helical coils with volume concentrations lessthan 1.0% in the laminar flow regime with 115.3 ≤ He ≤ 1311.4 and35 ≤ dp ≤ 50 nm.

00 10 20 30 40 50 60

Experimental Nu

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Pred

icte

d N

u

Experimental Nu

(b)

-25%

+18%

Fig. 13. Deviation between the predicted Nusselt number and experimental Nusseltnumber for (a) TiO2/water and (b) Al2O3/water nanofluids.

91M. Kahani et al. / Powder Technology 246 (2013) 82–92

7. Conclusion

The comparative study on thermal performance and pressure dropfor Al2O3 (35 nm)/water and TiO2 (50 nm)/water nanofluid flowsthrough helical coils was done. The experiments were carried outfor the laminar flow regime under constant heat flux boundary condi-tion with different concentrations of nanofluids, which vary from0.25% to 1.0%. The conclusions based on the experimental resultsare as follows:

1) For nanofluids, heat transfer rate and also pressure drop enhancewith increasing nanoparticle concentrations as well as Reynoldsnumber. Although, because of the larger thermal conductivityand smaller size of nanoparticles, Al2O3/water nanofluids showmore enhancement compared with TiO2/water.

2) All the helical coils have thermal performance factor greater thanunity. It means that using nanofluids inside helical coils is a suit-able choice in practical application.

3) The maximum thermal performance factor is found to be 3.82 for1.0 vol.% concentration of Al2O3/water nanofluid through HCT-II atRe = 1865.

4) According to the empirical data, HCT-II which has the smallestcurvature ratio and the largest pitch spacing shows the bestperformance among other helical coils.

5) The pitch spacing effect of helical coils is to some extent weakerthan the curvature ratio effect on the heat transfer rate.

6) Three experimental correlations are proposed to bring out theeffects of Helical number, Prandtl number, volume concentrationand particle size on Nusselt number and pressure drops of bothnanofluids.

Acknowledgment

The authors wish to thank the Iran Nanotechnology InitiativeCouncil (INIC) and the Ferdowsi University of Mashhad for financialsupport of this research.

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