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Applied Thermal Engineering 62 (2014) 20e27

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Applied Thermal Engineering

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Effects of titania nanoparticles on heat transfer performance of spraycooling with full cone nozzle

Ampere A. Tseng*, 1, Hana Bellerová 1, Michal Pohanka, Miroslav RaudenskyHeat Transfer and Fluid Flow Laboratory, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

a r t i c l e i n f o

Article history:Received 24 April 2013Accepted 22 July 2013Available online 15 August 2013

Keywords:Full cone nozzleHeat transfer coefficientImpingement durationNanofluidsNanoparticleSpray coolingTitania

* Corresponding author. School for Engineering of MArizona State University, 501 E. Tyler Mall, ECG 301, Te480 965 8201; fax: þ1 480 965 1384.

E-mail address: ampere.tseng@asu.edu (A.A. Tseng1 On leave from Arizona State University, Tempe, A

1359-4311/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.07.02

a b s t r a c t

Spray cooling using aqueous titania nanofluids was studied. The temperatures of a testing plate undervarious spraying conditions were first measured; an inverse heat conduction technique was then appliedto convert these measured temperatures into heat transfer coefficients (HTCs). It was found that the HTCincreased logarithmically with the volume flux, but was decreased with the increase of the nanoparticlefraction. A correlation analysis was performed to quantify the HTC reduction caused by the increase ofnanoparticles, and reconfirmed that the major cause for the HTC reduction was the difference in theimpact (or impingement) behavior between solid nanoparticles and fluid droplets. A comparison study ofthe present findings with the previous published results was also performed and indicated that all resultscompared were consistent to each other based on the similar spray cooling conditions with differentnanofluids or nozzles. The effects by using aquatic titania nanofluids instead of aquatic alumina nano-fluids and by using full-cone nozzle instead of solid jet nozzle were specifically assessed and the asso-ciated rationales for the differences in these effects were given.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Spray cooling has been used to remove heat from hot surfacesfor many applications, from cooling space systems [1] to nuclearreactor cooling [2], from coal gasification cooling [3] to fire sup-pression [4], from metal quenching [5] to cooling electronic sys-tems [6,7], and from continuous casting cooling [8,9] to steel roll-strip cooling [10,11]. This type of cooling can be very effective andsimple, because the momentum of the liquid coolant under highspray pressure can allow the liquid to get much closer to the hotsurface than it would be in pool boiling, inwhich the heated surfaceis immersed in the water, creating a thinner vapor film that greatlyreduces the heat transfer rates.

Recently, the technology of spray cooling has been furtherdeveloped by using aquatic based nanofluids instead of pureliquid. Nanofluids are fluids containing particles with the size lessthan 100 nm. As compared with the base fluid, these nano-particles, such as metal or oxide, possess much higher

atter, Transport, and Energy,mpe, AZ 85287, USA. Tel.: þ1

).Z 85287-6106, USA.

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conductivities and are expected to enhance the thermal proper-ties, including higher thermal conductivity and heat transfer co-efficient (HTC), of the nanofluids. A tremendous number ofpublications on nanofluids have been published. Among then, asubstantial number of experimental studies indeed indicate that,by adding high-conductivity nanoparticles, the HTCs can beenhanced as compared with that using only the base fluid in awide range of heat transfer problems [12,13]. On the other hand, amoderate number of studies report that the suspended nano-particles can deteriorate the heat transfer performance of thenanofluids. Pak and Cho [14] studied heat convection of waterbased TiO2 nanofluids moving in a circular pipe and found that theHTC of the nanofluid with a particle concentration of 3 vol% was12% smaller than that of pure water. In studying the naturalconvection of aqueous nanofluids between two horizontalaluminum disks, Wen and Ding [15] found that the HTC coulddecrease more than 50% as the wt% of TiO2 nanoparticlesincreased from 0 to 2.5%. By numerically evaluating the effect ofwater-based nanofluids on a square microchannel heat exchanger,Mohammed et al. [16] found that, with an increase in the fractionof titania nanoparticles, the overall heat transfer rate decreased. Inaddition to titaniaewater nanofluids, the degradation in HTCscould also be found in nanofluids with suspensions of Al2O3, CuO,and diamond nanoparticles [12,17].

Table 1Thermofluid properties of water and titania.

Property H2O at 50 �C TiO2 at 50 �C References

Density, r [kg/m3] 992 4069 26Conductivity, k [W/m K] 0.663 8.05 27Specific heat, c [J/kg K] 4175 713 30,31Viscosity, m [Pa s] 6.58 � 10�4 e 26

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e27 21

This inconsistency or anomaly in the heat transfer performanceby nanofluids can also be found in the problems of spray cooling.Bansal and Pyrtle [18] experimentally studied the effects of thealumina nanoparticles on the heat fluxes for spray cooling of metalblocks and observed that the heat transfer enhancement usingwater/alumina nanofluid could reverse from positive to negativedependent on the target surface temperatures. They also reportedthat no noticeable difference of the heat transfer performance ofthe nanofluids by varying the nanoparticle fraction from 0.25 to0.50 wt%. Duursma et al. [19] applied a needle type of nozzles toexperimentally investigate the spray cooling of a hot metal surfaceusing ethanol and DMSO (dimethyl sulfoxide) based Al nanofluidsand found that the heat fluxes of nanofluid spraying were deteri-orated for ethanol-based solutions but somewhat enhanced forDMSO nanofluids as comparing with their respective base-fluidcounterparts. Recently, Bellerová et al. [20,21] studied spray cool-ing using aquatic-alumina nanofluids and found that the HTC of thenanofluid cooling decreased as the nanoparticle volume fraction(4v) increased. Dependent on the type of nozzles used for spraycooling, they observed a 20%e40% reduction of HTC by increasing4v from 0 to 16.45% [20,21].

Several attempts have been made to provide the theoretical ba-ses for the thermal deterioration behaviors of nanofluids, but mostof them, at the best, have been appropriate only for a special case orcondition andnothingproposed so farhas beengenerallyacceptable[20e25]. For example, by using aquatic alumina nanofluids for spraycooling, Bellerová et al. [21] analytically illustrated and experi-mentally demonstrated that the difference in the impact (orimpingement) behavior between a solid particle and a fluid dropletwas the major cause for the thermal deterioration in spray cooling.Yang et al. [22] theoretically investigated the heat transfer perfor-mance of aquatic-titania nanofluids in a fully-developed channelflow subjected to constant heat-flux and found that whether theheat transfer enhancement being positive or negative was depen-dent on the ratio of the Brownian diffusivity to the thermophoreticaldiffusivity (NBT). They numerically illustrated that, at zero Browniandiffusivity orNBT¼0, the enhancementwas negative andhad lowestHTC and, by increasing NBT, the enhancement became positive. AtNBT near 0.5, the positive enhancement reached its maximum.However, by studying the same channel flowwith aquatic-aluminananofluids, they found that there was no negative enhancement,even at NBT ¼ 0 [22]. No discussion was given by Yang et al. for thereason to have no negative enhancement by using aquatic-aluminananofluids. Utomo et al. [25] discovered that the degree ofenhancement in titaniaewater nanofluids was somewhat muchlarger or stronger than that of aluminaewater nanofluids at thesame mass flow rate for the similar problem considered by Yanget al. [22]. Indeed, both of these two groups [22,25] believed that theheat transfer performance could be highly dependent on the type ofthe nanofluid used.

Consequently, since the spray cooling experiments conductedby Bellerová et al. [20,21] are limited to aquatic alumina nanofluids,in the present study, the effect of a different type of nanofluids, i.e.,TiO2ewater, used in spray cooling would be assessed and theanomaly previous found in the spray cooling performance, i.e., thecooling HTC decreases as 4v increases, is to be re-examined. Theapproaches adopted are similar to those used by Bellerová et al. Acomparison study is also conducted to examine the differencesbetween the present results and those previous reported. Theuniqueness in conducting the present study would be specificallydiscussed. A correlation between the HTCs and several spray pa-rameters would then be developed to quantify the effects of usingdifferent nanofluids or different nozzles. Finally, recommendationsfor future research and development in the area of nanofluid spraycooling are provided.

2. Experiment

An axisymmetric thermal probe developed was built to performthe experiment in the present study. The probe consisted of a testplate, a nozzle connected to a pressure-regulated flow tank, and aPC-based data acquisition system. The test plate was madeof stainless steel with a cooling surface of 20-mm in diameter and aK-type thermocouple was embedded 0.37-mm underneath thecooling surface. The surface was the spray cooling area and themeasured cooling curve by the probewas used as an input to an IHC(inverse heat conduction) model to inversely calculate the associ-ated HTC of the spray cooling. The full-cone nozzle, Lechler Model460.443CA, evaluated by Bellerova et al. [21] was selected for thepresent study. The nozzle had a bore diameter of 1.2 mm with a45�-spray angle (qs).

2.1. Titania/water nanofluids

A TiO2/water nanofluid, called Aerodisp� W 740X, produced byEvonik Industries, was selected. The Aerodisp� nanofluid con-tained 40 wt% TiO2 nanoparticles and was very stable by adding atiny amount of citric acid to neutralize the nanofluid. The meandiameter of the titania particles was 82 nm. In experiment, the 40-wt% TiO2/water nanofluid was diluted with the base fluid,deionized water, to two lower wt%. To ensure proper homogeni-zation of the nanoparticles and to obtain a stable and uniformcolloidal solution, the nanofluids were ultrasonically mixed for24 h.

The nanoparticle contents in the nanofluids studied were 0, 1,10, and 40 wt%; the corresponding volume fractions, 4v, could becalculated to be 0.0, 2.47 � 10�3, 2.65 � 10�2, and 1.405 � 10�1,respectively, where the water density (rf) at 20 �C used in thecalculation was 998.2 kg/m3 and TiO2 nanoparticle density (rs) at20 �C was 4073 kg/m3. The particle density was calculated based onthe nanofluid density (rnf) provided by the Evonik and agreed verywell with data provided by a material data website [26].

By measuring the recycled nanofluid temperature after spray-ing, the mean temperature of the nanofluid during spray experi-ment was approximately 50 �C, which was used as the referencetemperature for the determination of the physical properties of thenanofluids. The material properties of TiO2 and water at 50 �C weresummarized in Table 1. The ks value adopted was based on the datareported by Maekawa et al. [27] at 50 �C, which was close to thevalue reported by Teja et al. [28], but approximately 30% lower thanthat used byWang et al. [29]. In Table 1, the specific heat (cs) of TiO2at 50 �C was reported by Mitsuhashi and Watanabe [30] and wasabout 0.1% higher than that of 25 �C found in aweb-based reference[31].

2.2. Testing procedures

In testing, the test plate was heated to 200 �C by an electricalfurnace and was held at that temperature for 15 min to achieve auniform temperature distribution in the plate. The heated testplate was then loaded horizontally on the top of an airtight

Fig. 1. Spray cooling testing chamber, including full-cone nozzle, pressure gauge, andcoolant inlet and outlet with thermocouples (no show), where the test plate (no show)should be loaded on the top of impinging area.

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e2722

Plexiglas testing chamber with the test surface facing down, whilethe nozzle was placed under the test plate in the testing chamberas shown in Fig. 1. The distance between the nozzle and theheated plate or the spray head (hz) varied from 40, 100, and160 mmwith an accuracy of 0.1 mm. During cooling, the nanofluidat the ambient temperature (w20 �C) was driven through the full-cone nozzle to spray onto the heated test surface from below.After each spraying, the fluid was collected in the testing chamberand recycled back through an outlet hose back to the flow tank bygravity. The main reason to select upward spraying was to elim-inate the effect of gravity on the heat transfer measurement.

In the experiment, the mass flow rates (M) were 16.67 � 10�3,25.00 � 10�3, and 33.33� 10�3 kg/s. The corresponding volumetricflow rate, Q, could be found to be M/rnf, where rnf for all 4v werereported in Table 2. In addition to rnf, the procedures for thecalculation of the thermal conductivity (knf), specific heat (cnf),viscosity (mnf), Prandtl number (Prnf) of the nanofluids weredetailed in Ref. [21] and also summarized in Table 2 for the latercorrelation evaluation. The calculated Qs for all the conditionsconsidered were summarized in Table 3.

3. Characteristics of spray cooling

The temperature measurements of cooling curves and the IHCtechnique used for computing HTCs as well as the characteristics ofHTC are presented in this section.

Table 2Thermofluid properties of titania/water nanofluid.

Property at 50 �C TiO2 particle volume fraction, 4v

0.0 2.47 � 10�3

Density, rnf [kg/m3] 992 1000Conductivity, knf [W/m K] 0.663 0.667Specific heat, cnf [J/kg K] 4175 4140Viscosity mnf [Pa s] x103 0.658 0.670Prandtl No, Prnf ¼ cnfmnf/knf 4.14 4.16

3.1. Cooling curve measurement and calculated heat transfercoefficient

The temperature measured by the embedded thermal probewas shown as the dash-dot line in Fig. 2 for water spraying (4v ¼ 0)at hz ¼ 0.1 m and fv ¼ 4.542 � 10�3 m/s. As shown, the test plate atthe measurement location was cooled down from approximately190 �C to 100 �C within 1 s and the rate of temperature drop wasreduced as the measured temperature decreased. The measuredtemperature was then used as the input to a numerical IHC modelto inversely calculate the desired boundary value, i.e., the HTC ofspray cooling. The IHC model was previously developed forstudying the HTC for the spray cooling used in steel rolling [11].

The calculated HTC for water spraying was also plotted as thethick solid line in Fig. 2, where the HTC rapidly reached to its firstpeak at the cooling time equal to 0.14 s. This first peak was mainlydue to the fact that, at the instant when the spray droplets suddenlyimpinged on the test plate surface, a massive thermal shock causedthe surface temperature to drop rapidly. The corresponding HTC,especially at the center of the cooling surface rose abruptly to thefirst peak value, i.e., 21.15 kW/m2-K . The temperature variations atother instances were much moderate and decreased gradually,which suggested that the thermal shock did not appear at any otherinstances. As shown in Fig. 2, within 1 s, the HTC rapidly reduced toabout one-half of its maximum magnitude and then fluctuatedrestrainedly at its mean. It was believed that the fluctuationobserved was caused by the inherent discontinuity of the spraydroplets impinging on the hot surface, which dictated the heattransfer between the cold droplets and the hot surface. For theperiod of the cooling time considered, i.e., from 1 to 8 s, the cor-responding standard deviation (SD) of the HTC was less than 8% ofits mean.

The surface temperature at the impingement center was alsocalculated by the IHC model and plotted as the thin solid curve inFig. 2. By comparingwith themeasured temperature, the calculatedsurface temperature was several degrees lower for the cooling timeconsidered. For instance, at the cooling time equal to 5 s, thecalculated temperature was 58 �C, which was about 7 �C lower thanthe measured temperature. The temperature difference was causedby the fact that the thermocouple was embedded 0.37 mm belowthe surface. It always had a delay in the internal temperature ascompared with the surface temperature, which was the locationbeing cooled first during cooling impingement. As expected, theinternal measured and the calculated surface temperaturesdecreased as the cooling time increased.

3.2. Nanofluid spraying and mean heat transfer coefficient

The cooling behavior for nanofluid spraying at 4v ¼ 0.1405 wasshown in Fig. 3 for the cooling time varying from 0 to 9 s. As shown,the HTC immediately reached to its maximum,18.9 kW/m2 s within0.1 s and then fluctuated around a mean value of approximatelyone-half of its peak value. As compared with the water spray datashown in Fig. 2, the transient behaviors of the nanofluid

References

2.65 � 10�2 1.405 � 10�1 1.0

1074 1424 4069 36, 370.705 0.910 8.05 31

3827 2786 713 30, 36, 370.798 1.611 e 314.33 4.93 e Calculated

Table 3Experimental conditions for titania/water nanofluid spraying.

Spray head, hz [m] 0.04 0.10 0.16Volume flow rate,

Q ¼ M/rnf [m3/s] � 1064v ¼ 0 16.80 25.20 33.602.47 � 10�3 16.67 25.01 33.342.65 � 10�2 15.52 23.28 31.041.405 � 10�1 11.70 17.55 23.40

Spray head, hz [m] 0.04 0.10 0.16 0.04 0.10 0.16 0.04 0.10 0.16Impinging area, Ai [m2] � 103 0.926 5.547 14.05 0.926 5.547 14.05 0.926 5.547 14.05Volume flux, fv ¼ Q/Ai [m/s] � 103 4v ¼ 0 18.14 3.028 1.196 27.21 4.542 1.793 36.28 6.056 2.391

2.47 � 10�3 18.00 3.005 1.187 27.00 4.508 1.780 36.00 6.010 2.3732.65 � 10�2 16.76 2.798 1.105 25.14 4.197 1.657 33.52 5.596 2.2091.405 � 10�1 12.64 2.109 0.833 18.96 3.164 1.249 25.27 4.219 1.666

Particle impact duration, Dts [ns] 4v ¼ 0 0.150 0.150 0.151 0.138 0.138 0.138 0.130 0.130 0.1312.47 � 10�3 0.151 0.151 0.151 0.139 0.139 0.139 0.131 0.131 0.1312.65 � 10�2 0.153 0.153 0.153 0.141 0.141 0.141 0.133 0.133 0.1331.405 � 10�1 0.162 0.163 0.163 0.149 0.149 0.149 0.140 0.140 0.140

Nanofluid impact duration, Dtnf [ms] 4v ¼ 0 500.0 500.0 500.0 500.0 500.0 500.0 500.0 500.0 500.02.47 � 10�3 498.8 498.8 498.8 498.8 498.8 498.8 498.8 498.8 498.82.65 � 10�2 486.7 486.7 486.7 486.7 486.7 486.7 486.7 486.7 486.71.405 � 10�1 429.8 429.8 429.8 429.8 429.8 429.8 429.8 429.8 429.8

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e27 23

(4v ¼ 0.1405), including the HTC and the measured and calculatedtemperatures shown in Fig. 3, were similar to those of water spray,but the mean and the fluctuation of the HTC for the nanofluid spraywere approximately 35% lower and 25% higher than the respectivevalues of the water spray. Obviously, these differences, i.e., lowerthemean value and higher the fluctuation of HTC, should bemainlycaused by including the solid nanoparticles and would be specif-ically examined in the subsequent section.

To provide representative and practically useful data for spraycooling, the mean HTC in the roughly plateau region, i.e., from 1 to8 s, or in the region of the measurement temperature varying from100 to 50 �C, would be used. The mean HTC calculated based on the7-s cooling time interval agreed very well with that based on the50e100 �C plateau interval. In fact, the difference between themwas within 3%. Note that, using a single value to represent a typicalspray-cooling condition would be not only reliable to indicate thereal magnitude of HTC for further analyses, but also convenient tobe used in designing a cooling system. As a result, the mean HTCdata obtained for all spraying conditions considered should be usedas the basis for further spray cooling analyses.

3.3. Mean HTC versus volume flux at different volume fractions

Many investigators [32e34] found that the mean HTC (hnf) fornanofluid spray cooling could be correlated well with the volumeflux (fv) in a power-law form, which was also adopted for nanofluidspray cooling [20]:

Fig. 2. Measured internal and calculated surface temperatures and HTC for spraycooling with pure water (4v ¼ 0) at hz ¼ 0.1 m and fv ¼ 4.542 � 10�3 m/s.

hnf ¼ C1fmv (1)

where C1 and m were the correlation coefficient and exponent,respectively. In Fig. 4, the experimental results of the mean HTCobtained for all cooling conditions considered were plottedagainst fv in a double logarithmic scale at four different values of4v. Each HTC data shown was based on at least three measure-ments and the associated SD for each data was also calculated.Since the maximum SD was found to be relatively small, less than8% of the HTC value, the experimental data could be consideredreasonably consistent and would be expected to be reliable. Forthe sake of the clarity, the values of the SD were not depicted onFig. 4.

As shown in Fig. 4, the correlation exponents, m, were 0.660,0.610, 0.623, 0.623 for 4v ¼ 0.0, 2.47 � 10�3, 2.65 � 10�2, and1.405 � 10�1, respectively; the corresponding correlation coeffi-cient, C1 were 462.5 � 10�3, 288.0 � 10�3, 311.8 � 10�3, and292.4 � 10�3, if fv was in [m/s] and hs was in [W/m2 K]. The cor-responding coefficient of determination, R2, were 0.982, 0.974,0.972, and 0.973, which implied that all the correlations involvedagreed extremely well with the experiment data. The largestdisagreement was less than 3% for R2 ¼ 0.972 occurring at4v ¼ 2.65 � 10�2. The R2 coefficient is an overall measure of theaccuracy of a correlation regression or a measure of how well thecorrelation curve represents the data; it always lies between 0 and1. A value of zero occurs when the two variables are totally in-dependent of each other, while it reaches 1 when the two vari-ables correlate perfectly, i.e., no deviation from the correlatedcurve [35].

The present correlation exponent, m, varied from 0.610 to0.660, agreed reasonably well with the results reported by Abbasiet al. [34], where the correlation exponent varied from 0.5 to 0.61for fv correlations of pure water spraying. Ciofalo et al. [33]observed that the exponent should be 0.687 for a mass flux (fm)correlation of water spraying. It was also found that 4v had ad-versary effects on the HTC, showing that, the HTC decreased as 4v

increased. This finding, i.e., the HTC decrease by including nano-particle, was similar to those reported by Duursma et al. [19] andBellerová et al. [20]. It was believed that the effect of 4v on HTCshould be mainly due to the fact that the nanoparticles in thenanofluid could change the impingement or impact behaviors ofthe nanofluid spraying. Also, the change of the nanofluid thermalproperties could affect the HTC of the nanofluid spray cooling.These two effects on the HTC would be treated in the subsequentsection.

Fig. 3. Measured internal and calculated surface temperatures and HTC for spraycooling with TiO2 nanofluid at 4v ¼ 0.1405, hz ¼ 0.1 m, and fv ¼ 3.164 � 10�3 m/s.

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e2724

4. Correlation with Prandtl number and impingementduration

As indicated reported by Bellerová et al. [20], in addition to thevolume flux, fv, the nanofluid HTC (hnf) can be correlated well withthe nanofluid properties (Prnt) and the ratio of the spray impinge-ment duration times (Dtnf/Dtf) in the following form:

hnf ¼ C2Prknf f

mv

�Dtnf=Dtf

�n(2)

where C2, k, and n are the correlation parameters. Here, the sub-scribes nf and f represent the values related to nanofluid and basefluid, respectively. In the above equation, the ratio of theimpingement duration times (Dtnf/Dtf) is to quantify the effect ofthe nanoparticles on hnf, while the Prnf term is to count the influ-ence of the thermofluid properties on the HTC. The Pr has beenused to represent the thermofluid properties in various nanofluidHTC correlations [36,37] and in many spray cooling correlationsusing pure-fluids [38,39]. On the contrary, the use of theimpingement duration time to represent the nanoparticle effectshas only been reported by Bellerová et al. [20,21].

In spray cooling, most of the heat is transferred during the spraydroplets in contact with the heated surface. The impingement orimpact duration of the droplets can dictate the amount of heat that

Fig. 4. Correlations of heat transfer coefficient (HTC) of spray cooling with volumefluxes, fv, for volume fraction, 4v, equal to 0.0, 2.47 � 10�3, 2.651 � 10�2 and1.405 � 10�1.

can be conducted from the surface to the droplets. Since theimpingement behavior of solid particles is much different from thatof liquid droplets, the effect of the solid particles on the overallimpingement duration should be essential on the HTC. Based on theconservation of energy, Bellerová et al. [20] analytically derivedthat hnf was a linear function of (Dtnf/Dtf) at a specific fv, whichmeant n¼ 1. However, by experimental observation, Bellerová et al.[20,21] believed that hnf should be represented by a more generalform as (Dtnf/Dtf)n.

In the present spraying conditions, the impingement durationtime of solid nanoparticles, Dts, was extremely short and muchsmaller than Dtf, i.e., Dts << Dtfas indicated in the correspondingvalues of Dts and Dtnf in Table 3. Based on the proportional mixingprinciple, the mean duration time in nanofluid spray cooling, Dtnf,could be expressed as [20]:

Dtnf=Dtf ¼ ð1� 4vÞ (3)

By substituting the above equation into Eq. (2), one has

hnf ¼ C2Prknf f

mv ð1� 4vÞn (4)

Since the effect of 4v on hnf is included, the above equationshould be able to correlate all the HTC data obtained. Also, theabove correlation has a more attractive form than that of Eq. (2),since the solid fraction, 4v, is explicitly expressed in the correlationwithout the troublesome to evaluate the specific solid and fluidduration times.

4.1. Exponent k

The exponent k ¼ 0.37 was selected in the present correlationand was consistent with most data reported for spray cooling ex-periments. For nanofluid convention problems other than spraycooling, Rostamani et al. [36] investigated the turbulent forcedconvection of TiO2ewater and CuOewater nanofluids and foundthe corresponding HTC correlation having Pr in 0.35 powers. Inaddition, in studying convective heat transfer problems, Kakac andPramuanjaroenkij [37] reported that the exponent k in HTC corre-lations for nanofluids could vary from 0.35 to 0.4.

By studying nanofluid spray cooling with a solid jet nozzle,Bellerová et al. [20] found k¼ 0.33 was appropriate. For all the casescompared, 0.37 was a mean for the k exponent.

As reported in Table 2, the Pr number considered in the presentstudy was varying from 4.144 to 4.931. The maximum difference ofPrk in using k ¼ 0.33 and 0.40 for all Pr numbers considered wasabout 10%. If the mean was selected, the maximum possible errorcould be controlled within 5%.

4.2. Exponent n

As theoretically illustrated by Bellerová et al. [20], hnf was alinear function of (Dtnf/Dtf) at a specific fv, which implied that n ¼ 1.The validity of the theoretical prediction, i.e., n¼ 1, was first studiedbased on the experimental data presented in Fig. 4. As shown inFig. 5a, the four sets of data fit the overall correlation of Eq. (2) or (4)very well, with the R2 coefficient equal to 0.968. If the effect of theimpact impingement duration ratio was not included, i.e., n¼ 0, theR2 coefficient became smaller and equaled 0.953. This implied thatthe impact duration ratio should be included in counting thenanoparticle effect so that the correlation accuracy could be better.By trying other values of n, it was found that when n ¼ 1.2, theresulting R2 coefficient reached its maximum and equaled 0.970,which was at the same level of the R2 value with that of the fourindividual correlations presented in Fig. 4. This suggested that theimpingement duration times had major effects on HTC in spray

Fig. 5. Correlations of HTC, hnf, with volume fluxes, fv, Prandtl number, Prnf, and impactduration ratio, Dtnf/Dtf: a) correlation exponent, n ¼ 1.0, b) n ¼ 1.2.

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e27 25

cooling and that n ¼ 1.2 was a reliable number to quantify thenanoparticle effects on HTC, since the accuracy in correlating theHTC for all 4v should not be better than that of any correlationdeveloped for an individual 4v.

Consequently, although, based on the theoretical prediction, theexponent n equals 1, the value of n should be changed to 1.2, tobetter fit the experimental data. By substituting all the exponentvalues into Eq. (4), the final form of the correlation becomes

Table 4Parameters in power-law correlation of HTC with fv, where HTC in [W/m2 K] and fv in [m

Case Nano-particle Nozzle type Volume fraction Correlation coeff.

1 e Full-cone 0.0 452.5 � 103

2 Titania Full-cone All 4v 341.5 � 103

3 Titania Full-cone All 4v 212.5 � 103

4 Titania Full-cone All 4v 212.9 � 103

5 Titania Full-cone All 4v 215.1 � 103

6 Alumina Full-cone All 4ma 4647a

7 Alumina Solid jet All 4v 178.5 � 102

a Based on mass fraction, fm, where the unit of fm is in [kg/m3].

hnf ¼ 215:1 � 103Pr0:37nf f 0:630v ð1� 4vÞ1:2 (5)

where hnf is in [W/m2 K], fv is in [m/s] and 4v is dimensionless.

4.3. Correlation comparison

The present correlation developed are also compared with thetwo previously developed for spray cooling using alumina/waternanofluids; one is for a full-cone nozzle [21] while the other is for asolid jet nozzle [20]. The correlation parameters for the two pre-vious correlations (Cases 6 & 7) and those presently developed forthe titania/water nanofluids (Case 1e5) are all summarized inTable 4. The data of Case 1 is directly obtained from Fig. 4 for thecase of pure water spray and has highest R2 as compared with othercases. This implies that by adding nanoparticles, the associatedexperiment results are more scattering or less consistent. To havemore reliable nanofluid data, experiments might need to repeatmore times for a data point. Also, note that the mass flux (fm)instead of volume flux (fv) is used for Case 6 of the full-cone nozzlespraywith alumina/water nanofluids. Since fv¼ fm/rnf, if the changein rnf is relatively small, the difference in the correlation exponent,m, is negligible. In the present study, the exponent m obtained forcorrelating fm is considered to be equivalent to the exponent ob-tained for correlating fv.

As comparing Case 2 with Case 3, it can be found that, byincluding the Prnt term, the R2 coefficient increases from 0.947 to953, which implies that the correlation is more accurate byconsidering the thermofluid property effect or Pr number changes,although the accuracy improvement is moderate. Since the range ofthe Pr number variation for Cases 2 and 3 is relatively small, i.e.,from 4.144 to 4.931, to have a moderate accuracy improvementshould be reasonable.

By comparing Case 5 with Case 6, the effect of using differentnanoparticles (titania versus alumina) can be assessed. The expo-nent n of Case 5 (¼1.2) is approximately 30% higher than that ofCase 6 (¼0.92), which means that the titania nanoparticles havemore stronger effect on the heat transfer performance than that ofalumina. This discovery is quite consistent with those findingspreviously reported by Yang et al. [22], Utomo et al. [25], and Tri-saksri & Wongwises [40]. As mentioned earlier, by consideringnanofluids in a fully-developed channel, Yang et al. [22] discoveredthat, as compared with the aluminaewater nanofluid, the titaniaewater nanofluid not only had much higher impact on the heattransfer performance but also could change the HTC enhancementby nanofluids from positive to negative. By a different approach,Utomo et al. [25] found that the degree of enhancement by titaniaewater nanofluids was much larger than that of aluminaewaternanofluids at the same mass flow rate for the similar problemconsidered by Yang et al. Trisaksri and Wongwises [40] reportedthat the nanoparticles having higher density should have strongerdeterioration or negative enhancement on HTC. Since the densitytitania (¼4069 kg/m3 at T ¼ 50 �C) is about 20% higher than that of

/s].

Exponent k Exponent m Exponent n R2 coeff Reference

0 0.660 0 0.982 Present0 0.635 0 0.947 Present0.37 0.638 0 0.953 Present0.37 0.631 1.0 0.968 Present0.37 0.630 1.2 0.970 Present0 0.588 0.92 0.968 210.33 0.57 2.8 0.768 20

A.A. Tseng et al. / Applied Thermal Engineering 62 (2014) 20e2726

alumina (¼3376 kg/m3 at T ¼ 50 �C) [20], it is reasonable thattitaniaewater nanofluids have higher influence on the HTC or alarger n value.

By comparing Case 5with Case 7, the difference inm is 1.0 whichis much larger than the m difference between Case 5 and Case 6.This is reasonable because, in addition to the type the nanoparticlesused in Case 7 is different from that of Case 5 (alumina versustitania), the nozzle adopted by Case 7 is also different, solid jetversus full-cone. Consequently, the difference in the m value be-tween Case 5 and Case 7 would be expected to be larger than thatbetween Case 5 and Case 6. One of the reasons of the larger dif-ference could be due to the difference of the geometrical configu-ration of the spray nozzle used. In Case 5 a full-cone nozzle is usedwhile a solid jet nozzle is applied in Case 7. By studying fully-developed tube and channel flows with aluminaewater nano-fluids, Yang et al. [22] indicated that the heat transfer performancedepends highly on the configuration of the conduits and can havebig differences in HTCs if the flow change from tube flows tochannel flows.

5. Concluding remarks

The present study has focused on conducting the experimentaland theoretical study of spraying cooling using aqueous titaniananofluids. It has been found that that the HTC has increased withthe volume flux of spraying but decreased with the increase of thenanoparticle fraction, 4v, and that the HTC decrease has beencaused by the decrease of the impingement duration time ofnanofluid, which has been directly dependent on 4v. A generalcorrelation between the HTC and spraying parameters, includingvolume flux, Prandlt number (Pr), and 4v has then been developedto cover the whole range of the 4v considered.

The present correlation has also been compared with thosepreviously developed based on different types of nanofluids ornozzles. It has been found that all the correlations compared havebeen in a power-law function but the associated exponent valueshave had some differences. The rationales for these differenceshave been presented and discussed. It is also felt that morerigorous analyses and convinced evidences are needed to furtherstudy these differences. Since very limited nanofluid spray coolingstudies have been reported, more efforts related to this field,especially focusing on theoretical investigations, should beencouraged.

To widen the suitability or applicability of the correlationdeveloped, more spray cooling studies to consider wider ranges ofspray conditions, including the spray velocity, coolant temperature,and different types of nozzles and nanofluids, should be consid-ered. Also to enhance the reliability, the effects of the Browniandiffusivity or the thermophoretical diffusivity on the HTC of spraycooling should be theoretically and experimentally assessed.Furthermore, the correlations developed should be extended byconsidering higher surface temperatures, especially to the boilingregion. The interactions among the nanoparticles and between thenanoparticles and base-fluid droplets in the boiling regime couldalter the fundamental characteristics of spray cooling and, as aresult, the associated effects should have non-negligible influenceon the heat transfer performance.

Finally, based on the present study, it could be concluded thatthe heat transfer phenomena of spray cooling using nanofluids aremore complicated than that of pure-fluid spray cooling. There isonly limited theoretical understanding of the heat-transfer mech-anisms involving nanoparticle suspension at the present time,especially at higher particle concentrations in spray cooling.Consequently, research focusing on seeking the understanding ofthese fundamental phenomena should be encouraged.

Acknowledgements

The first author is grateful to National Tsing Hua University(NTHU) for providing the Chair Professorship for his sabbatical inTaiwan for performing the analysis. Special thanks are to ProfessorsWen-Hwa Chen and Pei-Lum Tso of NTHU for their hospitality andencouragement being extended to the first author. The contribu-tions of Parag S. Pathak and John B. Baron of Arizona State Uni-versity and Ms. Rosa Y. Z. Lin of NTHU for their assistance inpreparing the manuscript are gratefully recognized.

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