Al2O3 nanoﬂuid as a heat transfer ﬂuid.pdf

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Thermal properties and rheological behavior of water based Al 2O3nanouid as a heat transfer uid

M. Ghanbarpour , E. Bitaraf Haghigi, R. KhodabandehRoyal Institute of Technology (KTH), Department of Energy Technology, 100 44 Stockholm, Sweden

a r t i c l e i n f o

Article history:Received 24 September 2013Received in revised form28 November 2013Accepted 14 December 2013Available online 22 December 2013

Keywords:NanouidAl2O3 nanoparticleThermal conductivityViscosityHeat transfer

a b s t r a c t

An experimental investigation and theoretical study of thermal conductivity and viscosity of Al 2O3 /waternanouids are presented in this article. Various suspensions containing Al 2O3 nanoparticles were testedin concentration ranging from 3% to 50% in mass and temperature ranging from 293 K to 323 K. Theresults reveal that both the thermal conductivity and viscosity of nanouids increase with temperatureand particle concentration accordingly while the increase in viscosity is much higher than the increase inthermal conductivity. The thermal conductivity and viscosity enhancement are in the range of 1.187%and 18.1300%, respectively. Moreover, the results indicate that the thermal conductivity increases non-linearly with concentration, but, linearly with the increase in temperature. In addition, the experimentalresults are compared with some existing correlations from literature and some modications are sug-gested. Finally, the average heat transfer coefcient at different basis of comparisons including equalReynolds number, uid velocity and pumping power is studied based on the experimental thermal con-ductivity and viscosity in fully developed laminar and turbulent ow regimes. It is found that equal Rey-nolds number as a basis of comparison is highly misleading and equal pumping power can be used tostudy the advantage of using nanouid instead of the base uid.

2013 Elsevier Inc. All rights reserved.

1. Introduction

Conventional heat transfer uids such as oil, water andethyleneglycol which are widely used in many industrial applicationsmainly including in transport, energy storage, air-conditioning,chemical production and electronic cooling, have low thermal con-ductivity. Many researches and activities are being carried out toimprove the thermal properties of these heat transfer uids. Theidea of dispersing solid nanoparticles with higher thermal conduc-tivity to increase heat removal efciencies in cooling systems wassuggested to achieve higher thermal performance. In the last dec-ade, several articles have been published on thermal properties of nanouids. Based on different methods and techniques of prepara-tion, characterization and stabilization, the reported results areinconsistent. Although, some of the experimental results show asignicant relationship between nanouids thermal conductivityand preparation techniques, surfactants, mechanical stirring andpH, it is clear that base uid, particle size and volume fraction of nanoparticles have substantial effect on thermal conductivity of nanouids. Metal oxide nanoparticles are interesting and popularchoices to be used in nanouid suspensions because of their high

values of thermal conductivity and easier production method thanmetallic nanoparticles because of lower sensitivity of lighter oxideparticle than dense particles such as metals to the effects of agglomeration. In this paper a water-based nanouid containingaluminum oxide in various concentrations and temperatures hasbeen studied. Numerous studies on thermophysical properties of Al2O3 nanouids can be found in the literature and some selectedresults are shown in Table 1 .

As can be seen, the thermal conductivity of nanouid increasesin all cases but at different rates. Based on concentration and tem-perature effects on Brownian motion of the particles and theiragglomerations, different trends in the thermal conductivity andviscosity increment are expected. According to the selected tem-perature and concentration ranges, some analytical correlationsare evaluated to nd their accuracy to predict thermal conductivityand viscosity of nanouids. Beside thermal conductivity, it is veryimportant to consider rheological properties of the nanouids suchas viscosity in engineering applications, which strongly inuencespressure drop and consequently the pumping power of the nano-uids. Despite the important role of viscosity, only a few studieshave been reported in which the enhancement of thermal conduc-tivity and increment of viscosity is discussed. Most of experimentalstudies on rheological properties of nanouids revealed that theviscosity of nanouid is higher than of the base uid and increases

0894-1777/$ - see front matter 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.expthermusci.2013.12.013

Corresponding author. Tel.: +46 8 7907413.E-mail address: [email protected] (M. Ghanbarpour).

Experimental Thermal and Fluid Science 53 (2014) 227235

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with concentration [9,10] . In this study, thermal conductivity andviscosity of waterAl 2 O3 nanouid in mass concentration of 350% and in temperature ranging of 293323K were studied. Inaddition, experimental results of thermal conductivity and viscos-ity were compared with a number of correlations from theliterature.

2. Experimental procedures and apparatus

2.1. Material

The Al 2 O3water nanouid with Silane as the surface modi-er, manufactured by the two-step method, is produced by ItNNanovation AG (Germany) and the nanouid was adjusted topH 9.1. The tested samples at different concentrations were di-luted from the original samples with the concentration of 50 wt.% by adding distilled water. Transmission electron micros-copy (TEM) analysis of the nanoparticles size and morphologywere performed and presented in Fig. 1 . Also, for determinationof hydrodynamic size of Al 2O3 particles, DLS analysis was per-formed, and the result is shown in Fig. 2 . Al2 O3 average particlesize is about 75 nm and the shapes of primary particles can beassumed as spherical. Also, the curve broadening shows thatthe hydrodynamic particle size distribution is between 100 nmand 400 nm but most of the particles are in the range of 200 nm, an average DLS particle size is reported as 235 nm. Inorder to obtain homogeneous mixtures the nanouids sampleswere put into a sonication bath for 15 min before measurements,for avoiding or at least limiting the accumulation and settling of the nanoparticles.

2.2. Thermal conductivity and viscosity measurement

The Transient Plane Source (TPS) method is used for measuringthe thermal conductivity of nanouids. The sensorelement is madeof a 10 l m thickness nickel foil which is electrically conductingand in the shape of a double spiral. The TPS probe sensor acts bothas a heat source for increasing the temperature of the sample andas a resistance thermometer for recording the time dependenttemperature increase of the sensor. The thermal characteristicsare calculated from the recording of the average temperaturechange which is caused by the change in TPS sensor resistance ver-sus time response in the sensor and evaluated by the manufac-turers software Hot Disk Thermal Constants Analyzer. Thedynamic viscosity is measured with a rotating coaxial cylinderviscometer. The instrument can be used for viscosities rangingfrom 0.001 N S/m 2 to 0.6 N S/m 2 and for both Newtonian andnon-Newtonian liquids. In this work the thermal conductivitiesand the viscosities at 293 K, 303 K, 313 K, and 323 K are investi-gated. The instruments were tested several times with water andthe deviations from reference values were found to be within2% and 4% for the thermal conductivity and viscosity, respec-tively. Details of experiment instruments are listed in Table 2 .

3. Results and discussion

3.1. Thermal conductivity of waterAl 2O 3 nanouid

Thermal conductivity of Al 2 O3 nanouids was measured inmass fraction and temperatures ranges of 350% and 293323 K,

Nomenclature

A constantc p specic heat (J/kg K)d diameter (nm)D tube diameterh convective heat transfer coefcient (W/m 2 K)k thermal conductivity (W/m K)L tube lengthNu Nusselt numberP pressure (Pa)Pr Prandtl numberRe Reynolds numberT temperature (K)U max maximum particle packing fractionU agg effective volume fraction of aggregatesV velocityw mass concentration of nanouids, wt.%

Greek symbolsl dynamic viscosity (Pa s)/ volume fraction (%)q density (kg/m 3)

Subscriptsave averageb base uid f uidnf nanouid p particle

Superscript + dimensionless quantity

dimensionless length

Table 1

Literature review on thermal conductivity enhancement of Al 2O3 /water nanouid.

Author Base uid Particle size Concentration Enhancement (%)

Wang et al. [1] Water 28 nm 5 vol.% 14Das et al. [2] Water 38 nm 4 vol.% 8Chon et al. [3] Water 13 nm 1 vol.% 15Chon et al. [3] Water 50 nm 4 vol.% 30Timofeeva et al. [4] Water 40 nm 5 vol.% 10Chandrasekar et al. [5] Water 43 nm 3 vol.% 9.7Teng et al. [6] Water 20 nm 2 wt.% 14.7Beck et al. [7] Water 12 nm 4 vol.% 23Tavman et al. [8] Water 30 nm 2 vol.% 33

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respectively. The volume fraction can be estimated by the follow-ing correlation:

1 w

w

q p

q f

1 /

/ 1

To check the validity and repeatability the instruments thermalconductivity of distilled water was measured and compared withthe reference values from International Association for the Proper-ties of Water and Steam (IAPWS) [11] . As shown in Fig. 3 , it wasfound that the standard deviation and the accuracy of measure-ment for these measurements are better than 1.5% and 2%respectively.

Figs. 4 and 5 depict the temperature dependence of the thermalconductivity of the nanouids containing various mass fractions of Al2O3 nanoparticles and its enhancement, respectively. It is ob-served that the thermal conductivity increases with increase inmass fraction and temperature. Furthermore, a notable ndingfrom Fig. 4 is the linear slope of thermal conductivity changes withtemperature at different concentrations. Also, it is apparent fromFig. 5 that the thermal conductivity enhancement of Al 2O3waternanouid at higher concentrations shows temperature-depen-dency and has decreasing slope with temperature which may becaused by more agglomeration or aggregation of the nanoparticlesat higher concentrations because of increasing the particles num-

bers and motions and consequently increasing the particles colli-sions at higher concentrations and temperatures which increasesthe possibility of agglomeration or aggregation of thenanoparticles.

The results exhibit that the thermal conductivity of the nano-uid is strongly dependent on the concentration of nanoparticlesas well as temperature. The maximum increment obtained for50 wt.% at 293 K is 87% while the highest value of thermal conduc-tivity is 1.18 W/m K at 323 K and for nanouid at 50 wt.%. More-over, it is observed that the thermal conductivity increment isnot linear with increase in mass concentration at each tempera-ture. For example, at 323 K, the thermal conductivity of nanouidincreases about 20% by increasing the mass concentration from30 wt.% to 40 wt.% while the increment in thermal conductivityis 26% for the case that the mass concentration increases from40 wt.% to 50 wt.%.

Furthermore, to nd and analyze the difference between thepresent experimental results and previous studies, a comparisonbetween the experimental thermal conductivity ratio of Al 2O3 water nanouid and results from Das et al. [2] and Yiamsawasdet al. [12] studies at various temperatures and concentrations areshown in Fig. 6 .

Fig. 1. TEM images of alumina nanoparticles.

Fig. 2. Particle size distribution measured by DLS.

Table 2

Experimental equipments details.

Test equipment Manufacturer Model Details

Viscosity Brookeld DV-II + Pro LV-1 Spindle, accuracy: 1% of full scale range, reproducibility 0.2%Thermal conductivity Hot disk TPS 2500 5 double-spiral sensor, accuracy: 2% for thermal conductivity, reproducibility: 1%

Fig. 3. Thermal conductivity of distilled water.

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As can be seen, the experimental thermal conductivity ratio in-creases with concentration for all three studies but with different

slopes. It is observed that at Das et al. [2] study the thermal con-ductivity ratio increased with temperature increase while at pres-ent and Yiamsawasd et al. [12] studies these ratios decreased withtemperature. Furthermore, it is found that the differences betweenpresent experimental results and those of Yiamsawasd et al. [12] atthe same concentration and temperature are less than 3% while forDas et al. [2] the higher deviations is obtained which may becaused by different particle size. In Das et al. [2] study the particleradius was 19.7 nm which is about three times smaller than that of in Yiamsawasd et al. [12] and present studies.

3.2. Viscosity of waterAl 2O 3 nanouid

As well as thermal conductivity, the viscosity of nanouid is animportant transport property which affects the thermal

performance of heat transfer devices. Figs. 7 and 8 show the valuesof the viscosity and viscosity enhancement of the nanouids at dif-

ferent temperatures and concentrations, respectively. Results indi-cate that the viscosity strongly depends on the mass fraction of Al2O3 and the temperature, increasing considerably with particlemass concentration but decreasing with a temperature increase.Moreover, results reveal that the viscosity enhancement is almostconstant along different temperatures at a xed concentrationmeaning it is not temperature dependent. Also, it is obvious thatthe increment in viscosity of nanouid is much higher than thatof the thermal conductivity. For example, for nanouid at 30 wt.%the increment in viscosity is between 80% and 95% while the incre-ment is between 35% and 40% for the thermal conductivity. Besidethe effect of adding nanoparticles to the base uid on viscosity of the nanouid, it is very important to verify nanouids Newtonianor non-Newtonian behavior by evaluating the shear stress versus

shear rate as a function of particle loading and temperature. Theshear stress versus shear rate for different mass concentrations

Fig. 4. Thermal conductivity of Al 2O3water nanouids at different concentrations.

Fig. 5. Thermal conductivity enhancement of Al 2O3water nanouids at differentconcentrations.

Fig. 6. Thermal conductivity ratio for Al 2O3 nanouids at different studies.

Fig. 7. Viscosity of Al 2O3water nanouids at different concentrations.



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and temperatures for Al 2O3 nanouidare are shown in Fig. 9 . Thelinear relationship between shear stress and shear rate indicatesthat nanouid exhibits Newtonian behavior and the increment inthe slope of the lines indicates that the viscosity of the nanouidincreases with increase in mass concentration but decrease withthe temperature.

3.3. Prediction of experimental results with correlations

3.3.1. Thermal conductivityDuring last decades, several correlations have been proposed to

predict thermal conductivity of nanouids. The rst correlationwas introduced by Maxwell [13] considering thermal conductivi-ties of base uid and nanoparticle and also volume fractions of nanoparticles were included, while the particles were consideredspherical. Fig. 10 shows the comparison of experimental resultsat different temperatures and concentrations with Maxwell corre-lation. It is observed that Maxwell equation is in good agreementwith the experimental results at lower mass fraction and underes-timates the experimental results at higher concentrations. It can beseen that at lower volume concentration than 20% the deviation is

less than 5% while it is between 5% and 10% for higher concentra-tions with higher thermal conductivity.

Later, a modication which was done on Maxwell correlation byconsidering more parameters affecting the thermal conductivity of nanouids is studied. Although, there is no reliable correlation topredict the thermal conductivity of all kinds of nanouids with dif-ferent particle shapes and concentrations verywell, semi-empiricalcorrelations are usually derived based on limited experimental re-sults. The constants which are used in these correlations can bechecked and modied by evaluating these semi-empirical correla-tions with new experimental results at different working condi-tions. A well-known correlation for thermal conductivity of nanouid was proposed by Prasher et al. [14] . They modied Max-well equation considering the effect of Brownian motion and intro-ducing heat transfer coefcient basedon the convection of the baseuid around the solid particles. The correlation is dened as below:

knf 1 A Re m Pr0 :333 U

k p1 2 a km 2 Uk p1 a kmk p1 2 a 2 km Uk p1 a km k f

2

where a = 2 R f km /d p, km = k f [1 + (1/4)RePr] and the constants A and

m can be estimated from experimental results. In order to nd Aand m, in Prasher correlation, experimental results were used inconcentrations ranging between 3% and 50% in mass and tempera-ture ranging between 293 K and 333 K. The parameters A and mwere calculated as 30,000 and 2.5, respectively, by least squaresregression analysis. Comparison of Prasher correlation predictionswith experimental results are shown in Fig. 11 . Results reveal thatPrasher correlation with proposed values for constants A and m pre-dicts the thermal conductivity of Al 2O3 /water nanouids well.

Finally, based on limited available experimental results a newand simple correlation is suggested. This correlation is proposedbased on non-linear tting of data. According to the experimentalresults, the thermal conductivity increased non-linearly with con-centration increase at each temperature. So, a non-linear correla-

tion for prediction of the effective thermal conductivity isproposed as below.

knf k f

1 A1 U A2 U2 3

The values of constants A1 and A2 are calculated based on theexperimental results. The empirical correlation for thermal con-ductivity of nanouid can be derived by non-linear regression.Constants A1 and A2 were calculated as 3.5 and 2.5, respectively.So, the empirical correlation is obtained as follow:

Fig. 8 . Viscosity enhancement of Al 2O3water nanouids at differentconcentrations.

Fig. 9. Shear stress versus shear rate for different mass concentrations at T = 303 K (Left) and different temperatures for 20 wt.% (Right).

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knf k f

1 3 :5 U 2 :5 U2 4

Comparison of the predicted values (correlation 3) and theexperimental results are shown in Fig. 12 .

According to Fig. 12 , the experimental results deviations fromthe proposed non-linear pattern are less than 5% which showsthe capability of the proposed empirical correlation to predictthe thermal conductivity of Al 2O3water nanouid under the con-dition of this study.

3.3.2. ViscosityAs mentioned before, viscosity of nanouid is another property

which is needed to be studied because of its signicant effect onheat transfer and pressure drop. Einstein [15] correlation is themost well-known correlation for viscosity of nanouid which pre-dicts the effective viscosity of a nanouid according to the follow-ing equation:

l nf l f

1 2 :5 U 5

where U is the volume fraction of nanoparticles. In this studyBatchelor [16] , Krieger and Dougherty [17] and Corcione [18] corre-lations have been used to predict the viscosity of the nanouids.These correlations are listed in Table 3 .

Fig. 13 presents the comparison of dynamic viscosity of nano-uids with above correlations at T = 293 K and 313 K. The resultsdemonstrate that the viscosity of nanouid strongly depends onsolid particles concentration. It was found that the Einstein corre-

Fig. 10. Comparison of experimental thermal conductivity with Maxwellcorrelation.

Fig. 11. Comparison of the experimental results with Prasher et al. model with A = 30,000 and m = 2.5, (a) T = 293 K, (b) 313 K.

Fig. 12. Comparison of experimental result with proposed non-linear correlationfor effective thermal conductivity ( knf /k f ).

Table 3

Models for viscosity of nanouids.

Batchelor [16] l nf l f

1 2 :5U 6 :5U 2

Krieger and Dougherty [17] l nf l f

1 U agg U max l U max

Corcione [18] l nf l f

1 34 :87 d pd f 0 :3

U 1 :03 1



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lation underestimates the viscosity of nanouids, specially athigher concentrations.

Due to the fact that Batchelor correlation is an extended form of the Einsteins correlation, it underpredicts the experimental resultsas well but with lower error compared with Einstein correlation.The differences between theoretical and experimental results in-crease by increasing the mass concentration. Unlike Einstein andBatchelor correlations, Corcione and Krieger and Dougherty corre-lations predict the viscosity of Al 2O3 nanouid with higher accu-racy and lower deviation. At both temperatures of 293 K and313 K Krieger and Dougherty and Corcione correlations underesti-mate the experimental results for concentrations below 30 wt.%but overestimate the data for mass concentrations higher than30 wt.%. The average deviation for concentrations below 30 wt.%at 293 K, is 8.5% for Corcione and 7.4% for Krieger and Doughertycorrelations, respectively. At 313 K, Krieger and Dougherty correla-tion predicts the experimental results with an average difference of 9.2%, while with increasing the concentration the difference de-creases to 1.5%. The Corcione correlation shows good prediction(1% error) at 30 wt.% but the deviation increases for higher concen-trations than 30 wt.%. So, among above correlations, Krieger andDougherty correlation predicts viscosity of these nanouids within10% error in all concentrations.

3.4. Heat transfer coefcient enhancement prediction

The heat transfer coefcient enhancement of nanouids com-pared with the base uid for the hydrodynamically fully developedow can be predicted based on the thermo-physical properties of nanouids utilizing Shah [19] and DittusBoelter [20] correlationsin laminar and turbulent ow regimes, respectively. Shah correla-tion for laminar owis dened as:

Nu ave 1 :953 L

13 L 0 :03

4 :364 0 :0722 L 1 L > 0 :03( 6 where

L xn x1 =Di

Re Pr :

and DittusBoelter correlation for turbulent ow is dened as:

Nu ave 0 :023 Re 4 =5 Pr 2 =5 7

where Reynolds and Prandtl numbers are dened as:

Re qVdl

and

Pr l C pK

Based on the Shah and London correlation for laminar ow, theaverage heat transfer coefcient in the thermally developing re-gion can be related to the average velocity, V , density, q , thermalconductivity, k, viscosity, l , and specic heat, C p, as follow:

Laminar ow: have V 1=3 q 1 =3 c 1 =3 p k

2 =3

In thermally fully developed region the enhancement of heattransfer coefcient of nanouids only depends on thermal conduc-

tivity enhancement while the Nusselt number is constant in thisregion. Hence, it is expected that in simultaneously thermallyand hydrodynamically fully developed laminar ow the relativeheat transfer coefcient increases with thermal conductivity in-crease. So, in this study we consider the thermally developing,hydrodynamically developed laminar ow. For turbulent ow,based on DittusBoelter correlation, the average heat transfer coef-cient relation with the uid properties is as follow:

Turbulent ow: have V 4=5 q 4=5 c 2=5 p k3=5 l 2=5

Therefore, the relative heat transfer coefcient in a circular tubewith constant wall heat ux at different bases of comparisons canbe expressed as shown in Table 4 . The experimental thermal con-ductivity and viscosity of the nanouids are used to calculate therelative heat transfer coefcient while the specic heat and density

of nanouids are estimated by the following equations [21,22] :qnf C p;nf / q pC p; p 1 / q bf C p;bf 8

qnf / q p 1 / q bf 9

To investigate the advantageof using nanouids compared withtheir base uids in cooling applications, different bases of compar-ison are used in the literature. Although it is common to evaluate

Fig. 13. Comparison of the experimental viscosity with theoretical correlations at T = 293 K (Left) and 313K (Right).

Table 4

The relative heat transfer coefcient at different basis of comparisons.

Laminar ow Turbulent ow

V bf = V nf hrelative q1=3r c

1=3 p;r k

2 =3r hrelative q

4=5r c

2=5 p;r k

3=5r l

2=5r

P bf = P nf hrelative l1=6

r q1=3r c

1=3 p;r k

2=3r hrelative q

32 =55r c

2 =5 p;r k

3=5r l

26 =55r

Rebf = Renf hrelative l 1 =3r c 1=3 p;r k2=3r hrelative c 2=5 p;r k3=5r l 2=5r

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the heat transfer of the nanouid at equal Reynolds number, otherbases of comparison such as equal ow velocity and pumpingpower can be used as well. Figs. 14 and 15 show the relative heattransfer coefcient of the nanouid to that of the base uid in lam-inar and turbulent ow regimes, respectively. As shown in Fig. 14 ,in laminar ow regime, the relative heat transfer coefcient in-

creases with concentration increase in all bases of comparison. Itmeans that the heat transfer coefcient of the Al 2O3 nanouid ishigher than that of the base uid and the maximum values of rel-ative heat transfer coefcient at each concentration is obtained atequal Reynolds number. The relative heat transfer coefcient in-creased up to 90% at equal Reynolds number at highest concentra-tion (50 wt.%) while it increased up to 50% and 20% at equal owvelocity and pumping power, respectively at the sameconcentration.

The reason of higher increment at equal Reynolds number com-pared with equal ow velocity and pumping power is the higherow velocity of the nanouid which should be used in calculationto compensate the viscosity increment to make equality at this ba-sis of comparison. In fact, higher ow velocity of the nanouid atequal Reynolds number results in higher heat transfer coefcient.Hence, this basis of comparison (same Reynolds number) may be

highly misleading. Fig. 15 shows the relative heat transfer coef-cient in turbulent ow regime at two different inlet temperaturesof 293 K and 313 K.

As can be seen, the same as laminar ow regime the highest rel-ative heat transfer coefcient occurs at equal Reynolds number.But, at equal ow velocity the relative heat transfer coefcient is

almost constant while it is below one at equal pumping powerwhich means that the heat transfer coefcient of the nanouid isless than that of the base uid at equal pumping power. Sincethe relative heat transfer coefcient at equal pumping power isproportional to 1/6 and 26/55 power of the viscosity in laminarand turbulent ow regimes respectively and while it is propor-tional to 2/3 and 3/5 power of the thermal conductivity, it is foundthat the viscosity increment effect is much more dominant in tur-bulent ow regime compared with laminar ow regime. So,according to higher viscosity increment compared with thermalconductivity increment, a reduction in the relative heat transfercoefcient at equal pumping power is observed. Furthermore, itis found that the relative heat transfer coefcient at 313 K is quitesimilar to that of at 293 K in both laminar and turbulent ow re-gimes, suggesting that the working temperature does not affectheat transfer in nanouids signicantly.

Fig. 14. The relative heat transfer coefcient in Laminar ow regime at 293 K (Left) and 313 K (Right).

Fig. 15. The relative heat transfer coefcient in turbulent ow regime at 293 K (Left) and 313 K (Right).



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Al2O3 nanoﬂuid as a heat transfer ﬂuid.pdf