Available online at www.sciencedirect.com

Fluid Phase Equilibria 260 (2007) 275278

The thermal conductivity of alumeAm

ia Instatesuly 20007

Abstract

The therm ticlesfrom 298 to remeinvestigated ersusof nanoparti . Ouinherent in B re deresults also therHamilton an hapeliquid layer 2007 Elsevier B.V. All rights reserved.

Keywords: Thermal conductivity; Nanofluids; Alumina nanoparticles; Ethylene glycol

1. Introdu

The therparticles h[1], and thtivity of thehave been pand others.(or nanofluexhibit a gdicted byco-workersbehavior, wconductivitCu nanopaconductivitcarbon nanment increa

CorresponE-mail ad

0378-3812/$doi:10.1016/jction

mal conductivity of fluids containing dispersed solidas been studied for more than one hundred yearseories to describe the increase in thermal conduc-se dispersions with volume fraction of the particlesroposed by Maxwell [1], Hamilton and Crosser [2],More recently, dispersions containing nanoparticlesids) have attracted attention because they apparentlyreater thermal conductivity increase than that pre-the Maxwell model [3]. Choi, Eastman, and their

were some of the first to study such anomaloushen they reported a 40% enhancement in the thermaly of ethylene glycol with the addition of 0.3% (v/v)rticles [4], and a 150% enhancement in the thermaly of a synthetic oil with the addition of 1% (v/v)otubes [5]. Others have shown that this enhance-ses linearly with the volume fraction of nanoparticles

ding author. Tel.: +1 404 894 3098; fax. +1 404 894 2866.dress: amyn.teja@chbe.gatech.edu (A.S. Teja).

in the case of CuO in ethylene glycol [6], SiC in water andethylene glycol [7], and Al2O3 in several liquids [8]. How-ever, as noted in these and other studies [4,5], the Maxwell[1] and Hamilton and Crosser [2] models were not able to pre-dict these greatly enhanced thermal conductivities because themodels do not include any dependence on particle size. Theenhancement has been variously attributed to an ordered liq-uid layer at the particle surface [9], and to Brownian motionthat creates microconvection between the particles and liquidmolecules [10,11]. However, literature data have failed to con-clusively validate either mechanism for thermal conductivityenhancement.

The relationship between the thermal conductivity ofnanofluids and temperature has also proved to be somewhatdifficult to generalize. Das et al. [12] have reported a linearrelationship between the thermal conductivity of aqueous andethylene glycol-based nanofluids and temperature, and morerecently, Zhang et al. [13] have reported that the slope of the ther-mal conductivity versus temperature relationship for nanofluidsis linear and approximately the same as that of the base fluid.However, these and other studies have considered data over lim-ited temperature ranges so that it has proved difficult to draw

see front matter 2007 Elsevier B.V. All rights reserved..fluid.2007.07.034dispersed in ethylenMichael P. Beck, Tongfan Sun,

School of Chemical & Biomolecular Engineering, GeorgGA 30332-0100, United S

Received 29 March 2007; received in revised form 5 JAvailable online 17 July 2

al conductivities of several nanofluids (dispersions of alumina nanopar411 K using a liquid metal transient hot wire apparatus. Our measuto date for any nanofluid. A maximum in the thermal conductivity vcles, closely following the behavior of the base fluid (ethylene glycol)rownian motion models are not necessary to describe the temperatu

show that the effect of mass or volume fraction of nanoparticles on thed Crosser or Yu and Choi models with one adjustable parameter (the sthickness in the Yu and Choi model).ina nanoparticlesglycolyn S. Teja

titute of Technology, Atlanta,

07; accepted 10 July 2007

in ethylene glycol) were measured at temperatures rangingnts span the widest range of temperatures that have beentemperature behavior was observed at all mass fractions

r results confirm that additional temperature contributionspendence of the thermal conductivity of nanofluids. Our

mal conductivity of nanofluids can be correlated using thefactor in the Hamilton and Crosser model, or the ordered

276 M.P. Beck et al. / Fluid Phase Equilibria 260 (2007) 275278

general conclusions regarding the temperature dependence ofthe thermal conductivity.

The prethermal cona wider temstudies. Welene glycoversus tempethylene glTherefore,to be an ethe thermacontainingcles were iof 20 nm sthermal co

2. Models

Maxwelmal conduc

k = kp + 2kp +

where k is tmal conducthe pure fluton and Crofactor n to

k = kp + (kp

with n = 3Maxwell ndependencature depenthe same aextension oof particlethe solidlito exhibit aless than thparticles is

k = kpe +kpe +

where is tticle radiusparticles de

kpe =[2(1(

where islayer to thadependenc

of the base fluid, although size dependence is added via theparameter .

ar e

to Bts foode

= c

c isules oavera

on as

8kb q. (

he vition. Alsarticmor

nduted tused

(1

C1 ir conr de1k

3

q. (8f a lctivitenc

erim

eralf nanties o. Thl minsionsbecaarticlMatd byquidrmaureave aof asent work investigates the relationship between theductivity of several nanofluids and temperature overperature range than has been explored in previoushave chosen to investigate nanofluids based on ethy-

l because it is known that the thermal conductivityerature relationship for polar fluids such as water andycol is nonlinear and exhibits a maximum [14,15].one outcome of the present investigation is expectedlucidation of the role played by the base fluid onl conductivity of nanofluids. In addition, nanofluidsthree different mass fractions of alumina nanoparti-nvestigated in order to ascertain whether dispersionsize nanoparticles exhibit the anomalous behavior innductivity that has been reported in the literature.

for thermal conductivity enhancement

l [1] derived the following relationship for the ther-tivity of dilute dispersions of spherical particles:

k1 + 2(kp k1)2k1 (kp k1) k1 (1)

he thermal conductivity of the dispersion, kp the ther-tivity of the particles, k1 the thermal conductivity ofid, and is the volume fraction of particles. Hamil-sser [2] extended this model to include an empirical

account for the shape of the (nonspherical) particles:n 1)k1 + (n 1)(kp k1)+ (n 1)k1 (kp k1) k1 (2)

for spheres, and n = 6 for cylinders. Neither theor the Hamilton and Crosser models contain anye on particle size, and they imply that the temper-dence of the thermal conductivity is approximately

s that of the base fluid. Yu and Choi [9] proposed anf the Maxwell equation that incorporates the effect

size via a contribution from an ordered liquid layer atquid interface. This ordered liquid layer is assumedgreater thermal conductivity than the bulk liquid, butat of the solid. An effective thermal conductivity ofused in the Maxwell equation which becomes:

2k1 + 2(kpe k1)(1 + )32k1 (kpe k1)(1 + )3

k1 (3)

he ratio of the ordered layer thickness to the nanopar-, and kpe is the effective thermal conductivity of thefined as:

) + (1 + )3(1 + 2)] 1 ) + (1 + )3(1 + 2) kp (4)

the ratio of the thermal conductivity of the orderedt of the solid particle. Once again, the temperature

e of the model is approximately the same as that

Kummentaccoun

Their m

k k1k1

wheremolecup theequati

up =

In Eand tan addvia upwith p

In amal coattribution ca

k = k1

whereanothenumbe

Rep =

In Epath ocondudepend

3. Exp

Sevtions oquantiditionssevera

dispermentsnanopphousreporte

A lithe theprocedwho htivityt al. [10] attributed the thermal conductivity enhance-rownian motion and obtained a relationship thatr the effects of both particle size and temperature.l can be represented by the following equation:

up r1k1rp(1 ) (5)

an adjustable parameter, r1 is the radius of thef the base fluid, rp the radius of the nanoparticles, andge particle velocity derived from the StokesEinsteinfollows:

T

r2p(6)

6), kb is Boltzmanns constant, T is the temperature,iscosity of the fluid. The Kumar et al. model imposesal temperature dependence to that of the base fluido, the thermal conductivity enhancement increasesle size as 1/r3pe recent paper, Jang and Choi [11] described the ther-ctivity of nanofluids in terms of three contributionso the pure fluid, to the particles, and to microconvec-by motion of the particles as follows:

) + C1kp + 3 C2 r1rp

k1Rep2Pr, (7)

s a constant related to the Kapitza resistance, C2 isstant, Pr is the Prandtl number, and Rep the Reynolds

fined as:

bT2l1

(8)

), 1 is the density of the liquid, and l1 the mean freeiquid molecule. Once again, an additional thermaly contribution arises from the last term, as well as ae on particle size as 1/rp

ental

nanofluids (fluids containing specified mass frac-oparticles) were prepared by dispersing pre-weighedf alumina particles in ethylene glycol at ambient con-e mixtures were subjected to ultrasonic mixing forutes to obtain uniform dispersions, and the resultingremained uniform for the duration of the experi-

use of surface charges on the particles. The aluminaes were purchased from Nanostructured & Amor-erials, Inc., with a primary particle size of 20 nmthe vendor.metal transient hot wire device was used to measure

l conductivity of each nanofluid. The apparatus andhave been described by Bleazard and Teja [1620]lso reported measurements of the thermal conduc-variety of electrically conducting fluids using this

M.P. Beck et al. / Fluid Phase Equilibria 260 (2007) 275278 277

apparatus at temperatures as high as 465 K. Briefly, a mercury-filled glass capillary is suspended in the fluid or dispersion, withthe glass cfrom the ecury wire fis heated wtemperaturthe resistanthe voltageThe temperthe thermainfinite line

T = q4k

where Ttion per untime fromfluid, rw thestant. A linwire and this the primCorrectionacteristicsfinite extenan effectivewith a refernonuniformcalibrationthe therma[21]. Additable elsewhobtained fraccuracy otemperaturof the onse

The meTechne con2D).

4. Results

Our theTable 1. Eaments at adeviationsthe mass frtemperaturtemperaturwith tempethe thermalliterature [1thermal cobase fluida maximumtemperaturThese resu

Table 1Thermal conductivity data for nanofluids studied in this work

ction3 (%)

T (K) Volume fractionof Al2O3 (%)

Mean k (W m1 K1) Standarddeviation

302.0 1.00 0.258 0.004323.4 0.98 0.259 0.004347.3 0.97 0.262 0.001372.2 0.95 0.267 0.003392.4 0.94 0.264 0.002411.1 0.92 0.260 0.002296.3 3.00 0.276 0.003323.6 2.95 0.282 0.002349.0 2.90 0.284 0.005373.3 2.85 0.285 0.005392.1 2.81 0.287 0.003409.6 2.78 0.280 0.007304.0 3.99 0.290 0.005323.7 3.94 0.291 0.005348.5 3.87 0.294 0.003373.3 3.81 0.293 0.006391.0 3.76 0.288 0.007409.0 3.71 0.285 0.007

re bebase

mo

te thres

theonice thor ohis

] basotiotivitre atheratur

hermal conductivity of pure ethylene glycol and 3 nanofluids consistingne glycol and a specified mass fraction of 20 nm alumina nanoparticles.lines represent the HamiltonCrosser equation (with n = 3.4).apillary serving to insulate the mercury hot-wirelectrically conducting fluid or dispersion. The mer-orms one resistor in a Wheatstone bridge circuit andhen a constant voltage is applied to the bridge. Thee rise of the wire is calculated from the change ince of the mercury with time, obtained by measuringoffset of the initially balanced Wheatstone bridge.ature rise versus time data are then used to calculatel conductivity by solving Fouriers equation for anheat source in an infinite medium:

ln(

4tr2wC

)(9)

is the temperature rise of the wire, q the heat dissipa-it length, k the thermal conductivity of the fluid, t thethe start of heating, the thermal diffusivity of theradius of the wire, andC the exponent of Eulers con-ear relationship between the temperature rise of thee natural log of time is used to confirm that conductionary mode of heat transfer during the measurement.s to the temperature rise are made for the finite char-of the wire, the insulating layer around the wire, thet of the fluid, and heat loss due to radiation. Finally,wire length is obtained by calibrating the instrumentence fluid in order to account for end effects and thethickness of the capillary. In the present work, the

was performed using IUPAC suggested values forl conductivity of water [14] and dimethyl phthalateional details of the apparatus and technique are avail-ere [20]. Each value of the thermal conductivity was

om an average of 5 measurements with an estimatedf 2% and a reproducibility of 1%. The higheste measured in the present work was 411 K becauset of convection in the apparatus.asurements were performed by placing the cell in astant temperature fluidized sand bath (model SBL-

and discussion

rmal conductivity measurements are presented inch data point represents an average of five measure-specified mass fraction and temperature. Standard

for each data point are also given. Note that althoughaction remained constant for a sample over a range ofes, the volume fraction of the sample decreased withe because of the change in density of the base fluidrature. The data are plotted in Fig. 1, together withconductivity data for pure ethylene glycol from the5]. The results clearly demonstrate curvature in the

nductivity versus temperature behavior for both theand each nanofluid, with each nanofluid displaying

in thermal conductivity at approximately the samee as the maximum observed in the pure base fluid.lts suggest that the thermal conductivity versus tem-

Mass fraof Al2O

3.263.263.263.263.263.269.349.349.349.349.349.34

12.212.212.212.212.212.2

peratuof the

Theattribumotiondue tomonotthat thbehavidata. Tal. [22nian mconductherefoof thetemperfluid.

Fig. 1. Tof ethyleDashedhavior of the nanofluid closely follows the behaviorfluid.dels of Kumar et al. [10] and Jang and Choi [11]e thermal conductivity enhancement to Brownianulting in greater temperature dependence than thatbase fluid. Furthermore, the enhancement increasesally with temperature. Our results clearly demonstrateermal conductivity closely follows the temperaturef the base fluid within the standard deviation of theconclusion is supported by the analysis of Evans eted on kinetic theory which also suggests that Brow-n may play a minor role in determining the thermaly enhancement of nanofluids. Maxwell type modelsre likely to be superior in describing the dependencemal conductivity on temperature, since most of thee dependence in these models arises from the base

278 M.P. Beck et al. / Fluid Phase Equilibria 260 (2007) 275278

Fig. 2. Thermand 20 nm alwork. The solthe dashed linwith n = 3.4.

Fig. 2 dvolume frabehavior isand Crossewas obtainperatures,leading toof n lies bedata may amal conduthe same asset equal tofor all datathickness o

5. Conclu

A liquidsure the thenanofluidsdata span tfor any nanids exhibit

the same temperature as the base fluid. This dependence cannotbe reproduced by models that attribute the thermal conductivityenhancement in nanofluids to Brownian motion, and is best rep-resented by Maxwell type models. Our results also indicate thatMaxwell type models such as that of Hamilton and Crosser orYu and Choi with one adjustable parameter are able to success-fully correlate the data, suggesting that the ethylene glycol basednanofluids studied in this work do not exhibit anomalous ther-mal conductivity behavior. The value of the shape factor (n = 3.4)obtained by fitting our data with the Hamilton and Crosser modelsuggests that some clustering of nanoparticles occurs during ourexperiments and the resulting clusters are not spherical.

References

. Maxiversi. HamWang480. Eas(2001.S. C

tt. 79S. Liu06) 7Xie, J.Xie,845Yu, S. Ku

s, Phy. Jang. Das574

Zhan. Me

ies ofw YorDigui. Sunal conductivity at 373 K of nanofluids consisting of ethylene glycolumina nanoparticles. Circles represent experimental data of thisid line represents calculations using the Maxwell equation wherease represents calculations using the Hamilton and Crosser equation

emonstrates our results showing the dependence ofction of particles on the thermal conductivity. Thelinear and can be reproduced using the Hamilton

r model with n = 3.4. This value of the shape factored from a best fit of experimental data at all tem-and suggests that agglomeration of particles occursa mean shape that is nonspherical, since the valuetween that of spherical and cylindrical particles. Thelso be fitted with the Yu and Choi model, if the ther-ctivity of the ordered liquid layer is assumed to be

that of the particles and the thickness of the layer is0.4 nm by linear least squares to provide the best fit

. However, the calculations are very sensitive to thef the ordered liquid layer and its thermal conductivity.

sions

[1] J.CUn

[2] R.L[3] X.

474[4] J.A

78[5] S.U

Le[6] M.

(20[7] H.

195[8] H.

456[9] W.

[10] D.HDa

[11] S.P[12] S.K

567[13] X.[14] C.A

ertNe

[15] R.[16] T.Fmetal transient hot wire apparatus was used to mea-rmal conductivity of ethylene glycol based aluminaat temperatures ranging from 298 to 411 K. Thesehe widest range of temperatures hitherto measuredofluid and show that ethylene glycol based nanoflu-

a maximum in thermal conductivity at approximately

[17] T. Sun, A[18] T.F. Sun[19] J.G. Blea[20] J.G. Blea[21] K.N. Ma

Physicoc1987.

[22] W. Evanwell, A Treatise on Electricity and Magnetism, third ed., Oxfordty Press, London, 1892.

ilton, O.K. Crosser, Ind. Eng. Chem. Fundam. 1 (1962) 187., X. Xu, S.U.S. Choi, J. Thermophys. Heat Transfer. 13 (1999).tman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Appl. Phys. Lett.) 718720.hoi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Appl. Phys.(2001) 22522254., M.C.C. Lin, I.T. Huang, C.C. Wang, Chem. Eng. Technol. 29277.. Wang, T. Xi, Y. Liu, F. Ai, J. Mater. Sci. Lett. 21 (2002) 193

J. Wang, T. Xi, Y. Liu, F. Ai, Q. Wu, J. Appl. Phys. 91 (2002)72..U.S. Choi, J. Nanopart. Res. 5 (2003) 167171.mar, H.E. Patel, V.R.R. Kumar, T. Sundararajan, T. Pradeep, S.K.s. Rev. Lett. 93 (2004) 144301., S.U.S. Choi, Appl. Phys. Lett. 84 (2004) 43164318., N. Putra, P. Thiesen, W. Roetzel, J. Heat Transfer. 125 (2003).g, H. Gu, M. Fujii, J. Appl. Phys. 100 (2006) 044325.yer, ASME Steam Tables: Thermodynamics and Transport Prop-Steam, sixth ed., American Society of Mechanical Engineering,k, 1993.lio, A.S. Teja, J. Chem. Eng. Data 35 (1990) 117121., A.S. Teja, J. Chem. Eng. Data 49 (2004) 13111317..S. Teja, J. Chem. Eng. Data 49 (2004) 18431846.

, A.S. Teja, J. Chem. Eng. Data 48 (2003) 198202.zard, T.F. Sun, A.S. Teja, Int. J. Thermophys. 17 (1996) 111125.zard, A.S. Teja, J. Chem. Eng. Data 40 (1995) 732737.rsh, Recommended Reference Materials for the Realization ofhemical Properties, Blackwell Scientific Publications, Boston,

s, J. Fish, P. Keblinski, Appl. Phys. Lett. 88 (2006) 093116.

The thermal conductivity of alumina nanoparticles dispersed in ethylene glycolIntroductionModels for thermal conductivity enhancementExperimentalResults and discussionConclusionsReferences