Volume fraction and temperature variations of the effective thermal conductivity of nanodiamond fluids in deionized water

International Journal of Heat and Mass Transfer 53 (2010) 3186–3192

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Volume fraction and temperature variations of the effective thermal conductivity of nanodiamond fluids in deionized water M. Yeganeh a,b, N. Shahtahmasebi a,b, A. Kompany a,b, E.K. Goharshadi b,c, A. Youssefi d, L. Šiller e,* a

Department of Physics, Ferdowsi University of Mashhad, Iran Nano Research Center, Ferdowsi University of Mashhad, Iran c Department of Chemistry, Ferdowsi University of Mashhad, Iran d Pare-Taavous Research Institute, Mashhad, Iran e School of Chemical Engineering and Advanced Materials, Newcastle University, NE1 7RU, UK b

a r t i c l e

i n f o

Article history: Received 30 September 2009 Accepted 30 January 2010 Available online 19 April 2010 Keywords: Nanodiamond Thermal conductivity Nanofluid Suspensions Nanoparticles

a b s t r a c t Thermal conductivity enhancements of nanodiamond particles (NDs) suspended in pure deionized (DI) with different volume fractions in the range from 0.8% to 3% have been measured. The highest observed enhancement in the thermal conductivity is 7.2% for a volume fraction of 3% at a temperature of 30 °C. The thermal conductivity increases by about 9.8% as the temperature rises to 50 °C. The new Murshed model (Murshed et al. (2009) [31]) was used to describe the heat transfer enhancement in the ND fluid. While the predicted results overestimate the experimental data, they are in agreement within the experimental errors. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Conventional fluids such as water, ethylene glycol and oil are extensively employed as heat transfer fluids which have many applications in industry. These fluids have relatively poor thermal conductivity, so several methods have been proposed to enhance their heat transfer performance [1–3]. Since solid materials have higher thermal conductivity compared with those of fluids [4,5], researchers have tried to improve the thermal conductivity of conventional fluids by suspending solid particles in them [6]. The addition of nanoparticles to these fluids, creates nanofluids which show promise as the next generation of heat transfer fluids. The advantages of nanofluids compared with those containing micro- or milli- sized particles are their better stability and higher thermal conductivity [7]. For example, nanofluids containing small amounts of nanoparticles such as Cu, SiC, Al2O3, TiO2 and CuO have shown enhanced thermal conductivity [8–18]. The most promising results have been reported by Choi et al. [19] who demonstrated a large (up to 160%) enhancement in the thermal conductivity for multiwalled carbon nanotube (MWNT) suspensions in a synthetic poly (a-olefin) oil. A number of experiments have been performed by different groups on carbon nanotube (CNT) nanofluids, and varying results have been reported * Corresponding author. E-mail addresses: [email protected] (M. Yeganeh), Lidija.Siller @ncl.ac.uk (L. Šiller). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.03.008

[12,19–21]. Xie et al. [22] measured the thermal conductivity of suspensions of MWNTs in an organic liquid and in water and observed only a 10–20% increase in the thermal conductivity at 1 vol%. Wen and Ding [23] reported enhancement in the thermal conductivity of about 25% at 0.8 vol%. Hwang et al. [24] found an enhancement of up to 11.3% at a volume fraction of 1% in water. Ding et al. [25] also measured an increase in the thermal conductivity from 0.1 wt% to 18% for CNTs suspended in water at 30 °C. While several studies have been performed on CNTs dispersed in different fluids, recently research has been carried out on nanodiamonds (NDs) [25–28]. Assael et al. [26] attempted to measure the thermal conductivity of a suspension consisting of poorly dispersed NDs (1% by mass) with 45% by mass sodium dodecyl sulfate (SDS) surfactant in water and reported a 2% enhancement in thermal conductivity compared with water. Tyler et al. [29] studied the effect of ND on the heat transfer of Midel oil and polymer solids. Ding et al. [25] investigated the thermal conductivity of 0.1 wt% of NDs and 10 wt% anionic sodium dodecyl benzene sulfonate (SDBS) surfactant in deionized (DI) water and an enhancement of up to 8% relative to water was observed. Ma et al. has developed an ultrahigh performance cooling device which, when filled with ND fluid (1% by volume ND particles dispersed in water), has shown that with the same heating power ND fluids can substantially reduce the temperature difference between the evaporator and the condenser [28]. Xie at al. have studied the thermal conductivity enhancement of ND fluids dispersed in a mixture of distilled water with a volume fraction of 0.55 and ethylene glycol with

M. Yeganeh et al. / International Journal of Heat and Mass Transfer 53 (2010) 3186–3192

volume fraction of 0.45 over, the viscosity and convective heat transfer coefficient [27]. In their work, the nanofluid with a volume fraction of 0.005 had optimal overall performance [27]. Recently, Torii and Yang [30] measured the thermal conductivity of 0.1%, 0.4%, and 1% particle volume fractions of ND and they recorded a discrepancy of less than 1% between the measured values and values obtained by the Maxwell model. They also indicated that their prepared ND suspension were stable even after 60 days. In this work, we investigate the thermal conductivity of ND fluids in pure DI water over a wider range of volume fraction and temperatures than in the work by Ma et al. [28] and Torii and Yang [30]. We then compare our results to existing theoretical models in the literatures [1,31] which has not been shown previously. Since the thermal conductivity of crystalline and amorphous solids containing carbon atoms is high [4,5,32,33], we are interested in ND. NDs have a high thermal conductivity, like diamond, but can be produced in large quantities and are non-toxic [34]. ND can also survive in different chemical environments without causing any problems such as sedimentation [35], therefore, ND may be a potential substitute for CNTs in heat transfer fluids. Employing ND to enhance the thermal conductivity of fluids potentially also has significant advantages over the use of CNTs. In particular, the resemblance of CNTs to asbestos has raised debates about widespread application of CNTs, particularly when not encapsulated within, or bound to, a material since exposure has been linked to health issues such as mesothelioma [36,37].

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stored inside the bubbles, just before their implosion, and fierce shock waves are produced due to the cavitations process which result a very high temperature in a very small space and cause the disaggregation of soft agglomerates [41]. The prepared nanofluids were stable during the measurements. The volume concentrations are in the range from 0.8% to 3%. A transmission electron microscope (TEM) was used to monitor the morphology of nanoparticles before and after dispersion in DI water (Fig. 2). As it can be seen the average particle size in the suspension is below 10 nm. 3. Measurement of thermal conductivity of nanofluids ND suspensions were loaded into vertical cylindrical double layer glass containers of inner diameter 50 mm, length 100 mm. A circulating unit supplied by Thermo Haake (DC10) was utilized to keep the temperature of the nanofluids constant. Circulators transmit water at the relevant temperature into the second layer of the container and maintain the temperature of the nanofluid

2. Sample preparation and characterization The samples used in this study were agglomerate-free and purified (grade G01) NDs supplied by PlasmaChem GmbH (Germany) and synthesized by detonation of explosives with a negative oxygen balance in a hermetic tank, followed by oxidation of non-diamond sp2 and amorphous carbon phases using a wet oxidative treatment. The final material has a sp3 carbon purity of at least 96% [35,38,39]. The process produces nanoparticles with a size distribution between 2 and 20 nm with an average particle size of 4 nm [35,40]. The crystalline phases of the NDs were confirmed by X-ray diffraction (XRD) (see Fig. 1) which shows the prominent diffraction peaks corresponding to the diamond crystal. Peaks at diffraction angles of 43.9°, 75.4°, and 91.5° are related to diamond (1 1 1), (2 2 0), and (3 1 1) reflections, respectively. The nanofluids were prepared by suspending NDs in DI water with different volume fractions using a horn type ultrasound processor. By propagating the ultrasonic waves in the medium, many bubbles appear which develop as a result of altering pressure until they reach to a resonant size and then implode. A large amount of energy is (111)

(220)

Intensity (a.u.)

(311)

0

20

40

60

80

100

2θ (degree) Fig. 1. XRD pattern of ND.

Fig. 2. TEM images of ND (a) before and (b) after dispersion in DI water.

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at the desired temperature. A KD2 Pro instrument, supplied by Decagon Devices, is used to measure the thermal conductivity of the nanofluid samples using the transient line heat source method. The KD2 Pro takes measurements at one second intervals during 90 s (30 s for reading temperature, 30 s for heating time and 30 s for cooling time) by a 6 cm stainless steel needle. The system also analyzes the data and corrects for sample temperature drifting, providing accurate thermal property measurements. In addition, it has the capability to show how well the theoretical model (discussed below) fits the data by showing the square of the correlation coefficient r2. The correlation coefficient indicates how well the temperature curves correlate to the calculated thermal properties. If the model fits the data perfectly, then r2 = 1.0000. In general, acceptable values have r2 above 0.9950 and data with r2 below this value is discarded. 3.1. Theoretical basis of the transient line heat source method The temperature surrounding an infinite line heat source with constant heat output and zero mass, in an infinite medium is modeled by Carslaw and Jaeger [42]. When a quantity of heat, Q (J m1), is instantaneously applied to the line heat source, the temperature rise at a distance, r (m) from the source is:

DT ¼

 2 Q r exp 4pkt 4Dt

ð1Þ

where k (W m1 K1), D (m2 s1), and t (s) are the thermal conductivity, thermal diffusivity, and time, respectively. The temperature response for a constant amount of heat applied to a zero mass heater over a period of time, rather than as an instantaneous pulse, is

DT ¼ 

q 4pk

Ei



r 2 4Dt



0 < t 6 t1

ð2Þ

where q is the rate of heat dissipation (W m1), t1 is the heating time, and Ei is the exponential integral [43]. The temperature rise after the heat is turned off is given by:

DT ¼ 



q 4pk

 Ei

   r 2 r2 þ Ei t > t1 4Dt 4Dðt  t1 Þ

ð3Þ

The thermal properties of a material are determined by fitting the time series temperature data during heating to Eq. (2), and during cooling to Eq. (3). Thermal conductivity can be obtained from the temperature of the heated needle, with r taken as the radius of the needle. Kluitenberg et al. [44] provided solutions for pulsed cylindrical sources which closely approximate an infinitely long, thin line. The temperature rise during heating (0 < t < t1), for a heated cylindrical source of radius a (m) and length 2b (m) with the measurement of temperature at its center is:

DT ¼

q 4pk

Z

approaches unity as b/r approaches to infinity, and hence Eqs. (4) and (5) reduce to Eqs. (2) and (3). It was found that Eqs. (2) and (3) fit the temperature data as well as Eqs. (4) and (5), so this approximation has been used to determine the thermal properties. 4. Experimental results and discussions The thermal conductivity of nanofluids prepared with different volume fractions of NDs (0.008–0.03) were measured at 30 °C and 40 °C. The uncertainty of the measurement is around ±2%. Fig. 3 shows the thermal conductivity enhancements of NDs in a water medium (keff/kb) as a function of the volume fraction of NDs (/). This clearly confirms that the nanofluids have higher thermal conductivity compared with that of the base fluid. The results demonstrate a nonlinear relationship between the enhancement of thermal conductivity and particle volume fraction and, at higher volume fractions, a stronger nonlinear behavior appears which will be discussed in the next section. Fig. 4 represents the enhancement in the thermal conductivity for 1.5%, 2% and 3% volume fractions over a range of 30–50 °C It can be observed that by increasing the temperature a pronounced increase in the thermal conductivity of the nanofluid is measured. 4.1. Comparison of experimental results with theoretical predictions It has been established that the thermal conductivity of nanofluids depend upon different parameters such as the thermal conductivity of the nanoparticles and the base fluid, particle volume fractions, surface area, shape, and size of the nanoparticles and temperature of the medium. At present, there are no accurate theoretical formulas to predict the thermal conductivity of nanofluids [7]. The classical models such as Maxwell, Hamilton and Crosser, Bruggeman and Wasp [45–49] assume stationary particles in the base fluid in which the thermal transport properties are predicted by conduction-based theory. These models consider only the volume fraction and particle shape (in some cases) as variables and as a result, they underestimate the effective thermal conductivity of nanofluids and thus fail to explain the enhancement in the thermal conductivity. However, the models give a good prediction for the thermal conductivity for micrometer or larger-size particles

0

1.10

u1 expðuÞ ð4Þ

k eff /k b

Z

r 2 =4Dðtt 1 Þ

u1 expðuÞ

r 2 =4Dt

 exp½ða=rÞ2 uI0 ð2au=rÞerf

  b pffiffiffi u du r

ð5Þ

where I0(x) stands for a modified Bessel function of order zero, erf(x) is the error function, and u is an integration variable. As it pointed out by Kluitenberg et al. [44]

exp½ða=rÞ2 uI0 ð2au=rÞ

Experimental at T=30 C 0 T=40 C

1.08

and during cooling (t > t1) is:

4pk

  b pffiffiffi u r

r 2 =4Dt

  b pffiffiffi u du  exp½ða=rÞ uI0 ð2au=rÞerf r

q

erf

1

2

DT ¼

approaches unity as a/r approaches zero, and

1.06

1.04

1.02

1.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Volume fraction (%) Fig. 3. Enhancement of thermal conductivity of ND nanofluids against particle volume fraction at T = 30 °C and 40 °C.

M. Yeganeh et al. / International Journal of Heat and Mass Transfer 53 (2010) 3186–3192

In this work, we will compare the experimental results with the Maxwell model [1], and Murshed model [31]. The Maxwell model [1] calculates the thermal conductivity of spherical particles at low solid concentration by

1.10

1.5% Volume fraction 2% 3%

1.09

keff ¼ keff /k b

3189

1.08

kp þ 2kb þ 2ðkp  kb Þ/ kb kp þ 2kb  ðkp  kb Þ/

ð6Þ

where kp, kb, and / stand for the thermal conductivity of particles, thermal conductivity of base fluids, and volume fraction, respectively. Details of the Murshed model have been also explained in Ref. [31]. The effective thermal conductivity of nanofluids in this model [31] consists of two parts; static and dynamic:

1.07

1.06 30

40

50 o

Temperature ( C) Fig. 4. Enhancement of thermal conductivity against temperature at different particle volume fraction.

keffnf ¼ kst þ kdy

ð7Þ

They obtained the effective thermal conductivity as follows:

keffnf (

)   /p xðkp  xkf Þ 2c31  c3 þ1 þðkp þ2xkf Þc31 ½/p c3 ðx 1Þþ1   c31 ðkp þ2xkf Þðkp  xkf Þ/p c31 þ c3 1 ( !) 9K3 kcp þ2kf 3K4 þ 6 þ /2p c6 kf 3K2 þ 16 2kcp þ3kf 2 ( "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi #) 3K B Tð11:5c3 /p Þ 1 GT q cp—cp ds þ þ 2pqcp c3 r3p 2 cp 6pgcrp ds

¼ kf suspended in fluids [7]. In general, the conduction-based mechanisms cannot be wholly responsible for the observed thermal conductivity of nanofluids, therefore, some other mechanisms appear to be neglected in these models. Keblinski et al. [50,51] proposed four possible mechanisms for the anomalous nonlinear increase in the thermal conductivity of nanofluids. These are the existence of an interfacial layer at the particle/liquid interface, Brownian motion of the nanoparticles, the effects of clustering of particles, and the ballistic nature of heat conduction. In the last decade, many theoretical models have been suggested to predict the effective thermal conductivity of nanofluids. These models can be divided in two categories. The first category includes models [52–58] which use the concept of a liquid/ solid interface layer as a key role of the anomalous enhancement in the thermal conductivity of nanofluids and initially was proposed by Choi et al. [19]. Yu and Choi [52] have shown that the models based on the ordered liquid layer can possibly contribute to the enhancement in the thermal conductivity for particles smaller than 10 nm. However, it was necessary to assume both the thermal conductivity of the ordered liquid and the thickness of the liquid layer be very high to be consistent with the measured values of k [59]. In this category, models mostly were obtained from the modification of the classical models by considering the effect of nanolayers. The second category consists of the models which consider the contribution of the dynamic part due to the Brownian motion of particles. We can refer to the models proposed by Kumar et al. [60], Koo and Kleinstreuer [61,62], Jang and Choi [56,63], Prasher et al. [59,64], Xuan et al. [65] and Murshed et al. [31] between the several models offered in this category. Murshed et al. [31] reviewed the models proposed in this category. They expressed the weakness of the Kumar model [60] based on the unrealistic assumption for the mean free path of about 1 cm for a nanoparticle in its base fluid. The Jang and Choi model [56] which accounts for the contribution of Brownian motion in microconvection was criticized by Prasher et al. [59] also due to the assumptions made in this model, principally, the thermal boundary thickness, volume fraction of liquid layer, and also in choosing the parallel model of heat transfer. The Koo and Kleinstreuer model [61] has not been verified because of a function f which was introduced in this model which has no obvious definition. In addition the model is based on the kinetic theory which is not valid for composite liquid without considering significant correction as Murshed et al. [31] explained. The Prasher model [59,64] also includes a contributions from unknown constants (m and A) which are defined by matching the experimental data to the model [31].

ð8Þ where c ¼ 1 þ rtp ; c1 ¼ 1 þ 2rt p and kcp are the thermal conductivity of a complex particle as defined by:

kcp ¼ klr

2ðkp  klr Þ þ c3 ðkp þ 2klr Þ ðklr  kp Þ þ c3 ðkp þ 2klr Þ

ð9Þ

The thermal conductivity of a nanolayer is defined by klr = xkf, where x is an empirical parameter which depends upon the state of order of the fluid molecules in the interface, nature and surface chemistry of nanoparticles (x > 1). K is defined as:

K¼

kcp  kf kcp þ 2kf

ð10Þ

where GT is the total potential energy between two interacting colloidal nanoparticles and is defined as

" 2r 2cp 2r 2cp A þ 2 2 6 ds þ 4r cp ds ds þ 4rcp ds þ 4r2cp !# 2 ds þ 4r cp ds þ 2per e0 r cp f2 expðjds Þ þ ln 2 ds þ 4r cp ds þ 4r 2cp

GT ¼ 

ð11Þ

where e0, er, f and ds, are the dielectric constant for the vacuum, the dielectric constant for the medium, particle zeta potentialpand parffiffi ticle surface-to-surface distance respectively. j ¼ 3:288 I ðnmÞ1 and I is the ionic concentration and is attributed to the pH. The prediction made by the Maxwell and Murshed model was compared with the experimental results in Fig. 5. It can be observed that none of these models can be matched to the experimental results very well, but are within experimental error of ±2% for u < 3. Previously, it has been discussed that the prediction made by classical models such as the Maxwell model underestimates the experimental results. The thermal conductivity of nanofluids calculated by the Murshed model from Eq. (8) consists of three parts. The first term on the right hand side of this equation assumes the interfacial layer as a separate component in a static thermal conductivity model for non-interacting particles. The second term expresses the interactions in a stationary suspension between a pair of spherical particles and the third term, which is the

M. Yeganeh et al. / International Journal of Heat and Mass Transfer 53 (2010) 3186–3192

1.15 o

Experimental at T=30 C Maxwell model Murshed model and ω =1.1 Experimental data ±2%

keff / k b

1.10

1.05

1.00 0.5

1.0

1.5

2.0

2.5

3.0

Volume fraction(%) Fig. 5. comparison of the experimental results with the data obtained from Maxwell [1] and Murshed [31] model for T = 30 °C.

dynamic part, considers the effect of Brownian motion on the nanoparticles, particle surface chemistry and particle–particle interactions. The Murshed model has been applied for different fluid temperatures and volume fractions and is shown in Fig. 6. As it can be seen the model predicts almost the same value of the thermal conductivity of nanodiamond fluids for T = 30 °C and 40 °C and is not able to predict a measurable difference of thermal conductivity between the temperatures were examined in this study. As the dynamic part of Murshed model takes into account the effects of temperature; therefore this part of the model is unable to explain the strong dependence in the effective thermal conductivity on temperature As a consequence, this model has the capability to explain the enhancement in the thermal conductivity of ND within the experimental errors compared to the other dynamic models [61,64] which we have examined. However, this model does not agree with the experimental results at higher volume fraction (u > 2) and different temperatures for ND fluids which could be likely attributed to the difference in the quality of the interactions which has been viewed in the model and Brownian motion for this material which should be considered in the dynamic part of the model as a modification.

A plot of the enhancement in the thermal conductivity of NDs compared with MWNTs, as reported by Xie et al. [22] and Hwang et al. [24] is shown in Fig. 7. The ratio in the enhancement in the thermal conductivity of a 1% particle volume fraction of ND to MWNT obtained by Xie et al. and Hwang et al. are 0.67 and 0.42, respectively. The observed difference between the thermal conductivity of NDs and MWNTs could be explained by the difference in surface to volume ratio between them. The nonlinear behavior in the thermal conductivity as a function of volume fraction has been observed in MWNTs due to strong nanotube/nanotube interactions. This nonlinear behavior is expected in micrometer sized particle/fluid suspensions by over one order of magnitude larger than those used in their study (1%) [66]. Choi et al. [19] explained that these interactions could be possibly due to the large number of nanotubes in the liquid and the extremely high aspect ratio of the carbon nanotubes. Another possibility could be due to difficulties in dispersion of the NDs in the media relative to CNTs. NDs nanofluid suspensions have been compared with some other non-carbon based materials TiO2, CuO, and Al2O3 and the results are illustrated in Fig. 8. However, there are a variety of reports on thermal conductivity of these materials, only two sets of these data are used for each sample arbitrary [15,67–69], but it has been tried to choose at least one set of the data from the results reported recently.

15

(keff-kb)/kb*100

3190

Present work on ND Xie et al. [22] on MWNTs Hwang et al. [24] on MwNTs

10

5

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Volume fraction (%) Fig. 7. Comparison between results in present work on ND particles and those obtained by Xie et al. [22] and Hwang et al. [24] on CNT.

1.15 25

Nanodiamond in present work Al2O3 d=36 nm by Minsta et al. [67]

(keff-kb)/k b*100

20

keff / k b

1.10

Experimental at T=30oC o Experimental at T=40 C o Murshed model at T=30 C Murshed model at T=40o C

1.05

Al2O3 by Das et al. [68] TiO2 d=15 nm by Murshed et al. [15] TiO2 by Zhang et al. [69]

15

CuO d=29 nm by Minsta et al. [67] CuO by Das et al.

10

5

1.00

0.5

1.0

1.5

2.0

2.5

3.0

Volume fraction(%) Fig. 6. Comparison between experimental thermal conductivity and those of obtained by Murshed model [31] at different temperatures against particle volume fraction.

1

2

3

Volume fraction (%) Fig. 8. Comparison of the thermal conductivity of ND measured in present work with some oxide nanoparticles [15,67–69].

M. Yeganeh et al. / International Journal of Heat and Mass Transfer 53 (2010) 3186–3192

Fig. 8 reveals a significant discrepancy between data obtained by different authors. This disagreement can be attributed to a number of factors including particle size, particle shape, particle clustering, particle sedimentation, etc. Although considerable inconsistency exists, it can be seen that the thermal conductivity enhancement in ND fluids is similar to that observed when other nanoparticles are used. Several advantages exist for using ND particles over other nanoparticles such as similar thermal conductivity, cheap price, the availability of large quantities, and observed non-toxicity [34]. Torii and Yang [30] observed significant enhancement of heat transfer performance of ND suspension compared to pure water when they investigated the convective heat transfer behavior of aqueous suspension of ND particles flowing through a horizontal tube heated under a constant heat flux condition which would make this nanofluid ideal for practical applications. 5. Conclusions The thermal conductivity of dispersed NDs in DI water shows an enhancement in the thermal conductivity compared with DI alone. The thermal conductivity enhancement increases nonlinearly with the volume fraction of NDs up to a maximum of 3% volume fraction. At higher temperatures thermal conductivity also increases up to 7.2% at 30 °C and 9.8% at 50 °C. Different models were used to express the enhancement in the thermal conductivity of ND fluids. While classical models underestimate the effective thermal conductivity of nanofluids, the Murshed model predicts the experimental results to within the experimental error. We believe that by increasing the dispersion quality of the nanofluids, improvements in the thermal conductivity could be made. Acknowledgments We thank Mr. Ross Little and Dr. M.R.C. Hunt for critical reading of the manuscript. References [1] J.C. Maxwell, Electricity and Magnetism, Clarendon Press, Oxford, 1873. [2] U.S. Choi, Y.I. Cho, K.E. Kasza, Degradation effects of dilute polymer solutions on turbulent friction and heat transfer behavior, J. Non-Newtonian Fluid Mech. 41 (1992) 289. [3] U.S. Choi, D.M. France, B.D. Knodel, Impact of advanced fluids on costs of district cooling systems, in: Proceedings of the 83rd Annual International District Heating and Cooling Association, The International District Heating and Cooling Association, Conference, Danvers, MA, June 13–17,Washington, DC, 1992, p. 343. [4] Y. Touloukian, Thermophysical Properties of Matter, vol. 2, Plenum Press, New York, 1970. [5] Y. Touloukian, Thermophysical Properties of Matter, vol. 3, Plenum Press, New York, 1970. [6] S.U.S. Choi, Enhancing thermal conductivity of fluid with nanoparticles: developments and application of non-newtonian flows, FED-vol. 231/MD 66 (1995) 99. [7] X.-Q. Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: a review, Int. J. Therm. Sci. 46 (2006) 1. [8] J.A. Eastman, U.S. Choi, S. Li, L.J. thompson, S. Lee, Enhanced thermal conductivity through the development of nanofluids, Mater. Res. Soc. Symp. Proc. 457 (1997) 227. [9] S. Lee, U.S. Choi, S. Li, J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, J. Heat Transfer 121 (1999) 280. [10] X.B. Wang, X. Xu, U.S. Choi, Thermal conductivity of nanoparticle–fluid mixture, J. Thermophys. Heat Transfer 13 (1999) 474. [11] Y. Xuan, Q. Li, Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow 21 (2000) 58. [12] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (2001) 718. [13] H. Xie, J. Wang, T. Xi, Y. Liu, Thermal conductivity of suspensions containing nanosized SiC particles, Int. J. Thermophys. 23 (2002) 571. [14] K.-F.V. Wong, T. Kurma, Transport properties of alumina nanofluids, Nanotechnology 19 (2008) 345702 (8pp). [15] S.M.M. Murshed, K.C. Leong, C. Yang, Enhanced thermal conductivity of TiO2– water based nanofluids, Int. J. Therm. Sci. 44 (2005) 367.

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