Quantitative analyses of factors affecting thermal conductivity of nanofluids using an improved transient hot-wire method apparatus

Quantitative analyses of factors affecting thermal conductivity of nanofluids using an improved transient hot-wire method apparatus

International Journal of Heat and Mass Transfer 89 (2015) 116–123 Contents lists available at ScienceDirect International Journal of Heat and Mass T...

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International Journal of Heat and Mass Transfer 89 (2015) 116–123

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Quantitative analyses of factors affecting thermal conductivity of nanofluids using an improved transient hot-wire method apparatus Joohyun Lee a, Hansul Lee b, Young-Jin Baik c, Junemo Koo b,⇑ a

Korea Research Institute of Standards and Science, 267 Gajeongro, Yuseong-gu, Daejeon 305-340, South Korea Department of Mechanical Engineering, Kyung Hee University, Yongin 449-701, South Korea c Energy Efficiency Research Division, Korea Institute of Energy Research, 152, Gajeongro, Yuseong-gu, Daejeon 305-343, South Korea b

a r t i c l e

i n f o

Article history: Received 29 December 2014 Received in revised form 11 May 2015 Accepted 14 May 2015 Available online 30 May 2015 Keywords: Nanofluids Transient hot-wire method Effective thermal conductivity Volume fraction Particle size Number density Particle population density

a b s t r a c t While there are several factors affecting nanofluid thermal conductivity such as particle size, particle and fluid type, temperature and volume concentration, the effect of each factor on the thermal conductivity of the nanofluid is not clarified despite numerous experimental and theoretical efforts. In this work, four nanofluid samples with different particle size and volume fraction were prepared and the impact of the particle size and volume fraction on the effective thermal conductivity of the ethylene glycol/Al2O3 nanofluid was investigated using advanced transient hot wire system which avoids the capacitance influence and natural convection. The analysis result shows that particle size is more influential than volume fraction at the very low volume fraction less than 0.25% and the impact is more obvious with lesser volume fraction. Other than particle size and volume fraction, particle number density was turned out to be statistically very important factor affecting thermal conductivity of nanofluid when the volume fraction reaches to a certain degree of 0.2%. Under this volume fraction, the thermal conductivity of nanofluid decreases with the number density and this result may be attributed to hydrodynamic interactions induced by large fluid bodies traveling with nanoparticles in Brownian motion. This work provides not only the quantitative analyses of factors affecting the thermal conductivity of nanofluids but also the possible mechanisms of enhanced thermal conductivity. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction It has been reported that the nanofluids in which the metal or metallic oxide nanoparticles are added to the conventional heat transfer fluids such as water, ethylene glycol and engine oil have superior thermal conductivity to the same fluids without the nanoparticles. With this benefit, the nanofluids are considered as promising heat transfer liquid enabling operation cost reduction of cooling system and system miniaturization. Since the nanofluid was introduced by Choi and Eastman [1] in 1995, numerous works have been presented focusing on the experimental thermal conductivity measurements, and various research results were summarized in many review articles [2–6]. Wang and Mujumdar [2] reviewed previous works in terms of fluid flow and heat transfer characteristics of nanofluids in forced and free convection flows. Yu et al. [3] published a review article regarding the thermodynamic properties and the thermal conductivity enhancement of nanofluids. Sezer et al. [4] reviewed the published models of ⇑ Corresponding author. E-mail address: [email protected] (J. Koo). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.064 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

thermal conductivity enhancement. Kleinstreuer and Feng [5] reviewed the measuring techniques of thermal conductivity to investigate the causes of inconsistency of research results from different research groups. Fan and Wang [6] published a review article on the thermal conductivity enhancement mechanisms and prediction models, and they introduced a model based on theory of thermal waves. By virtue of those efforts, several factors affecting nanofluid thermal conductivity were identified such as particle size, particle and fluid type, temperature, pH, particle shape and volume fraction. However, the influence on the thermal conductivity of each parameter was not verified clearly. For example, the dependency of particle volume fraction is presented in almost all previous works. Most works show the thermal conductivity and volume fraction has linear relationship but some works revealed non-linear behavior. A brief summary of previous researches is as following: In the early phase of research period, the research group in Argonne National Laboratory made crucial contribution to start the study. Eastman et al. [7] reported that they prepared stable water based CuO nanofluids of 5 volume%, and observed 60% thermal conductivity enhancement. Wang et al. [10] measured thermal

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Nomenclature g L Q_ r R RO T k t V n N

gravitational acceleration (m/s2) length (m) heat transfer rate (W) radius (m) resistance (X) initial resistance (X) temperature (K) thermal conductivity (W/m K) time (s) volume particle number density, or particle population density particle number

conductivity of water based CuO and Al2O3 nanofluids using a steady-state parallel plate method, and reported that their thermal conductivity was higher than those of conventional predictions. Xuan and Li [11] prepared water based Cu nanofluids using two-step method, and investigated the effects of particle volume fraction, shape, size, and material properties on effective thermal conductivity. They reported that particle Brownian motion, sedimentation and dispersion would enhance convection heat transfer performance. Choi et al. [12] measured the thermal conductivity of oil based CNT nanofluids, and reported the large and non-linear increase of thermal conductivity with volume fraction. Eastman et al. [13] measured the thermal conductivity of ethylene glycol (EG) based Cu nanofluids of 0.3 volume%, and reported 40% thermal conductivity enhancement. Xie et al. [14] measured thermal conductivity of water/EG based SiC nanofluids using transient hot-wire method, and concluded that the thermal conductivity enhancement is independent of base fluid type, and it is a function of particle size and shape. Das et al. [15] measured thermal conductivity of nanofluids using temperature oscillation technique at different temperature and reported it increased linearly with temperature. Patel et al. [16] measured thermal conductivity of water/toluene based Au nanofluids of negligible volume fraction stabilized using citrate, and reported the temperature dependence of the thermal conductivity enhancement, the importance of interface between particle and fluid as well as 5–21% increase of thermal conductivity. Chon et al. [17] presented experimental results showing the thermal conductivity increase of nanofluids with increasing nanofluid temperature and with decreasing nanoparticle sizes. Three different sizes of Al2O3 nanoparticles were dispersed in deionized water at 1 volume% and sonicated for sufficient duration. The thermal conductivity of nanofluids were measured using transient hot-wire method and the result showed that the thermal conductivity difference between the nanofluids with 11 nm and 150 nm nanoparticles was approximately 20% and the thermal conductivity difference of nanofluids from 21 °C to 70 °C was around 6%. Murshed et al. [18] prepared water based TiO2 nanofluids of two different particle shapes, i.e., rod and sphere, and investigated the impact of particle shape on thermal conductivity enhancement. Zhang et al. [19] measured thermal conductivities of various nanofluids and claimed that they did not observe any abnormal thermal conductivity enhancement over the conventional prediction models. Timofeeva et al. [20] measured the thermal conductivity of EG based Al2O3 nanofluids, and performed theoretical study on the impacts of particle aggregation and Kapitza resistance on thermal conductivity. Lee et al. [21] measured effective viscosity and thermal conductivity of water based Al2O3 nanofluids of low volume fraction, i.e., 0.1–0.3%, and

Greeks

a /; u

x q D

temperature coefficient of resistivity (1/K) volume fraction of nanofluid angular velocity (rad/s) density (kg/m3) change

Subscripts n nanofluid f base fluid p particle w wire

observed the non-linear increase of viscosity and linear increase of thermal conductivity with volume fraction. Turgut et al. [22] measured the thermal conductivity of water based TiO2 nanofluids using 3-x method, and reported the thermal conductivity was rather lower than the predictions of conventional models. They claimed that the thermal conductivity enhancement was independent of temperature change, and the cost of viscosity increase outweighed the benefit of thermal conductivity enhancement. Recently, Hong et al. [23] investigated the effects of the temperature data range selection on thermal conductivity measurements using the transient hot-wire method, and reported that the range should be carefully chosen not to be affected by the impacts of the finite thermal capacity of hot-wire and natural convection. They highlighted the fact that the data selection range varied with the fluid type and set-up of measuring apparatus, and each measurement should be carefully analyzed to avoid the impacts. They claimed that the measurements tend to be overestimated if the temperature range was not properly selected. Han et al. [24] measured the particle volume fraction and size change with time as well as the thermal conductivity of water based Al2O3 and EG based ZnO nanofluids carefully to avoid the impacts of hot-wire thermal capacity and natural convection, and concluded that the thermal conductivity enhancement was independent of temperature. They reported the earlier onset of natural convection for nanofluids than base fluids as well. Lee et al. [25] suggested to monitor the particle volume fraction and particle size change with time by measuring the specific gravity of suspensions with a hydrometer and aggregated particle size with the dynamic scattering method. They claimed this is crucial because the thermal conductivity of nanofluids depends mainly on particle volume fraction as well as particle size. They analyzed the relation between particle aggregation/sedimentation and thermal conductivity enhancement of nanofluids. While a large number of experimental measurements have been conducted, there is wide data scattering, for example different thermal conductivity at the same particle type, size and volume fraction. In Table 1, the effective thermal conductivity data of deionized water/Al2O3 nanofluid is summarized and the data discrepancy is also observed. The different result of the same state may be caused by the errors originating from the device accuracy, data acquisition and reduction [23,24]. Furthermore, the thermal conductivity measurement without particle size and volume fraction measurement in the fluid state can affect the result since nanoparticles undergo aggregation and sedimentation with time [25]. There were researches on understanding the thermal conductivity enhancement mechanisms. Keblinski et al. [26] elucidated

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Table 1 Effective thermal conductivity enhancement (water base, c-Al2O3 particle). Authors

Size (nm)

Volume fraction (%)

Thermal conductivity enhancement (%)

Eastman et al. [7] Lee et al. [8] Xie et al. [9] Chon et al. [17]

33 38 60.4 13 50 182

4.3 5 5 1 4 1

9 12 22 15 30 5

Zhang et al. [19]

11 20 40

5 5 5

8 7 10

Timofeeva [20]

11 20 40

5 5 5

8 7 10

the impacts of particle Brownian motion, molecular-level layering of the liquid at the liquid/particle interface, the nature of heat transfer in the nanoparticles, and the effects of nanoparticle clustering, and they suggested the ballistic nature of heat transfer in nanoscale and the particle clustering effects were the key mechanisms of the thermal conductivity enhancement of nanofluids. Wang et al. [27] analyzed that the particle interaction and clustering were the key mechanisms. Jang and Choi [28] claimed that Brownian motion is important, and developed a model considering the particle Brownian motion. Yu and Choi [29] published an article elucidating the impact of molecular-level layering of the liquid at the liquid/particle interface on thermal conductivity of nanofluids. Koo and Kleinstreuer [30] developed a model considering the impact of particle Brownian motion and surrounding liquid package induced by particle motion on effective thermal conductivity of nanofluids based on data in previous articles. Koo and Kleinstreuer [31] also compared the impacts of Brownian motion, thermos-phoresis and osmo-phoresis on thermal conductivity of nanofluids, and concluded that the impact of Brownian motion is more important. Prasher et al. [32] developed a model considering the effects of particle aggregation kinetics, and claimed that there is an optimum level of particle aggregation to show the maximum thermal conductivity increase. Murshed et al. [33] developed a model taking the effects of particle Brownian motion, nanolayer and interaction potential between particles into account. Despite these attempts, the clear explanation of the heat transfer

mechanism is not provided so far and the reason may be attributed to several factors affecting the nanofluid thermal conductivity. So it is necessary to investigate each factor thoroughly with experimental validation. In this study, the thermal conductivities of nanofluids of containing particles of different size and volume fraction were estimated, and statistically analyzed to differentiate the impact of particle size from that of particle volume fraction. 2. Experimental setup 2.1. Thermal conductivity measurements Conductivities of fluids were measured using transient hot-wire method (THWM) as shown in Fig. 1. In case of setting up THWM apparatus using a Wheatstone bridge and analog–digital (AD) converter, there was a limitation in resolving the temperature change of wire due to the resolution of AD converter. A source measuring unit, which has resolution of 100 nV for voltage and 1 pA for current, was used to measure the voltage drop in the hot-wire as well as the applied electric current from which the temperature history of the hot-wire could be estimated using the relation between the changes in resistance and temperature.

Rw ¼ R0 ð1 þ aDTÞ

ð1Þ

where Rw, R0, a, and DT represent measured and initial resistances of hot-wire, temperature coefficient of resistance of hot-wire, and temperature rise from the initial temperature respectively. The thermal conductivity of fluids could be estimated from the obtained temperature history by using the relation presented by Carslaw and Jaeger [34],

kf ¼

Q_ d ln t  4pL dDT

ð2Þ

where kf, Q_ , L, and t represent fluid thermal conductivity, supplied Joule heating energy, hot-wire length and time respectively. In the current measurement apparatus, the wire length is 0.14 m and the diameter is 50 l with a 25 l Teflon coating layer. Hong et al. [23] reported that the impacts of initial delay due to thermal capacitance of wire and natural convection should be avoided in the measurements. In this study, the data processing method to avoid the two effects was modified to improve the accuracy of the measurements. A validation study using computational

Fig. 1. Schematics of transient hot-wire method used in the current study.

J. Lee et al. / International Journal of Heat and Mass Transfer 89 (2015) 116–123 Table 2 Specifications of prepared nanofluids. Type *

Centrifuge acceleration (RCF ) Sauter mean diameter (nm) Volume fraction (%) *

C1

C2

N1

N2

14,650 111 0.032

3663 139 0.078

NA 164 0.033

NA 202 0.20

RCF: relative centrifugal force ðrx2 =gÞ.

fluid dynamics was performed. The axi-symmetric version of continuity, momentum, and energy equations were solved with the no slip conditions on hot-wire surface and vessel walls, adiabatic conditions at the wall, coupled conditions at the interfaces between wire and fluid, and uniform volumetric heat generation in hot-wire according to applied electric energy. In the simulation, the thermal conductivity of ethylene glycol (EG) was set to be constant at 0.252 W/m K, whereas the density variation with temperature was considered as a piecewise linear function to investigate the natural convection effect. 2.2. Nanofluid preparation The preparation of nanofluids could be classified into two groups; one- and two-step methods. Using the one-step method, nanoparticles are produced physically or chemically from the raw material and directly dispersed into the base fluid to make nanofluids. With the two-step method, the particles are prepared in powder where the nano-size particles exist in aggregate form, and they are dispersed into the base fluid via ultra-sonication to break the aggregates and mix them up with base fluid. It has been reported that the suspended particle size in nanofluids prepared using two-step method is usually larger than that in nanofluids prepared by one-step method. The researchers [2–6] have reported that it was favorable to have smaller particles in nanofluids for thermal conductivity enhancement. However, they have reported only the primary particle size, which is the particle size of the smallest element in aggregate, as the particle size in nanofluids, although the size of aggregates might be more significant factor affecting the thermal conductivity enhancement. In this study, the EG base c-Al2O3 nanofluids of 25 nm primary particle diameter were prepared using the two-step method, and they were centrifuged for 30 min to obtain nanofluids of different particle size and volume fraction. At the end of the centrifuge process, the sediment particles were removed. They were compared with nanofluids prepared without the centrifuge process. Table 2 compares the specifications of prepared nanofluids of four types. The letter ‘C’ of C1 and C2 indicates that the nanofluids are centrifuged, and ‘N’ shows that they are not centrifuged. The particle size distribution was determined using the dynamic scattering method, from which the Sauter mean diameters (SMD) of nanofluids were estimated. The volume fractions of nanofluids and their variations in time were monitored by measuring the specific gravity of nanofluids using electronic hydrometer [25]. The nanofluids were centrifuged at two different conditions to test the impact of the process on the particle size, and it was found that the centrifuge at higher acceleration resulted in smaller particle size and lower volume fraction. 3. Results and discussion 3.1. Simulation analysis of measurement process Fig. 2(a) shows the different temperature histories from computer simulations according to the applied electric energy in hot-wire. The temperature history was gathered for 20 s in each

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case. The temperature rise was 0.75 K for 0.5 V case, and it increased to 3 K for 1 V and 12 K for 2 V case respectively. Big temperature rise is not desirable because it makes hard to tell the measuring temperature condition, and more prone to be affected by natural convection. Fig. 2(b) and (c) compare the thermal conductivity estimations with parts of the hot-wire temperature histories of varying start and end times at different levels of applied voltage. If the start time of the interval to estimate the thermal conductivity is earlier than 2 s, it tends to overestimate the thermal conductivity due to ‘‘initial delay’’ or ‘‘wire thermal capacitance’’ effect no matter what the end time is. No serious impact of natural convection is observed in Fig. 2(b), and the thermal conductivity could easily be read as the set value 0.252 W/m K without any problem. In Fig. 2(c), the thermal conductivity estimation does not vary either along the line A with the variation of end time at a fixed start time, or along the line B with the variation of start time at a fixed end time. Therefore, the thermal conductivity value along the line could be regarded not to be affected by natural convection. Along the line C, the thermal conductivity estimation increases with the start time of the interval, which indicates that the thermal conductivity estimation suffers from the natural convection effect, and the end time is selected too large. 3.2. Selection of proper voltage level Fig. 3(a)–(c) compare the thermal conductivity estimations at different applied voltage levels. The red lines in figures represent the contour lines of the same thermal conductivity estimation, and the blue ones show those of the same determinant coefficient R2 of the thermal conductivity estimation. They show the same trends shown in Fig. 2. In Fig. 3(a) and (b), no natural convection effect is observed. However, the effect of noise signal is observed for the cases of using short interval to estimate thermal conductivity unlike the results of simulated measurements in the previous section, and the estimated thermal conductivity is far from the true value for regions where start time is close to end time of the interval. The region affected by the noise signal becomes wider at lower applied voltage, to show lower determinant coefficients. A significant impact of natural convection is observed at 1.5 V, while the determinant coefficient improves. Therefore, the applied voltage was selected to be 1 V where the measurements were free from the natural convection effect and had high determinant coefficients not to be affected by noise signal. 3.3. Thermal conductivity measurements of nanofluids Fig. 4(a) and (b) represent the time history of volume fraction and boxplot of particle size of nanofluids. The volume fraction and particle size were measured by decanting a part of prepared nanofluid into a vessel, and it was poured back to the original vessel after the measurements. There could be variations of both volume fraction and particle size distribution originating from sampling. It was found that the volume fraction did not show time variation for the nanofluids C1, C2, and N1 from the results of regression analysis using the open source statistical software R [35], whereas N2 showed statistically meaningful decrease of volume fraction in time as shown in Fig. 4(a). In contrast, the particle size variation was statistically analyzed to be independent of time for the fluids C1, C2, and N1, while the particle size increased with time except for an outlier in the data set for the fluid N2. The thick lines in the box plot are medians of the measurements, and the circles in Fig. 4(b) represent the outliers, which are not included in the analysis. The boxes of the plot represent the regions between the first and the third quartiles, and the whiskers show the ranges where data stretch out.

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Fig. 2. The simulated impact of applied voltage on (a) temperature histories, and on the thermal conductivity measurements for the applied voltages of (b) 1 V and (c) 2 V.

Fig. 5(a) and (b) represent the results of the thermal conductivity measurements as a function of volume fraction and particle size respectively. The error bars in the figures represent the standard deviations of measurements. The thermal conductivity measurements of nanofluids were compared against the predictions using Maxwell relation in Fig. 5(a). The centrifuged nanofluids C1 and C2 showed higher thermal conductivities than the Maxwell relation predictions, and they were statistically higher than the Maxwell relation with 95% confidence level. In contrast, the average values of thermal conductivity measurements for fluids N1 and N2 were higher than the predictions of the Maxwell relation, while they could not be judged to be above the predictions considering the data scattering in measurements with confidence. The thermal conductivities of the centrifuged nanofluids C1 and C2 were higher than that of N1, where the particle sizes of C1 and C2 were smaller than that of N1 as shown in Fig. 5(b), while the volume fraction of N1 was about the same as that of C1. This shows that the particle size is more significant factor affecting the thermal conductivity under very low volume fraction condition (/ < 0.1%).

To quantitatively elucidate the impact of volume fraction and particle size on thermal conductivity, measured data for C1, C2 and N1 were compiled using regression analysis and analysis of variance (ANOVA). As a result, it turned out that thermal conductivity decreased with particle size (negative regression coefficient), and increased with volume fraction (positive regression coefficient), and the impact of particle size was more than 5 times greater than that of volume fraction comparing the F-values in Table 3, where F-value represents the ratio of the mean variance of observations with the change in a variable to that of errors. The impact of both volume fraction and particle size variations were determined to be statistically significant with the confidence level of 95%, since the p-values of both terms were below 0.05. Multiple linear regression analysis was applied to the valid measured data for fluids C1, C2, N1 and N2 with volume fraction and particle size as the independent factors. The determinant coefficient dropped to 0.33 as shown in Table 3, and the resulting regression formula failed to explain measured data. This could be

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Fig. 3. Comparison of the results of thermal conductivity estimation of EG at different level of voltages (a) 0.75 V, (b) 1 V, and (c) 1.5 V.

resolved by adding another factor, number density, or population density n, where it is defined as in Eq. (3).



N N  Vp 1 u ¼   V V p SMD3 V

ð3Þ

It was found that the determinant coefficient increased to 0.71. Comparing the F-values in Table 3, it was found that the impact of particle size and number density were about two and four times larger than that of volume fraction respectively. The three factors were found to be statistically significant ones affecting thermal conductivity of nanofluids. As the volume fraction increased, the impact of volume fraction increased. A new factor, number density, showed up from the analysis as a significant factor, and the sign of the regression coefficient was determined to be negative, which was found not to be significant for the case of considering the data for C1, C2 and N1 only. This means that thermal conductivity of nanofluids decreases with number density as the volume fraction increases. Koo and Kleinstreuer [30] tried to explain the impact

of fluid mixing induced by particle Brownian motion by considering the large liquid package traveling with a nanoparticle in Brownian motion. Due to huge size of the fluid body affected by the viscous effect of a moving particle in motion, the fluid bodies were considered under the effects of hydrodynamic interaction unless the interparticle distance is very far so that the suspensions are very dilute. They introduced a model factor to consider the fraction of fluid body volume traveling with a nanoparticle in a real nanofluid under hydrodynamic interaction to that without hydrodynamic interaction, and showed that it decreased with volume fraction. Under very dilute condition (e.g., / < 0.1%), the fluid body traveling with a particle would suffer less from the hydrodynamic interaction, and it would suffer more with the increase of volume fraction (e.g., / < 0.25%). Therefore, the negative sign in front of the term representing the impact of number density in the regression equation could be interpreted as the result of hydrodynamic interaction of fluid packages, and it is a key factor to explain the thermal conductivity variation with other factors. This result supports mixing enhancement mechanism considering liquid package

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Fig. 4. (a) Variation of particle volume fractions in time, and (b) comparison of particle size.

Fig. 5. Thermal conductivity measurements as a function of (a) volume fraction and (b) particle size.

Table 3 The results of F-test for regression analyses. Considered datasets

C1, C2, N1 C1, C2, N1, N2 C1, C2, N1, N2

R2

0.67 0.33 0.71

F-value

p-value

/

SMD

n

/

SMD

n

6.5 0.06 8.3

34.5 11.7 17.7

NA NA 30.0

0.017 0.80 8.5  103

9.4  106 2.3  103 3.4  104

NA NA 1.4  105

motion with nanoparticles in Brownian motion as a possible enhancement mechanism of nanofluid thermal conductivity. 4. Conclusions In this study, a detailed process to estimate the thermal conductivity using transient hot-wire method was presented, and the impacts of particle volume fraction and size on effective thermal conductivity of nanofluids were analyzed statistically. The following conclusions were drawn from this study:

 The thermal conductivity measurement process using transient hot-wire method could be improved by adopting a source measuring unit as the replacement of a Wheatstone bridge circuit, and by carefully analyzing the map of estimated thermal conductivities of different sample intervals to avoid the influences of capacitance and natural convection.  Under very low volume fraction condition (/ < 0.25%), the particle size was found to be more important factor than the volume fraction affecting the effective thermal conductivity of nanofluids.

J. Lee et al. / International Journal of Heat and Mass Transfer 89 (2015) 116–123

 The impact of the particle size on the effective thermal conductivity of nanofluids became more important with decreasing volume fraction.  Although the number density of nanoparticles in nanofluids was found not to affect the effective thermal conductivity of nanofluids under very dilute condition (/ < 0.1%), it was analyzed as an important factor affecting thermal conductivity as volume fraction increased to about 0.2%. The number density was found to decrease the thermal conductivity, which could be explained as a result of the hydrodynamic interaction among affected fluid volumes for cases where the interparticle distance is not long enough for neighboring affected volumes to travel independently. Conflict of interest None declared. Acknowledgement This work was jointly supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MEST) (No. R01-2008-000-20458-0(2009)) and by the framework of Research and Development Program of the Korea Institute of Energy Research (KIER) (No. B5-2417-01). References [1] S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Singer, H.P. Wang (Eds.), Development and Applications of Non-Newtonian Flows, ASME, New York, 1995, pp. 99–106 (FED-vol. 231/ MD-vol. 66). [2] X. Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: a review, Int. J. Therm. Sci. 46 (2007) 1–19. [3] W. Yu, D.M. France, J.L. Routbort, S.U.S. Choi, Review and comparison of nanofluid thermal conductivity and heat transfer enhancements, Heat Transfer Eng. 29 (5) (2008) 432–460. [4] S.Ö. Sezer, K. Sadık, A.G. Yazıcıog˘lu, Enhanced thermal conductivity of nanofluids: a state-of-the-art review, Microfluid. Nanofluid. 8 (2010) 145–170. [5] C. Kleinstreuer, Y. Feng, Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review, Nanoscale Res. Lett. 6 (229) (2011) 1–13. [6] J. Fan, L. Wang, Review of heat conduction in nanofluids, J. Heat Transfer 133 (2011) 040801-1–040801-13. [7] J.A. Eastman, U.S. Choi, S. Li, L.J. Thompson, S. Lee, Enhanced thermal conductivity through the development of nanofluids, MRS Proc. 457 (1996) 3–11. [8] S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, J. Heat Transfer 121 (1999) 280–289. [9] H. Xie, J. Wang, T. Xi, Y. Liu, F. Ai, Thermal conductivity enhancement of suspensions containing nanosized alumina particles, J. Appl. Phys. 91 (7) (2002) 4568–4572. [10] X. Wang, X. Xu, S.U.S. Choi, Thermal conductivity of nanoparticle-fluid mixture, J. Thermophys. Heat Transfer 13 (4) (1999) 474–480. [11] Y. Xuan, Q. Li, Heat transfer enhancement of nanofluids, Int. J. Heat Fluid Flow 21 (2000) 58–64. [12] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions, Appl. Phys. Lett. 79 (14) (2001) 2252–2254.

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