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Effect of clustering on the thermal conductivity of nanofluids
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Materials Chemistry and Physics 109 (2008) 50–55
Effect of clustering on the thermal conductivity of nanofluids N.R. Karthikeyan, John Philip ∗ , Baldev Raj Metallurgy & Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India Received 16 August 2007; received in revised form 23 October 2007; accepted 27 October 2007
Abstract We synthesis CuO nanoparticles of average diameter 8 nm by a simple precipitation technique and study the thermal properties of the suspensions. The thermal conductivity enhancement observed in water and ethylene glycol based nanofluids with 1 vol.% CuO nanoparticles loading are 31.6 and 54%, respectively. The large enhancement in thermal conductivity is attributed to the finer particle size and monodispersity of nanoparticles. It has been found that the thermal conductivity of the nanofluid increases nonlinearly with the volume fraction of nanoparticles. The time-dependent thermal conductivity in water based CuO nanofluid shows that the thermal conductivity decreases with elapsed time due to clustering of nanoparticles with time, as confirmed microscopically. The experimental results show that the nanoparticles size, polydispersity, cluster size and the volume fraction of particles have a significant influence on thermal conductivity. © 2007 Elsevier B.V. All rights reserved. Keywords: CuO nanoparticles; Nanofluid; Thermal properties; Heat transfer fluid
1. Introduction It has been demonstrated that at nano-scale it is possible to fine tune the electrical, optical, mechanical, thermal and chemical properties by modifying the size and shape of the nano materials [1–7]. An understanding of the process of particle growth is a prerequisite to tailor nanoparticles of desired size and properties. Among the nanocrystals, copper oxide (CuO) nanoparticles have many technological applications such as gas sensors [8], magnetic phase transistor [9], catalysts [10], and high temperature superconductors [11]. Conventional technique to prepare CuO nanoparticles includes thermal decomposition [12], mechanical milling [13], single step solid state reaction, etc. [14]. Very recently an interesting scheme to synthesis of metal nanoparticles in deionized water, using multi-beam laser ablation in liquids, is reported [15], where the laser parameters that control the nanoparticles size and distribution has been studied. Many other routes are used for production of ultrapure nanoparticles like co-precipitation [16–20] alcohol-thermal [21], sonochemical technique [22], sol–gel [23] and hydrothermal [24]. In our study, we synthesized CuO nanoparticles by a novel quick precipitation technique [25].
∗
Corresponding author. Tel.: +91 94 431 51 536; fax: +91 44 27480356. E-mail address: [email protected] (J. Philip).
0254-0584/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2007.10.029
Nanofluids are a new kind of heat transfer fluid containing a very small quantity of nanoparticles that are stably suspended in a carrier liquid [26]. Fluids have typically very low thermal conductivity compared with crystalline solids. However, a dispersion with small amount of solid nanoparticles in traditional fluid dramatically changes their thermal conductivities [27]. Nanofluids containing ceramic or metallic nanoparticles showed large enhancement of thermal conductivity that cannot be explained by conventional theories [28]. Many factors, such as particle size, surfactant coating, carrier fluid, etc., have an effect on the thermal conductivity of the nanofluid. The stability of suspension is one of the crucial factors required for improving the thermal conductivity of the fluid and its applications as an efficient coolant [29]. The most common techniques used to measure the effective thermal conductivity of nanoparticle suspensions is transient hot wire method [30], steady state method [31], temperature oscillation method [32] and hot strip method [33]. In all these techniques, the natural convention of the base fluid can affect the heat flow mechanism and hence induce some additional error. In spite of many experimental and theoretical studies to understand the mechanism and thermal characteristic of nanofluid, the science behind the thermal conductivity enhancement is still unclear [34–37]. Herein, we undertake systematic studies to understand the parameters affecting the thermal conductivity in water and ethylene glycol based CuO nanofluids and
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the effect clustering on the thermal conductivity of the nanofluids. 2. Experimental For synthesis of CuO nanoparticles, Cu (CH3 COO)2 ·2H2 O, CH3 COOH, and solid NaOH are procured from E-Merck. All the chemicals were GR grade and used without any further purification. In our typical procedure, 600 ml of 0.2 M copper acetate aqueous solutions is mixed with 2 ml glacial acetic acid in a round bottomed flask. Under vigorous stirring, 0.16 g of solid NaOH (pellets) is added rapidly to the boiling solution at 100 ◦ C, until the pH value of the mixture is reached 6–7. At this stage, the color of the solutions changes from blue to black and a black precipitate is produced simultaneously. After cooling to room temperature, the precipitate is centrifuged, washed twice with triply distilled water, ethanol and acetone and finally dried at room temperature. Techniques for suspending nanoparticles are crucial to make stable and uniformly dispersed nanofluid. A known amount of dried nanoparticle is mixed with water or ethylene glycol base fluid. The suspension is then homogenized by using an ultrasonic horn (Vibronic ultrasonic processor P1-250 W), for 30 min. Using this method, stable fluids are prepared without addition of surfactants. The different volume fractions of CuO nanoparticles suspension in water and ethylene glycol are prepared by this approach.
Fig. 1. The XRD pattern of CuO nanoparticles prepared by precipitation route.
4. Results and discussion 4.1. Crystal structure and particle size
3. Characterization Philips-X’pert MPD® X-ray diffaractometer is used to obtain X-ray diffraction pattern of the particles. 2θ values are taken ˚ with a from 20 to 80◦ using Cr K␣ radiation (λ = 2.2897 A) step size of 0.04◦ . Acquisition and preliminary analysis of the data were performed by the Philips X’pert Pro® software and the XRD patterns were verified by comparing with the JCPDS data. Thin layered dried powder (25 ± 3 mg) spread over 5 cm2 plate area is prepared to minimize the error in peak location and also the broadening of peaks due to reduced thickness of the particle [38]. The broadening of the peak at full width half maximum (FWHM), is related to the average diameter (d) of the particles according to Debye–Scherrer’s formula [39], i.e. d = 0.9λ/B cos θ, where λ is X-ray wavelength, B is line broadening measured at half height and θ is Bragg angle. The average particles size is obtained from most predominant peak, corresponding to (1 1 1) reflection by using Debye–Scherrer formula. The transmission electron microscopy (TEM) instrument used is a Philips CM12 with an acceleration voltage of 100 kV. One drop of CuO dispersion is placed on carbon coated copper grid (0.3 cm diameter, mesh size of 300 holes cm−1 ) and left to dry for 1 h at room temperature. The thermal conductivity of CuO nanofluid is measured by monitoring of heat dissipation from a line heat source. When a long, electrically heating probe is applied to the fluid, the rise in temperature is calculated using the equation: T − T0 ∼ =
q 4πλh
ln(t) − γ − ln
r2 4k
The XRD pattern of CuO nanoparticles shown in Fig. 1. It has been found that the nanoparticles are single-phase CuO with monoclinic structure. Further comparison of the XRD patterns with the JCPDS file (JCPDS 80-1268) data also confirms ˚ b = 3.42 A, ˚ and the same. The lattice constants a = 4.68 A, ˚ obtained from the pattern are consistent with the litec = 5.12 A, rature values [40]. No impurity peaks are observed in the XRD pattern. The broadening of the most predominant peak (1 1 1) indicates the smaller particles size. Average size of the CuO particles is estimated to be 7.7 nm according to the Debye–Scherrer equation [39]. The typical transmission electron microscopy (TEM) image of the as-prepared CuO nanoparticles is shown in Fig. 2. From the micrograph, it is clear that the specimen consists of spherical
(1)
where T is temperature, t time, k is thermal diffusivity, r is radial distance, q is the heat produced per unit length per unit time, λh is the thermal conductivity of the medium, γ is Euler’s Constant (0.5772).
Fig. 2. The TEM image of CuO nanoparticles.
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Fig. 3. The ratio of thermal conductivity of water based CuO nanofluid and the percentage of enhancement of thermal conductivity as a function of volume fraction.
particles with narrow size distribution and the particles are well dispersed. The size of the particles observed in the TEM image is in the range of 7–9 nm, in good agreement with that result obtained from the XRD pattern. 4.2. Thermal properties of CuO nanofluid Figs. 3 and 4 shows the thermal conductivity ratio and percentage enhancement as a function of volume fraction in water and ethylene glycol based CuO nanofluids respectively. To the best of our knowledge, this is the first experimental report on nanofluid containing fairly monodispersed CuO particles of 8 nm diameter. From Figs. 3 and 4, it is apparent that the thermal conductivity of CuO nanofluid increases nonlinearly with increase in volume fraction of the nanoparticles, as observed earlier [41]. Despite considerable efforts for optimizing the synthesizing parameters, it is quite possible that the processing of CuO nanoparticles can results in incomplete oxidation that results in the presence of a small amount of unoxidizied Cu atoms on the surface of the
Fig. 4. The ratio of thermal conductivity and percentage of enhancement of thermal conductivity as a function of volume fraction in ethylene glycol based CuO nanofluid.
nanoparticles. This could be the reason for the enhanced thermal conductivity. As heat transfer in solid\liquid suspension occurs at the particle–fluid interface, an increase in the interfacial area can lead to more efficient heat transfer properties. The existing theoretical models fail to work when the nanofluid contain particles of less than 10 nm. One major assumption, in the models are that the particles are motionless in the fluid, which is a wrong assumption for nanofluids [42]. This assumption is contradicting to the fact that the nanoparticle exhibits Brownian movement when suspended in a liquid. As a result of Brownian motion, the fluid molecule in the immediate vicinity creates a locally ordered micro-convection effect around each particle within the base fluid [31–37]. It is believed, that this ordered arrangement of molecule lead to heat transfer enhancement in the fluid. Therefore, adding nanoparticles to the fluid results in two possible effects—higher thermal conductivity enhancement due to formation of highly ordered arrangement of molecule around each particles and the other effect is the stirring action caused by Brownian motion of the particles. As the particles size decreases, the motion becomes larger, that could contribute to larger thermal conductivity enhancement [42,43]. Therefore, small nanoparticles are better for maximum enhancement of thermal conductivity of the fluid. Presently, it is believed that the enhancement in thermal conductivity in a colloidal dispersion is mainly due to microconvection caused by the Brownian motion of the nanoparticles and aggregation of nanoparticles causing a local percolation [37,47]. Heat conduction in nanoparticles is assumed to be ballistic in nature, which is associated with the large phonon mean-free path in the nanoparticles. Basically, ballistic conduction of heat is much faster than thermal diffusion. There are several factors which will limit the ballistic conduction in nanoparticles [41]. Recent studies show that liquid molecules form a highly ordered structure very much like in solid at the interface between solid and liquid [34,41–45]. Although, the presence of an interfacial layer may play a role in heat transport, it is unlikely to be the sole reason for the thermal conductivity enhancement. Clustering to the nanoparticles occurs more actively in fluid with higher concentration. This clustering has major impact on the thermal conductivity measurement of the fluid. When the nanofluid is sonicated, the cluster breaks into primary nanoparticles. There has been some works on the effect of sonication time on thermal conductivity of nanofluids [43]. The nano-clusters are likely to settle in the fluid due to larger mass that results in particle gradient in the fluid. The “particle free” zone has higher thermal resistance compared particle rich zone. The suppression of clustering of the nanoparticles is also very important for designing effective heat transfer fluids. There are some reports on the formation of clusters and aggregates in the fluid that enhance the thermal conductivity of the fluid [46,47]. It is believed that the heat transport can be much faster along the back bone of the clusters. A comparison of thermal conductivity results from various studies in CuO nanofluid is shown in Table 1. As the particle size decreases, the surface to volume ratio gets increases, which leads to large enhancement in the thermal conductivity of the fluid since heat transfer is a surface phenomenon. The comparison of the experimental data suggest that thermal conductivity of base
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Table 1 Thermal conductivity data from various studies in CuO nanofluid Size (nm)
Base fluid
Thermal conductivity enhancement (%) & volume fraction of particles
Reference
36 23.6
Water Ethylene Glycol(EG) water EG Water Water EG
60% for 5 vol.% 20% for 4 vol.%
[29] [28]
12% for 3 vol.% 4% for 1 vol.% 52% for 6 vol.% 31% for 1 vol.% 54% for 1 vol.%
[53] [50] [31] Present Present
23 30.8 29 8 8
fluid, particles, volume fraction of particles and the particle size play a dominant role in the thermal conductivity enhancement in a nanofluid. The sedimentation in CuO nanofluid is observed when the nanoparticles concentration was above 1 vol.%. Below 1 vol.%, the CuO nanofluids were quite stable for more than after 3 week. To produce a stable nanofluid, either the particles size should be small enough to be suspended by Brownian motion or the particles must be protected against aggregation by electric charge or other protective coatings. The stability of nanoparticles in the fluid has a major impact on the effective thermal conductivity of the fluid [48,49]. In our studies, the volume fraction of CuO nanoparticle suspension in both water and ethylene glycol is varied from 0.01 to 1%. It is well recognized that the effective thermal conductivity of nanoparticles suspension is not simply a function of the particle loading in the base fluid [34,35]. As the size of CuO nanoparticle is very small, even at very low volume fraction, their suspensions in both water and ethylene glycol are stable. Furthermore, nanoparticles suspensions show excellent kinetic stability as a result of enhanced Brownian motion of the nanoparticles in the base fluid. Earlier studies reveal that the EG based CuO nanofluid (4 vol.%, 23.6 nm) exhibits 20% increase in effective thermal conductivity of the fluid [28], 60% in water based CuO nanofluid (5 vol.%, diameter 36 nm) [30] and 52% for water based CuO nanofluid (6 vol.%, diameter 29 nm) [31] and very recently, 22% increase in effective thermal conductivity of CuO (5 vol.%, diameter 30–50 nm) is achieved [50]. Compared to previous results [28,30,31,50], the observed increase in effective thermal conductivity is quite significant, as the volume fractions used in our experiments were low compared to the previous studies. For 0.01 v fraction of CuO (water) nanofluid, the thermal conductivity enhancement is 31.6%, whereas for the same volume fraction in ethylene glycol, the thermal conductivity enhancement is 54.16%. The large variations in the thermal conductivity of ethylene glycol and water based nanofluid shows that the base fluid also plays role in thermal conductivity of nanofluid [31]. We speculate that the presence of some un-oxidized copper atom on the surface of copper oxide nanoparticles contributes to the large increase in thermal conductivity of CuO nanofluid. The TEM image reveals that the particles are highly mono-dispersed with average size about 8 nm and are spherical in shape. The
Fig. 5. The time-dependent characteristic of CuO-water nanofluid.
mono-dispersity of the particles may also have an influence on the thermal conductivity enhancements due to negligible sedimentation. Compared with conventional micron sized particles, the surface to volume ratio of nanoparticles is very high. For instance, the surface area to volume ratio of particles with 10 nm is thousand times greater than conventional particles with size 10 m [28]. Thus by using nanoparticles of smaller size the thermal properties of the liquid can be enhanced effectively. Earlier studies reveal that nanofluids with finer nanoparticles exhibit better thermal conductivity compared to fluids containing coarse particles [30,51]. Fig. 5 shows the ratio of thermal conductivity as a function of time. It has been observed that the thermal conductivity decreases with elapsed time. Initially, the effective thermal conductivity of water based CuO nanofluid with concentration 0.8 and 0.3 vol.% were 1.225 and 1.175, respectively, which decreases with increasing time, probably due to appreciable particle agglomeration. The ratio k/kw is almost unity after an elapsed time of 14 min. Similar trend is observed in water based Cu nanofluids [52] and Fe based nanofluid [29]. It has also been observed that the thermal conductivity decrease with the cluster size [29]. In general, it is accepted that heat transfer is a surface phenomenon and the thermal energy interaction takes places at the surface of nanoparticles. When the particles get agglomerated, the effective surface area to volume ratio decreases, thus reducing the effective area of thermal interaction of particles causing a decrease in the thermal conductivity of the fluid. It has been observed that the thermal conductivity of the fluid is increased with decrease in particles size [34,51]. Microscopic observation of the suspension (water based CuO nanofluid of 0.1 vol.%) with time shows formation of aggregates in the nanofluid and the size of the aggregate increases with time. The clusters as large as few m have been observed several minutes after the sonification. As the cluster size increases, the sedimentation rate also increases and hence the number of primary particles available for the heat transport is reduced. The mesh like structures are formed in the nanofluid suspension at time intervals of 20, 60 and 70 min after sonication
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Fig. 6. Mesh-like structure observed, in water based CuO nanofluid of 0.1 vol.%, after sonication for (a) 20 min, (b) 60 min and (c) 70 min.
is shown in Fig. 6a–c, respectively. It can be seen the structure formation begins only after 60 min from the sonication. When the mesh-like structures are formed the thermal conductivity begins to drop. The size of cluster not only depends on average particle diameter but also the particle concentration in the fluid. The higher the particle concentration in the fluid, the smaller the inter-particle distance between the particles, as a result the probability of agglomeration is more due to van der Waals attraction. 5. Conclusion In this paper, we investigated the parameters influencing the thermal conductivity enhancement in water and ethylene glycol based nanofluids of CuO nanoparticles of average diameter 8 nm. The thermal conductivity enhancement observed with 1 vol.% of CuO nanoparticles is 54%, which is the highest value reported for CuO nanofluid. The large enhancement in thermal conductivity is attributed to the smaller particle size and monodispersity of particles. The thermal conductivity of nanofluid increases nonlinearly with the volume fraction of nanoparticles. The time-dependent thermal conductivity of water based CuO nanofluid shows that the thermal conductivity decreases with elapsed time due to clustering of nanoparticles. The clustering of nanoparticles are also confirmed microscopically. The experimental results show that the nanoparticle size, polydispersity, particle clustering and the volume fraction of particles in the suspensions have significant influence on thermal conductivity of suspensions. Acknowledgement We thank Dr. P.R. Vasudeva Rao and Dr. T. Jayakumar for support and encouragements. References [1] F.X. Redl, C.T. Black, G.C. Papaefthymiou, R.L. Sandstrom, M. Yin, H. Zeng, C.B. Murray, S. O’Brien, J. Am. Chem. Soc. 126 (2004) 14583. [2] I. Gur, N.A. Fromer, M.L. Geier, A.P. Alivistos, Science 310 (2005) 462. [3] A.S. Arico, P. Bruce, B. Scrosati, J.-M. Tarascon, W.V. Schalkwijk, Nat. Mater. 4 (2005) 366. [4] O. Tegus, E. Bruck, K.H.J. Buschow, F.R. de Boer, Nature 415 (2002) 150. [5] E. Hutter, J.H. Fendler, Adv. Mater. 16 (2004) 1685. [6] A.N. Goldstein, C.M. Echer, A.P. Alivistos, Science 256 (1992) 1425.
[7] R.L. Whetten, D.M. Cox, D.J. Trevor, A. Kaldor, Appl. Phys. Lett. 54 (1985) 1494. [8] M. Frietsch, F. Zudock, J. Goschnick, M. Bruns, Sens. Actuators B 65 (2000) 379. [9] Y.P. Sukhorukov, N.N. Loshkareva, A.A. Samokhvalov, S.V. Naumov, A.S. Moskvin, A.S. Ovchinnikov, J. Magn. Magn. Mater. 183 (1993) 356. [10] C.L. Cames, K.J. Klabunde, J. Mol. Cat. A Chem. 194 (2003) 227. [11] P.C. Dai, H.A. Mook, G. Aeppli, S.M. Hayden, F. Dogan, Nature 406 (2000) 965. [12] J.F. Xu, W. Ji, Z.X. Shen, S.H. Tang, X.R. Ye, D.Z. Jia, X.Q. Xin, J. Sol. State Chem. 147 (1999) 516. [13] C. Carel, M.M. Bahout, J.C.Gaude, Sol. State Ionics 117 (1999) 47. [14] R.A. Borzi, S.J. Stewart, R.C. Mercader, G. Punte, F. Garacia, J. Magn. Magn. Mater. 226 (2001) 1513. [15] T.X. Phuoca, Y. Soonga, M.K. ChyubPhuoc, Opt. Lasers Eng. 45 (2007) 1099. [16] G. Gnanaprakash, J. Philip, T.J. Kumar, B. Raj, J. Phys. Chem. B 111 (2007) 7978. [17] G. Gnanaprakash, J. Philip, B. Raj, Mater. Lett. 61 (2007) 4545. [18] G. Gnanaprakash, S. Mahadevan, T. Jayakumar, P. Kalyanasundaram, J. Philip, B. Raj, Mater. Chem. Phys. 103 (2007) 168. [19] G. Gnanaprakash, S. Ayyappan, T. Jayakumar, J. Philip, B. Raj, Nanotechnology 17 (2006) 5851. [20] J.-C. Bacri, R. Perzynski, D. Salin, V. Cabuil, R. Massart, J. Magn. Magn. Mater. 85 (1990) 27. [21] Z.S. Hong, Y. Cao, J.F. Deng, Mater. Lett. 52 (2002) 34. [22] R.V. Kumar, Y. Diamant, A. Gedanken, Chem. Mater. 12 (2000) 2301. [23] V.S. Gurin, A.A. Alexeenko, S.A. Zolotovskaya, K.V. Yumashev, Mater. Sci. Eng. C 26 (2006) 952. [24] Z.S. Li, Z. Hui, J. Yujie, Y. Deren, Nanotechnology 15 (2004) 1428. [25] J. Zhu, D. Li, H. Chen, X. Yang, L. Lu, X. Wang, Mater. Lett. 58 (2004) 3324. [26] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME, Nework, FED, vol. 231, 1995, p. 99. [27] S.U.S. Choi, Z. George, P. Keblinski, Encyclopedia Nanosci. Nanotechnol. 6 (2004) 757. [28] S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, J. Heat Transf. 121 (1999) 280. [29] T.-K. Hong, H.-S. Yang, C.J. Choi, J. Appl. Phys. 97 (1999) 280. [30] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, J. Appl. Phys. 78 (2001) 718. [31] C.H. Li, G.P. Peterson, J. Appl. Phys. 99 (2006) 084314. [32] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, J. Heat Transf. 125 (2003) 567. [33] J. Vadasz, S. Govender, p. Vadasz, Int. J. Heat Mass Transf. 1 (1987) 343. [34] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman, Int. J. Heat Mass Transf. 45 (2002) 855. [35] X.-Q. Wang, A.S. Mujumdar, Int. J. Thermal Sci. 46 (2007) 1. [36] J. Eapen, W.C. Williams, J. Buongiorno, L. Hu, S. Yip, R. Rusconi, R. Piazza, Phys. Rev. Lett. 99 (2007) 095901. [37] R. Prasher, P. Bhattacharya, P.E. Phelan, Phys. Rev. Lett. 94 (2005) 025901. [38] L.S. Zeven, G. Kimmel, in: I. Mureinik (Ed.), Quantitative X-ray Diffractometry, Springer-Verlag, New York, 1995. [39] L.S. Birks, H. Friedman, J. Appl. Phys. 17 (1946) 687. [40] S. Asbrisk, L.J. Norby, Acta Crystallogr. B 26 (1970) 8.
N.R. Karthikeyan et al. / Materials Chemistry and Physics 109 (2008) 50–55 [41] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grudle, Appl. Phys. Lett. 79 (2001) 2252. [42] S.P. Jang, S.U.S. Choi, Appl. Phys. Lett. 84 (2004) 4316. [43] K.S. Hong, T.K. Hong, H.S. Yang, Appl. Phys. Lett. 88 (2006) 031901. [44] C.-J. Yu, A.G. Richter, A. Datta, M.K. Durbin, P. Dutta, Phys. Rev. Lett. 82 (1999) 2326. [45] J.R. Henderson, F. van Swol, Mol. Phys. 51 (1984) 991–1010. [46] B.-X. Wang, I.P. Zhou, X.F. Peng, Int. J. Heat Mass Transf. 46 (2003) 2665. [47] R. Prasher, E. William, P. Meakin, F. Jacob, P. Patrick, P. Keblinski, App. Phys. Lett. 89 (2006) 143119.
55
[48] Y. Xuan, L. Qiang, Int. J. Heat Fluid Flow 21 (2000) 58. [49] J. Philip, P.D. Shima, B. Raj, Appl. Phys. Lett. 91 (2007) 203108. [50] M.S. Liu, M.C.C. Lin, I. Huang, C.C. Wang, Chem. Eng. Techn. 29 (2006) 71. [51] D.H. Kumar, E.H. Patel, V.R. Rajeev, T. Sundararajan, T. Pradeep, S.K. Das, Phys. Rev. Lett. 93 (2004) 144301. [52] M.-S. Liu, M.C.-C. Lin, C.Y. Tsai, C.-C. Wang, Int. J. Heat Mass Transf. 49 (2006) 3028. [53] X. Wang, X. Xu, S.U.S. Choi, J. Thermophys. Heat Transf. 13 (2002) 4568.
Materials Chemistry and Physics 109 (2008) 50–55
Effect of clustering on the thermal conductivity of nanofluids N.R. Karthikeyan, John Philip ∗ , Baldev Raj Metallurgy & Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India Received 16 August 2007; received in revised form 23 October 2007; accepted 27 October 2007
Abstract We synthesis CuO nanoparticles of average diameter 8 nm by a simple precipitation technique and study the thermal properties of the suspensions. The thermal conductivity enhancement observed in water and ethylene glycol based nanofluids with 1 vol.% CuO nanoparticles loading are 31.6 and 54%, respectively. The large enhancement in thermal conductivity is attributed to the finer particle size and monodispersity of nanoparticles. It has been found that the thermal conductivity of the nanofluid increases nonlinearly with the volume fraction of nanoparticles. The time-dependent thermal conductivity in water based CuO nanofluid shows that the thermal conductivity decreases with elapsed time due to clustering of nanoparticles with time, as confirmed microscopically. The experimental results show that the nanoparticles size, polydispersity, cluster size and the volume fraction of particles have a significant influence on thermal conductivity. © 2007 Elsevier B.V. All rights reserved. Keywords: CuO nanoparticles; Nanofluid; Thermal properties; Heat transfer fluid
1. Introduction It has been demonstrated that at nano-scale it is possible to fine tune the electrical, optical, mechanical, thermal and chemical properties by modifying the size and shape of the nano materials [1–7]. An understanding of the process of particle growth is a prerequisite to tailor nanoparticles of desired size and properties. Among the nanocrystals, copper oxide (CuO) nanoparticles have many technological applications such as gas sensors [8], magnetic phase transistor [9], catalysts [10], and high temperature superconductors [11]. Conventional technique to prepare CuO nanoparticles includes thermal decomposition [12], mechanical milling [13], single step solid state reaction, etc. [14]. Very recently an interesting scheme to synthesis of metal nanoparticles in deionized water, using multi-beam laser ablation in liquids, is reported [15], where the laser parameters that control the nanoparticles size and distribution has been studied. Many other routes are used for production of ultrapure nanoparticles like co-precipitation [16–20] alcohol-thermal [21], sonochemical technique [22], sol–gel [23] and hydrothermal [24]. In our study, we synthesized CuO nanoparticles by a novel quick precipitation technique [25].
∗
Corresponding author. Tel.: +91 94 431 51 536; fax: +91 44 27480356. E-mail address: [email protected] (J. Philip).
0254-0584/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2007.10.029
Nanofluids are a new kind of heat transfer fluid containing a very small quantity of nanoparticles that are stably suspended in a carrier liquid [26]. Fluids have typically very low thermal conductivity compared with crystalline solids. However, a dispersion with small amount of solid nanoparticles in traditional fluid dramatically changes their thermal conductivities [27]. Nanofluids containing ceramic or metallic nanoparticles showed large enhancement of thermal conductivity that cannot be explained by conventional theories [28]. Many factors, such as particle size, surfactant coating, carrier fluid, etc., have an effect on the thermal conductivity of the nanofluid. The stability of suspension is one of the crucial factors required for improving the thermal conductivity of the fluid and its applications as an efficient coolant [29]. The most common techniques used to measure the effective thermal conductivity of nanoparticle suspensions is transient hot wire method [30], steady state method [31], temperature oscillation method [32] and hot strip method [33]. In all these techniques, the natural convention of the base fluid can affect the heat flow mechanism and hence induce some additional error. In spite of many experimental and theoretical studies to understand the mechanism and thermal characteristic of nanofluid, the science behind the thermal conductivity enhancement is still unclear [34–37]. Herein, we undertake systematic studies to understand the parameters affecting the thermal conductivity in water and ethylene glycol based CuO nanofluids and
N.R. Karthikeyan et al. / Materials Chemistry and Physics 109 (2008) 50–55
51
the effect clustering on the thermal conductivity of the nanofluids. 2. Experimental For synthesis of CuO nanoparticles, Cu (CH3 COO)2 ·2H2 O, CH3 COOH, and solid NaOH are procured from E-Merck. All the chemicals were GR grade and used without any further purification. In our typical procedure, 600 ml of 0.2 M copper acetate aqueous solutions is mixed with 2 ml glacial acetic acid in a round bottomed flask. Under vigorous stirring, 0.16 g of solid NaOH (pellets) is added rapidly to the boiling solution at 100 ◦ C, until the pH value of the mixture is reached 6–7. At this stage, the color of the solutions changes from blue to black and a black precipitate is produced simultaneously. After cooling to room temperature, the precipitate is centrifuged, washed twice with triply distilled water, ethanol and acetone and finally dried at room temperature. Techniques for suspending nanoparticles are crucial to make stable and uniformly dispersed nanofluid. A known amount of dried nanoparticle is mixed with water or ethylene glycol base fluid. The suspension is then homogenized by using an ultrasonic horn (Vibronic ultrasonic processor P1-250 W), for 30 min. Using this method, stable fluids are prepared without addition of surfactants. The different volume fractions of CuO nanoparticles suspension in water and ethylene glycol are prepared by this approach.
Fig. 1. The XRD pattern of CuO nanoparticles prepared by precipitation route.
4. Results and discussion 4.1. Crystal structure and particle size
3. Characterization Philips-X’pert MPD® X-ray diffaractometer is used to obtain X-ray diffraction pattern of the particles. 2θ values are taken ˚ with a from 20 to 80◦ using Cr K␣ radiation (λ = 2.2897 A) step size of 0.04◦ . Acquisition and preliminary analysis of the data were performed by the Philips X’pert Pro® software and the XRD patterns were verified by comparing with the JCPDS data. Thin layered dried powder (25 ± 3 mg) spread over 5 cm2 plate area is prepared to minimize the error in peak location and also the broadening of peaks due to reduced thickness of the particle [38]. The broadening of the peak at full width half maximum (FWHM), is related to the average diameter (d) of the particles according to Debye–Scherrer’s formula [39], i.e. d = 0.9λ/B cos θ, where λ is X-ray wavelength, B is line broadening measured at half height and θ is Bragg angle. The average particles size is obtained from most predominant peak, corresponding to (1 1 1) reflection by using Debye–Scherrer formula. The transmission electron microscopy (TEM) instrument used is a Philips CM12 with an acceleration voltage of 100 kV. One drop of CuO dispersion is placed on carbon coated copper grid (0.3 cm diameter, mesh size of 300 holes cm−1 ) and left to dry for 1 h at room temperature. The thermal conductivity of CuO nanofluid is measured by monitoring of heat dissipation from a line heat source. When a long, electrically heating probe is applied to the fluid, the rise in temperature is calculated using the equation: T − T0 ∼ =
q 4πλh
ln(t) − γ − ln
r2 4k
The XRD pattern of CuO nanoparticles shown in Fig. 1. It has been found that the nanoparticles are single-phase CuO with monoclinic structure. Further comparison of the XRD patterns with the JCPDS file (JCPDS 80-1268) data also confirms ˚ b = 3.42 A, ˚ and the same. The lattice constants a = 4.68 A, ˚ obtained from the pattern are consistent with the litec = 5.12 A, rature values [40]. No impurity peaks are observed in the XRD pattern. The broadening of the most predominant peak (1 1 1) indicates the smaller particles size. Average size of the CuO particles is estimated to be 7.7 nm according to the Debye–Scherrer equation [39]. The typical transmission electron microscopy (TEM) image of the as-prepared CuO nanoparticles is shown in Fig. 2. From the micrograph, it is clear that the specimen consists of spherical
(1)
where T is temperature, t time, k is thermal diffusivity, r is radial distance, q is the heat produced per unit length per unit time, λh is the thermal conductivity of the medium, γ is Euler’s Constant (0.5772).
Fig. 2. The TEM image of CuO nanoparticles.
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Fig. 3. The ratio of thermal conductivity of water based CuO nanofluid and the percentage of enhancement of thermal conductivity as a function of volume fraction.
particles with narrow size distribution and the particles are well dispersed. The size of the particles observed in the TEM image is in the range of 7–9 nm, in good agreement with that result obtained from the XRD pattern. 4.2. Thermal properties of CuO nanofluid Figs. 3 and 4 shows the thermal conductivity ratio and percentage enhancement as a function of volume fraction in water and ethylene glycol based CuO nanofluids respectively. To the best of our knowledge, this is the first experimental report on nanofluid containing fairly monodispersed CuO particles of 8 nm diameter. From Figs. 3 and 4, it is apparent that the thermal conductivity of CuO nanofluid increases nonlinearly with increase in volume fraction of the nanoparticles, as observed earlier [41]. Despite considerable efforts for optimizing the synthesizing parameters, it is quite possible that the processing of CuO nanoparticles can results in incomplete oxidation that results in the presence of a small amount of unoxidizied Cu atoms on the surface of the
Fig. 4. The ratio of thermal conductivity and percentage of enhancement of thermal conductivity as a function of volume fraction in ethylene glycol based CuO nanofluid.
nanoparticles. This could be the reason for the enhanced thermal conductivity. As heat transfer in solid\liquid suspension occurs at the particle–fluid interface, an increase in the interfacial area can lead to more efficient heat transfer properties. The existing theoretical models fail to work when the nanofluid contain particles of less than 10 nm. One major assumption, in the models are that the particles are motionless in the fluid, which is a wrong assumption for nanofluids [42]. This assumption is contradicting to the fact that the nanoparticle exhibits Brownian movement when suspended in a liquid. As a result of Brownian motion, the fluid molecule in the immediate vicinity creates a locally ordered micro-convection effect around each particle within the base fluid [31–37]. It is believed, that this ordered arrangement of molecule lead to heat transfer enhancement in the fluid. Therefore, adding nanoparticles to the fluid results in two possible effects—higher thermal conductivity enhancement due to formation of highly ordered arrangement of molecule around each particles and the other effect is the stirring action caused by Brownian motion of the particles. As the particles size decreases, the motion becomes larger, that could contribute to larger thermal conductivity enhancement [42,43]. Therefore, small nanoparticles are better for maximum enhancement of thermal conductivity of the fluid. Presently, it is believed that the enhancement in thermal conductivity in a colloidal dispersion is mainly due to microconvection caused by the Brownian motion of the nanoparticles and aggregation of nanoparticles causing a local percolation [37,47]. Heat conduction in nanoparticles is assumed to be ballistic in nature, which is associated with the large phonon mean-free path in the nanoparticles. Basically, ballistic conduction of heat is much faster than thermal diffusion. There are several factors which will limit the ballistic conduction in nanoparticles [41]. Recent studies show that liquid molecules form a highly ordered structure very much like in solid at the interface between solid and liquid [34,41–45]. Although, the presence of an interfacial layer may play a role in heat transport, it is unlikely to be the sole reason for the thermal conductivity enhancement. Clustering to the nanoparticles occurs more actively in fluid with higher concentration. This clustering has major impact on the thermal conductivity measurement of the fluid. When the nanofluid is sonicated, the cluster breaks into primary nanoparticles. There has been some works on the effect of sonication time on thermal conductivity of nanofluids [43]. The nano-clusters are likely to settle in the fluid due to larger mass that results in particle gradient in the fluid. The “particle free” zone has higher thermal resistance compared particle rich zone. The suppression of clustering of the nanoparticles is also very important for designing effective heat transfer fluids. There are some reports on the formation of clusters and aggregates in the fluid that enhance the thermal conductivity of the fluid [46,47]. It is believed that the heat transport can be much faster along the back bone of the clusters. A comparison of thermal conductivity results from various studies in CuO nanofluid is shown in Table 1. As the particle size decreases, the surface to volume ratio gets increases, which leads to large enhancement in the thermal conductivity of the fluid since heat transfer is a surface phenomenon. The comparison of the experimental data suggest that thermal conductivity of base
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Table 1 Thermal conductivity data from various studies in CuO nanofluid Size (nm)
Base fluid
Thermal conductivity enhancement (%) & volume fraction of particles
Reference
36 23.6
Water Ethylene Glycol(EG) water EG Water Water EG
60% for 5 vol.% 20% for 4 vol.%
[29] [28]
12% for 3 vol.% 4% for 1 vol.% 52% for 6 vol.% 31% for 1 vol.% 54% for 1 vol.%
[53] [50] [31] Present Present
23 30.8 29 8 8
fluid, particles, volume fraction of particles and the particle size play a dominant role in the thermal conductivity enhancement in a nanofluid. The sedimentation in CuO nanofluid is observed when the nanoparticles concentration was above 1 vol.%. Below 1 vol.%, the CuO nanofluids were quite stable for more than after 3 week. To produce a stable nanofluid, either the particles size should be small enough to be suspended by Brownian motion or the particles must be protected against aggregation by electric charge or other protective coatings. The stability of nanoparticles in the fluid has a major impact on the effective thermal conductivity of the fluid [48,49]. In our studies, the volume fraction of CuO nanoparticle suspension in both water and ethylene glycol is varied from 0.01 to 1%. It is well recognized that the effective thermal conductivity of nanoparticles suspension is not simply a function of the particle loading in the base fluid [34,35]. As the size of CuO nanoparticle is very small, even at very low volume fraction, their suspensions in both water and ethylene glycol are stable. Furthermore, nanoparticles suspensions show excellent kinetic stability as a result of enhanced Brownian motion of the nanoparticles in the base fluid. Earlier studies reveal that the EG based CuO nanofluid (4 vol.%, 23.6 nm) exhibits 20% increase in effective thermal conductivity of the fluid [28], 60% in water based CuO nanofluid (5 vol.%, diameter 36 nm) [30] and 52% for water based CuO nanofluid (6 vol.%, diameter 29 nm) [31] and very recently, 22% increase in effective thermal conductivity of CuO (5 vol.%, diameter 30–50 nm) is achieved [50]. Compared to previous results [28,30,31,50], the observed increase in effective thermal conductivity is quite significant, as the volume fractions used in our experiments were low compared to the previous studies. For 0.01 v fraction of CuO (water) nanofluid, the thermal conductivity enhancement is 31.6%, whereas for the same volume fraction in ethylene glycol, the thermal conductivity enhancement is 54.16%. The large variations in the thermal conductivity of ethylene glycol and water based nanofluid shows that the base fluid also plays role in thermal conductivity of nanofluid [31]. We speculate that the presence of some un-oxidized copper atom on the surface of copper oxide nanoparticles contributes to the large increase in thermal conductivity of CuO nanofluid. The TEM image reveals that the particles are highly mono-dispersed with average size about 8 nm and are spherical in shape. The
Fig. 5. The time-dependent characteristic of CuO-water nanofluid.
mono-dispersity of the particles may also have an influence on the thermal conductivity enhancements due to negligible sedimentation. Compared with conventional micron sized particles, the surface to volume ratio of nanoparticles is very high. For instance, the surface area to volume ratio of particles with 10 nm is thousand times greater than conventional particles with size 10 m [28]. Thus by using nanoparticles of smaller size the thermal properties of the liquid can be enhanced effectively. Earlier studies reveal that nanofluids with finer nanoparticles exhibit better thermal conductivity compared to fluids containing coarse particles [30,51]. Fig. 5 shows the ratio of thermal conductivity as a function of time. It has been observed that the thermal conductivity decreases with elapsed time. Initially, the effective thermal conductivity of water based CuO nanofluid with concentration 0.8 and 0.3 vol.% were 1.225 and 1.175, respectively, which decreases with increasing time, probably due to appreciable particle agglomeration. The ratio k/kw is almost unity after an elapsed time of 14 min. Similar trend is observed in water based Cu nanofluids [52] and Fe based nanofluid [29]. It has also been observed that the thermal conductivity decrease with the cluster size [29]. In general, it is accepted that heat transfer is a surface phenomenon and the thermal energy interaction takes places at the surface of nanoparticles. When the particles get agglomerated, the effective surface area to volume ratio decreases, thus reducing the effective area of thermal interaction of particles causing a decrease in the thermal conductivity of the fluid. It has been observed that the thermal conductivity of the fluid is increased with decrease in particles size [34,51]. Microscopic observation of the suspension (water based CuO nanofluid of 0.1 vol.%) with time shows formation of aggregates in the nanofluid and the size of the aggregate increases with time. The clusters as large as few m have been observed several minutes after the sonification. As the cluster size increases, the sedimentation rate also increases and hence the number of primary particles available for the heat transport is reduced. The mesh like structures are formed in the nanofluid suspension at time intervals of 20, 60 and 70 min after sonication
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Fig. 6. Mesh-like structure observed, in water based CuO nanofluid of 0.1 vol.%, after sonication for (a) 20 min, (b) 60 min and (c) 70 min.
is shown in Fig. 6a–c, respectively. It can be seen the structure formation begins only after 60 min from the sonication. When the mesh-like structures are formed the thermal conductivity begins to drop. The size of cluster not only depends on average particle diameter but also the particle concentration in the fluid. The higher the particle concentration in the fluid, the smaller the inter-particle distance between the particles, as a result the probability of agglomeration is more due to van der Waals attraction. 5. Conclusion In this paper, we investigated the parameters influencing the thermal conductivity enhancement in water and ethylene glycol based nanofluids of CuO nanoparticles of average diameter 8 nm. The thermal conductivity enhancement observed with 1 vol.% of CuO nanoparticles is 54%, which is the highest value reported for CuO nanofluid. The large enhancement in thermal conductivity is attributed to the smaller particle size and monodispersity of particles. The thermal conductivity of nanofluid increases nonlinearly with the volume fraction of nanoparticles. The time-dependent thermal conductivity of water based CuO nanofluid shows that the thermal conductivity decreases with elapsed time due to clustering of nanoparticles. The clustering of nanoparticles are also confirmed microscopically. The experimental results show that the nanoparticle size, polydispersity, particle clustering and the volume fraction of particles in the suspensions have significant influence on thermal conductivity of suspensions. Acknowledgement We thank Dr. P.R. Vasudeva Rao and Dr. T. Jayakumar for support and encouragements. References [1] F.X. Redl, C.T. Black, G.C. Papaefthymiou, R.L. Sandstrom, M. Yin, H. Zeng, C.B. Murray, S. O’Brien, J. Am. Chem. Soc. 126 (2004) 14583. [2] I. Gur, N.A. Fromer, M.L. Geier, A.P. Alivistos, Science 310 (2005) 462. [3] A.S. Arico, P. Bruce, B. Scrosati, J.-M. Tarascon, W.V. Schalkwijk, Nat. Mater. 4 (2005) 366. [4] O. Tegus, E. Bruck, K.H.J. Buschow, F.R. de Boer, Nature 415 (2002) 150. [5] E. Hutter, J.H. Fendler, Adv. Mater. 16 (2004) 1685. [6] A.N. Goldstein, C.M. Echer, A.P. Alivistos, Science 256 (1992) 1425.
[7] R.L. Whetten, D.M. Cox, D.J. Trevor, A. Kaldor, Appl. Phys. Lett. 54 (1985) 1494. [8] M. Frietsch, F. Zudock, J. Goschnick, M. Bruns, Sens. Actuators B 65 (2000) 379. [9] Y.P. Sukhorukov, N.N. Loshkareva, A.A. Samokhvalov, S.V. Naumov, A.S. Moskvin, A.S. Ovchinnikov, J. Magn. Magn. Mater. 183 (1993) 356. [10] C.L. Cames, K.J. Klabunde, J. Mol. Cat. A Chem. 194 (2003) 227. [11] P.C. Dai, H.A. Mook, G. Aeppli, S.M. Hayden, F. Dogan, Nature 406 (2000) 965. [12] J.F. Xu, W. Ji, Z.X. Shen, S.H. Tang, X.R. Ye, D.Z. Jia, X.Q. Xin, J. Sol. State Chem. 147 (1999) 516. [13] C. Carel, M.M. Bahout, J.C.Gaude, Sol. State Ionics 117 (1999) 47. [14] R.A. Borzi, S.J. Stewart, R.C. Mercader, G. Punte, F. Garacia, J. Magn. Magn. Mater. 226 (2001) 1513. [15] T.X. Phuoca, Y. Soonga, M.K. ChyubPhuoc, Opt. Lasers Eng. 45 (2007) 1099. [16] G. Gnanaprakash, J. Philip, T.J. Kumar, B. Raj, J. Phys. Chem. B 111 (2007) 7978. [17] G. Gnanaprakash, J. Philip, B. Raj, Mater. Lett. 61 (2007) 4545. [18] G. Gnanaprakash, S. Mahadevan, T. Jayakumar, P. Kalyanasundaram, J. Philip, B. Raj, Mater. Chem. Phys. 103 (2007) 168. [19] G. Gnanaprakash, S. Ayyappan, T. Jayakumar, J. Philip, B. Raj, Nanotechnology 17 (2006) 5851. [20] J.-C. Bacri, R. Perzynski, D. Salin, V. Cabuil, R. Massart, J. Magn. Magn. Mater. 85 (1990) 27. [21] Z.S. Hong, Y. Cao, J.F. Deng, Mater. Lett. 52 (2002) 34. [22] R.V. Kumar, Y. Diamant, A. Gedanken, Chem. Mater. 12 (2000) 2301. [23] V.S. Gurin, A.A. Alexeenko, S.A. Zolotovskaya, K.V. Yumashev, Mater. Sci. Eng. C 26 (2006) 952. [24] Z.S. Li, Z. Hui, J. Yujie, Y. Deren, Nanotechnology 15 (2004) 1428. [25] J. Zhu, D. Li, H. Chen, X. Yang, L. Lu, X. Wang, Mater. Lett. 58 (2004) 3324. [26] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME, Nework, FED, vol. 231, 1995, p. 99. [27] S.U.S. Choi, Z. George, P. Keblinski, Encyclopedia Nanosci. Nanotechnol. 6 (2004) 757. [28] S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, J. Heat Transf. 121 (1999) 280. [29] T.-K. Hong, H.-S. Yang, C.J. Choi, J. Appl. Phys. 97 (1999) 280. [30] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, J. Appl. Phys. 78 (2001) 718. [31] C.H. Li, G.P. Peterson, J. Appl. Phys. 99 (2006) 084314. [32] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, J. Heat Transf. 125 (2003) 567. [33] J. Vadasz, S. Govender, p. Vadasz, Int. J. Heat Mass Transf. 1 (1987) 343. [34] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman, Int. J. Heat Mass Transf. 45 (2002) 855. [35] X.-Q. Wang, A.S. Mujumdar, Int. J. Thermal Sci. 46 (2007) 1. [36] J. Eapen, W.C. Williams, J. Buongiorno, L. Hu, S. Yip, R. Rusconi, R. Piazza, Phys. Rev. Lett. 99 (2007) 095901. [37] R. Prasher, P. Bhattacharya, P.E. Phelan, Phys. Rev. Lett. 94 (2005) 025901. [38] L.S. Zeven, G. Kimmel, in: I. Mureinik (Ed.), Quantitative X-ray Diffractometry, Springer-Verlag, New York, 1995. [39] L.S. Birks, H. Friedman, J. Appl. Phys. 17 (1946) 687. [40] S. Asbrisk, L.J. Norby, Acta Crystallogr. B 26 (1970) 8.
N.R. Karthikeyan et al. / Materials Chemistry and Physics 109 (2008) 50–55 [41] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grudle, Appl. Phys. Lett. 79 (2001) 2252. [42] S.P. Jang, S.U.S. Choi, Appl. Phys. Lett. 84 (2004) 4316. [43] K.S. Hong, T.K. Hong, H.S. Yang, Appl. Phys. Lett. 88 (2006) 031901. [44] C.-J. Yu, A.G. Richter, A. Datta, M.K. Durbin, P. Dutta, Phys. Rev. Lett. 82 (1999) 2326. [45] J.R. Henderson, F. van Swol, Mol. Phys. 51 (1984) 991–1010. [46] B.-X. Wang, I.P. Zhou, X.F. Peng, Int. J. Heat Mass Transf. 46 (2003) 2665. [47] R. Prasher, E. William, P. Meakin, F. Jacob, P. Patrick, P. Keblinski, App. Phys. Lett. 89 (2006) 143119.
55
[48] Y. Xuan, L. Qiang, Int. J. Heat Fluid Flow 21 (2000) 58. [49] J. Philip, P.D. Shima, B. Raj, Appl. Phys. Lett. 91 (2007) 203108. [50] M.S. Liu, M.C.C. Lin, I. Huang, C.C. Wang, Chem. Eng. Techn. 29 (2006) 71. [51] D.H. Kumar, E.H. Patel, V.R. Rajeev, T. Sundararajan, T. Pradeep, S.K. Das, Phys. Rev. Lett. 93 (2004) 144301. [52] M.-S. Liu, M.C.-C. Lin, C.Y. Tsai, C.-C. Wang, Int. J. Heat Mass Transf. 49 (2006) 3028. [53] X. Wang, X. Xu, S.U.S. Choi, J. Thermophys. Heat Transf. 13 (2002) 4568.