New Measurements of the Apparent Thermal Conductivity of Nanofluids and Investigation of Their Heat Transfer Capabilities

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1 This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. pubs.acs.org/jced New Measurements of the Apparent Thermal Conductivity of Nanofluids and Investigation of Their Heat Transfer Capabilities Georgia J. Tertsinidou, Chrysi M. Tsolakidou, Maria Pantzali, and Marc J. Assael* Laboratory of Thermophysical Properties & Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54636, Greece Laura Colla, Laura Fedele, and Sergio Bobbo Downloaded via on January 22, 2019 at 19:15:49 (UTC). See for options on how to legitimately share published articles. Consiglio Nazionale delle Ricerche, Istituto per le Tecnologie della Costruzione, Corso Stati Uniti 4, Padova 35127, Italy William A. Wakeham Chemical Engineering Department, Imperial College London, London SW7 2BY, U.K. ABSTRACT: The aim of this paper is to investigate in depth whether adding nanoparticles or nanotubes to a fluid enhances its heat transfer capabilities. For this reason, the thermal conductivities and viscosities of a selection of nanofluids were thoroughly examined. The systems studied were (a) ethylene glycol with added CuO, TiO 2,orAl 2 O 3 nanoparticles and (b) water with TiO 2 or Al 2 O 3 nanoparticles or multiwall carbon nanotubes (MWCNTs). All of the measurements were conducted at K. In a very recent paper, it was shown that instruments employing the transient hot-wire technique can produce excellent measurements when a finite element method (FEM) is employed to describe the instrument for the geometry of the hot wire. Furthermore, it was shown that an approximate analytic solution can be employed with equal success over the time range from 0.1 to 1 s, provided that four specific criteria are satisfied. Subsequently a transient hot-wire instrument was designed, constructed, and employed for the measurement of the thermal conductivities of nanofluids with an uncertainty of about 2%. A second, validated technique, namely, a hot-disk instrument, was also employed to conduct measurements on some of the systems to provide mutual support for the results of the thermal conductivity measurements. To investigate the effect of any enhancement of the thermal conductivity of the fluids on their application in practical heat transfer, the viscosities of typical concentrations of several of the nanofluids were also measured. A parallel-plate rotational rheometer, able to measure the viscosities of Newtonian and non-newtonian liquids with an uncertainty of better than 5%, was employed for these measurements because most of the nanofluids considered showed behavior comparable to a Bingham plastic. All of these measurements have allowed an investigation of the change in the heat transfer capability of the base fluid when nanoparticles or MWCNTs are added to it for a typical heat exchanger. It is shown that in general the combined changes in physical properties that accompany suspension of nanoparticles in fluids mean that the heat transfer benefits are all rather modest, even when they are achieved. 1. INTRODUCTION The aim of this paper is to investigate in depth whether adding nanoparticles or nanotubes to a fluid enhances its heat transfer capabilities. For this reason, the thermal conductivities and viscosities of a selection of nanofluids were thoroughly examined. The systems studied were (a) ethylene glycol with added CuO, TiO 2,orAl 2 O 3 nanoparticles and (b) water with added TiO 2 or Al 2 O 3 nanoparticles or multiwall carbon nanotubes (MWCNTs) at K. In a very recent paper, 1 the conditions that are necessary to secure accurate measurements of the apparent thermal conductivities of two-phase systems comprising nanoscale particles of one material suspended in a fluid phase of a different material were carefully examined. It was shown that instruments operating according to the transient hot-wire technique can produce excellent measurements with an uncertainty of better than 0.5% when a finite element method (FEM) is employed to describe the operation of the instrument for the geometry of the hot wire. Furthermore, it was shown that an approximate analytic solution can be employed with equal success over the time range from 0.1 to 1 s provided that (a) two wires are employed, so that end effects are canceled; (b) each wire is very thin (less than 30 μmin Received: August 30, 2016 Accepted: October 25, 2016 Published: November 16, American Chemical Society 491

2 diameter), so that the line source model and the corresponding corrections are valid; (c) low values of the temperature rise (less than 4 K) are employed in order to minimize the effect of convection on the heat transfer by conduction in the time of measurement of 1 s; and (d) insulated wires are employed for measurements in electrically conducting or polar liquids to avoid current leakage or other electrical distortions. According to these criteria, a transient hot-wire instrument was designed, constructed, and commissioned. 1 Because the systems included in this study are not a single phase, the apparent thermal conductivity is not a thermophysical property of the system dependent only on the thermodynamic state parameters for a single phase, and the quantity measured may depend upon the method of measurement. For that reason, we also employed a second validated technique, namely, a hot-disk instrument, able to measure thermal conductivity with an uncertainty of 5%. The principal interest in nanofluids has been driven by an argument that their enhanced thermal conductivity, relative to that of the base fluid, makes them superior agents for heat transfer in a variety of circumstances. In order to test this argument rigorously, we also measured the viscosities of typical concentrations of the above nanofluids. A parallel-plate rotational rheometer, able to measure the viscosities of Newtonian and non-newtonian liquids with an uncertainty of better than 5%, was employed for these measurements because the nanofluids considered display the character of a Bingham plastic. Finally, we examined the performance of the studied nanofluids in a typical heat exchanger relative to the performance of the base fluid on its own. 2. PREPARATION AND CHARACTERIZATION OF NANOFLUIDS 2.1. Nanofluid Preparation. In the present study, two different groups of nanofluids were examined, which are detailed in Table 1. The first group included ready-made nanofluids provided by a commercial source, while the second group consisted of nanofluids prepared in our laboratory using the twostep method. In the case of ready-made nanofluids, poly- (vinylpyrrolidone) (PVP) was employed as a dispersant in the samples provided by the supplier. We note here that although PVP produces very good and stable solutions, as is necessary for industrial use, it also increases the viscosity of the material compared with those of systems without such a dispersant. In the case of MWCNTs, a nonionic dispersant (no further information was provided by the supplier) was employed Ready-Made Nanofluids. All of the ready-made nanofluids were purchased from US Research Nanomaterials, Inc. The original nanoparticles concentration was 20 mass % in all cases except case 6 in Table 1, while the MWCNT concentration was 3 mass %. In order to produce fluids with different particle volume fractions, dilution with deionized water or ethylene glycol followed by a stirring action was employed Nanofluids Prepared in Our Laboratory. The CuO and Al 2 O 3 nanoparticles were obtained from US Research Nanomaterials Inc., while the TiO 2 nanoparticles were purchased from Nanostructured & Amorphous Materials, Inc. Desired solutions were made using the two-step method. First of all, the masses of the solid and liquid phases were determined by means of a precision balance. It may be mentioned here that the true density of particles (neglecting the mass of air trapped inside), can be up to 20 times the apparent bulk density, as shown in Table 2. Table 2. True and Bulk Densities of Nanopowders As Given by the Corresponding Suppliers density/(kg m 3 ) nanopowder true bulk CuO (40 or >80 nm) TiO 2 (5 nm) Al 2 O 3 (5 nm) Because it is the volume fraction of the particles in the suspension that is the relevant parameter for comparison with the most relevant theories of transport in nanofluids, e.g., the Hamilton Crosser model, 2 we need the true density of the nanoparticles to derive this quantity from the known masses of the materials. No dispersant was added. Following weighing, the liquid and solid phases were mixed, and homogenization was implemented with an ultrasonic vibrator (HF-generator GM2200, Bandelin) which was employed to sonicate the solution continuously for about 1 h in order to break down any existing agglomerations. The time period of 1 h was found to be the optimum sonication time because additional sonication time had no further effect on the stability of the sample. During the sonication period, it was crucial to avoid dissipative heating of the sample, and thus, an external water bath was employed to keep the temperature at ambient conditions. Table 1. Nanofluids (in Water or Ethylene Glycol) and Nanopowders Purchased a nanopowder + nanofluid diameter/nm dispersant or stabilizer b company c 1 CuO < CuO rutile TiO 2 (20%) + H 2 O % PVP 1 4 rutile TiO 2 (15%) + H 2 O % PVP 1 5 rutile TiO 2 (20%) + C 2 H 6 O % PVP 1 6 TiO γ-al 2 O 3 (20%) + H 2 O 30 1% PVP 1 8 γ-al 2 O 3 (20%) + H 2 O 10 1% PVP 1 9 γ-al 2 O 3 (20%) + C 2 H 6 O % PVP 1 10 hydrophilic γ-al 2 O MWCNTs (3%) + H 2 O 5 15 (50 μm length) 2% nonionic 1 12 MWCNTs (3%) + H 2 O (10 20 μm length) 2% nonionic 1 a All percentages are in mass percent. b PVP = poly(vinylpyrrolidone). c Companies: (1) US Research Nanomaterials, Inc.; (2) Nanostructured & Amorphous Materials, Inc. 492

3 This procedure ensured that all of our suspensions were stable for at least 2 3 h. Even though in many practical applications a suitable third agent is employed to stabilize the particles, this was not desirable in the present study for two reasons: (a) the time required for the experiments was much less than the time required for the first sedimentation to occur, and (b) the addition of a third agent may further influence the thermal conductivity or the viscosity of the system itself, as we observed above. Finally, we note that it was impossible to obtain a stable suspension of CuO nanoparticles (40 and <80 nm diameter) in water without a dispersant. Thus, we studied only its dispersion in ethylene glycol, where the same problem was not encountered Transmission Electron Microscopy Analysis. To illustrate that the above preparation procedure resulted in uniform suspensions, indirect transmission electron microscopy (TEM) analysis of the suspensions of Al 2 O 3 nanoparticles as well as of MWCNTs in water are discussed here as examples. For the TEM analysis, the samples were prepared by placing a drop of the respective nanofluid on the sample holder and drying it at ambient temperature to evaporate. This process is indicative of the state of dispersion of the nanoparticles in the suspension because the shapes and sizes of the nanoparticles can be observed, but not, of course, the intrinsic three-dimensional (3D) dispersion of the nanoparticles in the fluid Al 2 O 3 Nanoparticles in Water. Two separate cases were considered. First, to investigate the effect of sonication, TEM of evaporated suspensions of 5 nm diameter nanoparticles in water prepared in this work (a) without sonication and (b) after applying 1 h of sonication were examined. Second, to investigate the effect of PVP addition, TEM of evaporated suspensions of 10 nm diameter nanoparticles in water with 1 mass % PVP (purchased from US Research Nanomaterials, Inc.) was also examined Effect of Sonication. Figures 1 and 2 depict TEM images, with the corresponding selected-area electron diffraction Figure 2. TEM image of 5 nm diameter Al 2 O 3 nanoparticles in water prepared in the laboratory with 1 h of sonication and (inset) the corresponding SAED pattern. shows the same nanofluid with sonication for 1 h. It can be seen that for both cases examined, the average particle size is about 5 nm and the shape of the nanoparticles seems to be uniformly spherical. In a compariso of the two figures, it can be seen that Figure 1 shows a higher degree of agglomeration, as indicated by the closely packed nanoparticles, while in Figure 2 the much more loosely connected Al 2 O 3 particles indicate a lower degree of agglomeration. In all cases, the SAED pattern consists of concentric circles with light spots, characteristic of a polycrystalline sample. The circles and positions of the light spots in the SAED pattern are typical of high-purity γ-alumina for both cases. The spots are not so pronounced in Figure 2, indicative of the better dispersion of the particles in the suspension. Therefore, it is clear that 1 h of sonication produced a more uniform suspension with a much lower degree of agglomeration Effect of Dispersant. Figure 3 depicts a TEM image and (inset) the corresponding SAED pattern of an evaporated Figure 1. TEM image of 5 nm diameter Al 2 O 3 nanoparticles in water prepared in the laboratory without sonication and (inset) the corresponding SAED pattern. Figure 3. TEM image of 10 nm diameter Al 2 O 3 nanoparticles in water with PVP and (inset) the corresponding SAED pattern. (SAED) patterns as insets. SAED is a crystallographic experimental technique performed inside a transmission electron microscope that results in a diffraction pattern characteristic of the sample s nanoparticulate crystal structure. Figure 1 shows the nanofluid prepared in the laboratory by adding a specific amount of Al 2 O 3 nanoparticles with a nominal diameter of 5 nm in deionized water without employing sonication, while Figure 2 sample of 10 nm diameter Al 2 O 3 nanoparticles suspended in water containing 1 mass % PVP. No sonication was employed, and the sample was used as purchased. It can be seen that the average particle size is on the order of nm and that the shape of the nanoparticles seems to be cylindrical, in contrast with the spherical shape observed in section In this case, it seems that no agglomerates are present, which can be attributed 493

4 to the presence of PVP, which causes a better distribution. The presence of PVP can be seen as lighter-colored spots on the surface of the particles, as shown in Figure 4 (4 times higher resolution than in Figure 3). Figure 6. TEM image of 5 15 nm diameter MWCNTs in water (agglomeration is present). Figure 4. TEM image of 10 nm diameter Al 2 O 3 nanoparticles in water with PVP MWCNTs in Water. A suspension of nanotubes with diameters of 5 15 nm and lengths of 50 μm in water was also examined. As previously noted, because TEM requires vacuum, the photographs were taken after the nanofluids were dried at ambient temperature without heating. Hence, the shapes and sizes of the nanotubes can be observed but not the 3D dispersion of the nanotubes in the fluid. Figures 5 and 6 depict TEM images of an evaporated sample of a nanofluid containing MWCNTs in water; Figure 5 presents the evaluate the size of the nanoparticles and their tendency to aggregate, the nanoparticle size distribution in the fluid over time was selected as a control parameter. The average dimension of the nanoparticles in the suspensions was analyzed using a DLS-based Zetasizer Nano ZS analyzer (Malvern) operating at K. A detailed description of the working principles and components of the instrument is given elsewhere. 3 Here we simply recall that the analyzer is based on a laser beam scattered by the sample particles and a detector measuring the intensity of the scattered light at a scattering angle of 173. A correlator processes the signal intensity, and commercial software derives the size information by conventional methods. The range of sizes that can be measured is from 0.6 nm to 6 μm. The size distributions within a nanofluid containing nominally 10 nm diameter Al 2 O 3 nanoparticles in water with 1 mass % PVP and a second suspension of nominally nm diameter, 50 μm long nanotubes in water are shown in Figure 7. Each test Figure 5. TEM image of 5 15 nm diameter MWCNTs in water. typical situation, whereas Figure 6 shows an agglomerate that was found. It can be seen that the average diameter of the nanotubes is about 10 nm, while the length seems to be of the order of micrometers. The overlap of the nanotubes in this 2D picture may not represent entanglements of the 3D fluid Dynamic Light Scattering Analysis. In contrast to the TEM analysis, which reports the morphology and the dry particle size, dynamic light scattering (DLS) analysis provides further information on the nanoparticulate dispersion in the base fluid. If particles are too large or tend to aggregate, they can sediment, changing the nanoparticle concentration in solution and modifying the physical properties of the nanofluids. In order to Figure 7. DLS analysis of water with (a) 1 mass % MWCNTs (50 80 nm diameter + nonionic dipersant) added ( ) and (b) 1 mass % Al 2 O 3 nanoparticles (10 nm diameter + PVP) added ( ). using the Zetasizer was repeated three times, and the results shown here are the mean values of the three measurements with a spread of no more than 5%. It can be seen that the average diameter measured for the Al 2 O 3 particles in the water nanofluid is about 100 nm, which is very considerably larger than the nominal value. In the case of MWCNTs in water, the average nanotube size is around 200 nm. It is worth noting that in the latter case the average size is probably overestimated by DLS 494

5 since MWCNTs have a very high aspect ratio, far from the ideal spherical shape necessary to have accurate size measurements. We note that even in the first case the overestimation of the Al 2 O 3 nanoparticle diameter might also be attributed to their cylindrical shape, as shown in the TEM image in Figure THERMAL CONDUCTIVITY MEASUREMENTS The apparent thermal conductivity measurements described in this work were carried out using two techniques in the case of some of the fluids studied. First, we studied the fluids in a purpose-built transient hot-wire instrument. Second, in order to ascertain whether the measurements were influenced by the technique itself (as may be possible for this apparent thermophysical property), a hot-disk thermal constants analyzer was additionally employed for a selection of measurements. The two techniques will in turn be described here Transient Hot-Wire Instrument. The transient hotwire instrument designed and built according to the criteria set out in an earlier section is described in detail elsewhere. 1 Here it is only briefly presented. Two 25 μm diameter tantalum wires with lengths of 50 and 20 mm are employed. The wires are spotwelded to 1 mm diameter tantalum wires, which in turn are attached to a 3 mm thick stainless steel (SS) rod by small Teflon supports. 1 The two wires are placed in a 30 mm diameter cylindrical glass vessel to allow measurements at atmospheric pressure. Tantalum was selected for the wire so that the wires can be insulated using electrolytic formation in situ to form a thin surface layer of tantalum pentoxide, which is an electrical insulator. To ensure the stability of the oxide layer on both wires, 4 6 a bias is applied to them by means of a direct-current supply so that the wires are positive with respect to the top lid of the vessel and the SS rod, which are themselves maintained at ground potential. This arrangement also provides the means of registering the leakage current from the wires to the lid through the fluid at all times. In the measurements reported here, this leakage current through the liquid was always less than 1 μa. The wire sensor within the fluid vessel is mounted in an ethylene glycol/water bath, and its temperature is recorded using a Pt 100 thermometer calibrated versus a class I Tinsley Pt 25 thermometer to better than ±20 mk. The wires are transiently heated by passing an electrical current through them, producing temperature rises of about 3 K that are measured during the period from 20 ms to 1 s. A computer-controlled Wheatstonetype bridge is employed in order to heat the wires and to measure the voltage changes on each resistance at the same time, as described in detail elsewhere. 7 During a run, 400 measurements of the temperature rise are obtained. Figure 8 shows the percentage deviations of the experimental temperature rise from the value obtained by the straight-line fitting of the analytic model 1 as a function of the time. The agreement is within ±0.05% (at the 95% confidence level). The uncertainty of the thermal conductivity values obtained by this technique, if a G.U.M. analysis is carried out, 8 is 0.5% (at the 95% confidence level), and a full analysis is given by Charitidou et al. 9 However, on the basis of our experiences in relation to the uniformity and stability of nanofluids, we prefer to quote an uncertainty of less than 2% (at the 95% confidence level). Tables 3 5 present our measurements with this instrument of the thermal conductivities of (a) CuO in ethylene glycol and TiO 2 in water and ethylene glycol, (b) Al 2 O 3 in water and in ethylene glycol, and (c) MWCNTs in water, respectively, at K and different concentrations. The enhancements of the thermal conductivity in relation to that of the base fluid (λ BF ), i.e., water Figure 8. Percentage deviations of the experimental temperature rise from the value obtained by the straight-line fitting of the analytic model 1 as a function of the time. (606.5 mw m 1 K 1 ) 10 or ethylene glycol ( mw m 1 K 1 ), are also shown Hot-Disk Thermal Constants Analyzer. Because the systems being studied are two-phase systems, there is strictly no defined thermophysical property of thermal conductivity that depends only on the thermodynamic parameters of the state of the fluid such as density, temperature, and pressure. Instead, the apparent thermal conductivity may depend upon the state of aggregation of the two phases and also upon the length or time scale of the measurement technique. In order to investigate this possibility, we also performed measurements on a selection of nanofluids using a hot-disk thermal constants analyzer (TPS 2500 S), which is based on the transient plane source (TPS) technique. 12 Here, only few details about the experimental apparatus are given. More information on the experimental apparatus and procedure can be found in Fedele et al. 13 The hot-disk sensor is made of a double spiral of thin nickel wire and works as a continuous-plane heat source. The hot-disk sensor supplies a constant electric power that results in a temperature increase, which is measured directly by the hot disk itself by means of the variation of the sensor resistance. From the electric power supplied and the temperature rise, the thermal conductivity is calculated by solving the Fourier equation of heat conduction. A theoretical description of this method is provided by He. 12 In the case of liquids, the sensor is completely immersed in the fluid in a specially built container maintained under isothermal conditions by a thermostatic water bath. A low thermal power (around mw) and a short power input time (4 s) were considered for the measurements to avoid natural convection effects. In order to check the continuing good operation of the probe, the thermal conductivity of pure water was measured before and after the measurements. The deviations between the experimental and reference data for water 14 were less than 1.5%, which is well within the 5% declared experimental uncertainty (at the 95% confidence level) by the hot-disk manufacturer. It is useful here to note that the rate of change with time of the transient hot-wire temperature varies from about 52 to 0.3 K/s during an experiment, while that of the hot disk with the studied samples is in the range from 0.5 to 3 K/s. The spatial gradient of the hot-wire temperature varies from about to 100 K/m, while that of the hot-disk temperature for the considered experiments always ranges from 250 to 3000 K/m. Thus, the two instruments do probe significantly different temporal and spatial regions. 495

6 Table 3. Measurements of the Thermal Conductivities of CuO in Ethylene Glycol, TiO 2 in Water, and TiO 2 in Ethylene Glycol at K a transient hot-wire instrument hot-disk thermal analyzer size/nm mass % vol % λ/mw m 1 K 1 (λ λ BF )/λ BF /% λ/mw m 1 K 1 (λ λ BF )/λ BF /% dispersant or stabilizer b CuO + C 2 H 6 O 2 < none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication TiO 2 +H 2 O mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP none/2 h sonication none/2 h sonication none/2 h sonication none/2 h sonication none/2 h sonication TiO 2 +C 2 H 6 O mass % PVP mass % PVP mass % PVP mass % PVP none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication a Transient hot-wire U c (λ) = 2% (level of confidence = 0.95); hot-disk U c (λ) = 5% (level of confidence = 0.95). b PVP = poly(vinylpyrrolidone). Tables 3 5 include the measurements performed in the hotdisk thermal constants analyzer. It should be pointed out that the samples examined by this technique were exactly the same (ready-made with PVP dispersant) as those employed in the transient hot-wire instrument. In all cases the agreement is within 2%, which is considered excellent. Thus, the hot-disk thermal constants analyzer measurements were supportive of the more accurate transient hot-wire ones despite the difference of scales involved. This also lends credence to the notion of an apparent thermal conductivity for practical purposes for these two-phase systems Discussion of the Thermal Conductivity Measurements. In this section, the results of the thermal conductivity measurements performed in this work will be presented graphically together with those from other critically evaluated measurements. An overall discussion will be presented at the end CuO in Ethylene Glycol. In a recent paper, Tertsinidou et al. 15 discussed the conflicting statements in the literature of the last 20 years about the behavior of the thermal conductivity of liquids containing nanoparticles. An analysis of experimental measurements, almost all of which were conducted with implementations of experimental techniques that are significantly less accurate than those applied to single-phase liquids, led to the conclusion that the apparent thermal conductivity of a nanofluid exhibits no anomalous behavior. Consequently, excluding measurements performed in simplified transient hot-wire instruments, transient needle probes, 3ω instruments, and heat flux experiments (for the reasons discussed in detail by Tertsinidou et al. 15 ), Figure 9 shows the previously reported thermal conductivity enhancement of ethylene glycol when CuO nanoparticles are added to ethylene glycol as a function of the particulate volume fraction for nanoparticles with different diameters. In the same figure our latest measurements performed using the transient hot-wire (THW) instrument are also shown (the dashed lines are there to guide the eye of the reader to our measurements and do not represent correlations) TiO 2 in Water or Ethylene Glycol. Following the work of Tertsinidou et al. 15 on the importance of the proper application of a technique, Antoniadis et al. 1 discussed the criteria that should be satisfied for a transient hot-wire instrument to operate according to its theoretical model. In that paper the thermal conductivity enhancement of water when TiO 2 nanoparticles are added was examined. It was consequently also shown that if measurements performed in short, large-diameter transient hotwire, 3ω, and heat flux experiments are excluded, the remaining measurements seem to follow the trend of the Hamilton Crosser model, 2 as shown in Figure 10. In the same figure, our new transient hot-wire measurements are shown (the dashed lines are there to guide the eye of the reader to our measurements and do not represent correlations). Furthermore, measurements 496

7 Table 4. Measurements of the Thermal Conductivities of Al 2 O 3 in Water and in Ethylene Glycol at K a transient hot-wire instrument hot-disk thermal analyzer size/nm mass % vol % λ/mw m 1 K 1 (λ λ BF )/λ BF /% λ/mw m 1 K 1 (λ λ BF )/λ BF /% dispersant or stabilizer b Al 2 O 3 +H 2 O mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication Al 2 O 3 +C 2 H 6 O mass % PVP mass % PVP mass % PVP mass % PVP none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication a Transient hot-wire U c (λ) = 2% (level of confidence = 0.95); hot-disk U c (λ) = 5% (level of confidence = 0.95). b PVP = poly(vinylpyrrolidone). Table 5. Measurements of the Thermal Conductivity of MWCNTs in Water at K a transient hot-wire instrument hot-disk thermal analyzer size/nm mass % vol % λ/mw m 1 K 1 (λ λ BF )/λ BF /% λ/mw m 1 K 1 (λ λ BF )/λ BF /% dispersant or stabilizer b b mass % nonionic mass % nonionic mass % nonionic mass % nonionic 5 15 c mass % nonionic mass % nonionic mass % nonionic mass % nonionic a Transient hot-wire U c (λ) = 2% (level of confidence = 0.95); hot-disk U c (λ) = 5% (level of confidence = 0.95). b μm in length. c 50 μm in length. obtained with the hot-disk thermal constants analyzer (HDTCA) are also shown. In contrast with the CuO nanofluids, where no dispersant was employed, two of the three nanofluids with TiO 2 (see Figure 10) included PVP as a dispersant. As PVP produces better-dispersed solutions, these solutions show higher thermal conductivity enhancement than the nanofluid with no PVP dispersant. Whether this is a result of including the dispersant or of the small size of the particles for which the dispersant was not needed is currently unknown. In the case of the enhancement of the thermal conductivity of ethylene glycol when TiO 2 nanoparticles are added, only a very few measurements exist. These are shown in Figure 11, together with our own measurements performed with the transient hotwire instrument Al 2 O 3 in Water or Ethylene Glycol. Figures 12 and 13 show the measurements by the investigators whose techniques were critically assessed by Tertsinidou et al. 15 together with the results of measurements presented in Table 3. Again the dashed lines are there to guide the eye of the reader to our measurements and do not represent correlations. It is apparent that our new measurements performed using the transient hot-wire instrument and also those obtained with the hot-disk thermal constants analyzer agree very well. The agreement between the THW and HDTCA results for particles with a size of 10 nm is particularly gratifying MWCNTs in Water. Antoniadis et al. 1 also examined the enhancement of the thermal conductivity of water when MWCNTs are added. Following the previous arguments, Figure 14 shows the enhancement of the thermal conductivity of water when MWCNTs are added as a function of the volume fraction for MWCNTs with different diameters (excluding measurements performed in transient needle-probe, 3ω, and heat flux experiments 1 ). In the same figure our latest measurements performed in the transient hot-wire instrument and the HDTCA are also shown. As discussed by Antoniadis et al., 1 nanotubes with larger diameters (>100 nm) show higher enhancement than the rest. 497

8 Figure 9. Thermal conductivity enhancement of ethylene glycol in the presence of CuO nanoparticles as a function of the composition for nanoparticles with different diameters. Previous work:, 44 nm, Kazemi-Beydokhti et al.; 16, 40 nm, Liu et al.; 17, 33 nm, Penãs et al.; 18,31nm,Pateletal.; 19, 30 nm, Barbes et al.; 20,24nm, Kazemi-Beydokhti et al.; 16,23nm,Leeetal.; 21,23nm,Wang et al.; 22, 18 nm, Kazemi-Beydokhti et al.; 16 triangle with vertical bar, 12 nm, Kwak and Kim; 23, Hamilton Crosser model. 2 Present work:, <80nm,THW;, 40nm,THW. Figure 11. Thermal conductivity enhancement of ethylene glycol in the presence of TiO 2 nanoparticles as a function of the composition for nanoparticles with different diameters. Previous work:, 15 nm, Murshed et al.; 30, 15 nm Longo and Zilio; 31, Hamilton Crosser model. 2 Present work:, 15 nm (+PVP), THW,, 5 nm, THW. Figure 10. Thermal conductivity enhancement of water in the presence of TiO 2 nanoparticles as a function of the composition for nanoparticles with different diameters. Previous work: bottom-half-solid diamonds, 76 nm, Fedele et al.; 13, 40 nm, Zhang et al.; 24, 26 nm, Duangthongsuk and Wongwises; 25, 25 nm, Yoo et al.; 26, 21 nm, Reddy and Rao; 27, 21 nm, Yiamsaward et al.; 28, 20 nm, Haghighi et al.; 29, Hamilton Crosser model. 2 Present work:, nm (+PVP), THW;, 5 15 nm (+PVP), THW; triangle with vertical bar, 5 nm, THW; triangle with horizontal bar, 5 15 nm (+PVP), HDTCA. Our new measurements (<80 nm diameter) are in good agreement with the lower-diameter group of measurements Thermal Conductivity Measurements: Conclusions. The investigation of the thermal conductivity measurements resulted in the following conclusions: (1) When measurements are obtained with well-proven techniques, the apparent thermal conductivities of nanofluids do not show any large unexpected enhancements or anomalous behavior compared with simple theories, nor are there very large deviations among the various results. (2) The model of Hamilton and Crosser, 2 which simply takes account of the volume occupied by the more highly conducting nanoparticles and thus does not include any 498 Figure 12. Thermal conductivity enhancement of water in the presence of Al 2 O 3 nanoparticles as a function of the composition for nanoparticles with different diameters. Previous work: left-half-solid diamonds, 182 nm, Chon et al.; 32, 150 nm, Patel et al.; 19 top-half-solid diamonds, 150 nm, Murshed et al.; 30,120nm,Yiamsawasdetal.; 28 bottom-half-solid diamonds, 80 nm, Murshed et al.; 30 triangle with vertical bar, 50 nm, Chon et al.; 32 right-half-solid diamonds, 50 nm, Longo and Zilio; 33,48nm, Yoo et al.; 26, 45 nm, Barbes et al.; 34 triangle with horizontal bar, 45 nm, Colangelo et al.; 35, 45 nm, Patel et al.; 19, 38 nm, Das et al.; 36, 38 nm, Lee et al.; 21 +, 33 nm, Eastman et al.; 37, 32 nm, Lee et al.; 38, 30 nm, Kazemi-Beydokhti et al.; 16, 28 nm, Wang et al.; 22,20nm, Zhang et al.; 24, 13 nm, Chon et al.; 32, 11 nm, Patel et al.; 19, Hamilton Crosser model. 2 Present work:, 30 nm (+PVP), THW;, 10 nm (+PVP), THW,, 5nm,THW;, 10 nm, HDTCA. effect of different diameters of nanoparticles, performs as follows: (a) It reproduces the enhancement of all of the present thermal conductivity measurements for concentrations less than 4 vol % and for diameters around 5 nm, with no dispersant present, within 5% (see Figure 10, TiO 2 +H 2 O, 5%; Figure 11, TiO 2 + EG, 4%; Figure 12, Al 2 O 3 +H 2 O, 5%; and Figure 13, Al 2 O 3 + EG, <1%). (b) The remainder of the present measurements on nanofluids containing particles of larger diameter or with PVP dispersant are reproduced within 15%.

9 (4) The present measurements do not seem to indicate a clear dependence of the thermal conductivity enhancement on the diameter of the nanoparticles. (5) In the case of large-diameter (>80 nm) carbon nanotubes, it seems that an additional heat transfer mechanism might be present. Figure 13. Thermal conductivity enhancement of ethylene glycol in the presence of Al 2 O 3 nanoparticles as a function of the composition for nanoparticles with different diameters. Previous work: bottom-half-solid diamonds, 302 nm, Xie et al.; 39, 150 nm, Patel et al.; 19, 80 nm, Murshed; 40, 60 nm, Xie et al.; 39 triangle with horizontal bar, 45 nm, Barbes et al.; 34, 45 nm, Patel et al.; 19, 38 nm, Lee et al.; 21, 35 nm, Xie et al.; 41, 28 nm, Wang et al.; 22, 26 nm, Xie et al.; 39 triangle with vertical bar, 15 nm, Xie et al.; 39, 10 nm, Longo and Zilio; 31, 11 nm, Patel et al.; 19, Hamilton Crosser model. 2 Present work:, 15nm (+PVP), THW;, 5 nm, THW. 4. VISCOSITY MEASUREMENTS Because the overall aim of this work was to investigate the heat transfer capabilities of the selected nanofluids, we also measured their viscosities, as this property can contribute to or quite strongly hinder the heat transfer. It is worth stating from the beginning that although both water and ethylene glycol are Newtonian fluids, this is not necessarily the case when nanoparticles are added to these two fluids. Figure 15 depicts the Figure 15. Shear stress and viscosity as functions of the shear rate for water at K. results of measurements of the viscosity of water at K, which show the typical Newtonian behavior, i.e., the viscosity is constant and obtained from the ratio of the shear stress to the shear strain. Figure 16 shows the results of similar measurements Figure 14. Thermal conductivity enhancement of water in the presence of MWCNTs as a function of the composition for MWCNTs with different outside diameters. Previous work:, 150 nm, Zhang et al.; 42 box with horizontal bar, 130 nm, Assael et al.; 43 left-half-solid diamonds, nm, Glory et al.; 44 triangle with vertical bar, 100 nm, Assael et al.; 4 bottom-half-solid diamonds, 15 nm, Chen et al.; 45, 15 nm, Xie et al.; 46 top-half-solid diamonds, nm, Hwang et al.; 47,10 30 nm, Hwang et al.; 48,10 15 nm, Gu et al.; 49,8 15 nm, Pantzali et al. 50 Present work:, nm/10 20 μm, THW;, 5 15 nm/50 μm, THW;, nm/10 20 μm, HDTCA. (3) We have shown that the addition of PVP dispersant results in better and more stable suspensions, and Figures 9 12 indicate that there is a modest extra thermal conductivity enhancement for the systems studied here compared with expectations from the Hamilton Crosser theory. This observation may or may not reveal interesting physics, but for our purposes here, its modest nature imposes some real constraints on the use of such fluids as improved heat transfer media, as will be shown later. In particular, the increased viscosity of these fluids offsets entirely the gain from enhanced thermal conduction on the scale found. Figure 16. Shear stress and viscosity as functions of the shear rate for water containing 2 vol % Al 2 O 3 nanoparticles with a diameter of 5 nm at K. on water to which 2 vol % Al 2 O 3 particles with a diameter of 5 nm has been added. It is clear that the situation is now completely different. Unlike fluids that exhibit Newtonian behavior, which means that viscosity remains constant and is independent of the shear rate, the fluid shown in Figure 16 shows non-newtonian, Bingham plastic behavior, as its viscosity appears to be infinite until a certain shear stress is achieved. For Bingham plastic fluids, there is a finite shear stress, η pl0 (called the yield point), below which they will not flow. Above the yield point, the shear rate is linear with shear stress, just as for a Newtonian fluid. The shear stress, τ, can be written as τ = η + η γ pl0 pl (1) where τ and η pl0 are in pascals, η pl (in Pa s) is the plastic viscosity of the fluid, and γ (in s 1 ) is the shear rate Viscometer. Since the addition of nanoparticles or nanotubes to water or ethylene glycol can result in Bingham plastic behavior, it was necessary to employ a viscometer that can 499

10 Table 6. Measurements of the Viscosities of Nanofluids at K a AR550 rotational rheometer size/nm mass % vol % η b pl /mpa s η c pl0 /mpa dispersant or stabilizer d shear rate/s 1 CuO + C 2 H 6 O 2 < none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication none/1 h sonication TiO 2 +H 2 O mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP mass % PVP none/2 h sonication none/2 h sonication TiO 2 +C 2 H 6 O none/1 h sonication none/1 h sonication none/1 h sonication Al 2 O 3 +H 2 O mass % PVP mass % PVP mass % PVP mass % PVP none/1 h sonication none/1 h sonication none/1 h sonication Al 2 O 3 +C 2 H 6 O mass % PVP mass % PVP none/1 h sonication none/1 h sonication none/1 h sonication MWCNTs + H 2 O e mass % nonionic mass % nonionic f mass % nonionic mass % nonionic mass % nonionic a U c (η) = 5% (level of confidence = 0.95). b η pl is the viscosity or plastic viscosity (for Newtonian or Bingham plastic fluids, respectively). c η pl0 is the yield point (for Bingham plastic fluids). d PVP = poly(vinylpyrrolidone). e μm in length. f 50 μm in length. impose a specific shear rate and record the shear stress. For these measurements, an AR550 rheometer (TA Instruments) was employed. This is a rotational rheometer with a parallel-plate geometry. For all of the experiments, a plate diameter of 60 mm was employed. The temperature was controlled with a Peltier temperature control device located below the lower plate. The upper plate was supported, controlled, and lowered to its position by the computer. The sample loading and imposed gap are very important because the sample should fill the gap between the upper and lower plates exactly. All of the measurements were performed at constant ambient pressure and K with a variable shear rate ranging from 50 to 2500 s 1. Two typical graphs are shown in Figure 16. Before the measurements, the rheometer was carefully calibrated according to the manufacturer s recommendation. In addition, at the beginning and at the end of each measurement, the viscosities of water, squalene, and ethylene glycol were measured in order to validate the proper use of the instrument (the declared instrument uncertainty is 5% at the 95% confidence level). In the case of water, the viscosity value obtained at K was mpa s, which deviates by only 0.03% from the IAPWSrecommended value 51 of mpa s (uncertainty of 1% at the 95% confidence level). The value of the viscosity of squalene obtained at K was 27.5 mpa s, which differs by 2.5% from the recommended value 52 of 28.2 mpa s (uncertainty of 1.5% at the 95% confidence level). To check the middle-range viscosities, the viscosity of ethylene glycol was measured at K and found to be equal to 17.2 mpa s, which differs by only 0.17% from the value of mpa s found in the literature. 53 Table 6 shows the measurements of the viscosities of the nanofluids considered. It can be seen that in most cases the nanofluids show Bingham plastic behavior and that only at very dilute concentrations do they behave like a Newtonian fluid (η pl0 0). The only exception to this general statement is in the 500

11 case of nanofluids with CuO, which showed Newtonian behavior at all concentrations. It is also worthwhile to note that in general, for a particular system the viscosity increases as the nanoparticle or nanotube diameter decreases Discussion of the Viscosity Measurements CuO in Ethylene Glycol. Figure 17 shows viscosity Figure 17. Viscosity of ethylene glycol in the presence of CuO nanoparticles as a function of the composition for nanoparticles with different diameters at K. Previous work:,5 10 nm, Yu et al.; 54,10 30 nm, Kwak and Kim; 23, 200 nm, Garg et al. 55 Present work:, <80 nm;, 40 nm. measurements on ethylene glycol with added CuO nanoparticles as functions of the composition for nanoparticles with different diameters. We do note that because in the case of viscosity measurements the enhancement is an order of magnitude more than the equivalent thermal conductivity one, it was preferred to show actual viscosity values in the figures that follow. Obviously, a nanoparticle concentration of 0 vol % refers to the viscosity of the base fluid (water or ethylene glycol). As has already been mentioned, as the particular nanofluid was prepared in our laboratory without adding any dispersant, it was not possible to prepare stable nanofluids with water. Yu et al., 54 Kwak and Kim, 23 and Garg et al. 55 employed rotational rheometers. However, the measurements of Liu et al. 17 were not included in the figure because no information whatsoever about the viscometer employed was given. In Figure 17, our new viscosity measurements for CuO nanoparticles with diameters of 40 and <80 nm in ethylene glycol are also presented. The agreement among all of the measurements is within 5%, with the exception of the measurements of Yu et al. 54 who used PVP as a dispersant. The addition of PVP, as already noted, results in 3-fold viscosity enhancement compared with the corresponding value for pure ethylene glycol TiO 2 in Water and Ethylene Glycol. Figures 18 and 19 show the viscosities of ethylene glycol with added TiO 2 nanoparticles as functions of the composition for nanoparticles with different diameters. In Figure 18, rotational rheometers were employed by Haghighi et al., 29 Fedele et al., 13 Longo and Zilio, 33 Pak and Cho, 56 Duangthongs and Wongwises, 25 Pantzali et al., 50 Murshed et al., 30 He et al., 57 and Wen and Ding, 58 while Tavman and Turgut 59 employed a vibrating viscometer. The measurements by the above investigators are in good agreement with each other. The measurements of viscosity performed in capillary or falling-ball instruments (Jarahnejad et al. 60 ) were excluded because the nanofluids show non-newtonian behavior which is incompatible with the use of such devices for accurate Figure 18. Viscosity of water in the presence of TiO 2 nanoparticles as a function of the composition for nanoparticles with different diameters at K. Previous work:, 20 nm, Haghighi et al.; 29 +, 75 nm, Fedele et al.; 13 and,30 50 nm, stirred and sonicated, respectively, Longo and Zilio; 33, 21 nm, Tavman and Turgut; 59, 27 nm, Pak and Cho; nm, Duangthongsuk and Wongwises; 25 cross with vertical bar, Pantzali et al.; 50, 15 nm, Murshed et al.; 30, 95 nm, He et al.; 57, 34 nm, Wen and Ding. 58 Present work:, nm (+PVP);, 5 15 nm (+PVP); ( ) 5 nm. measurements. As can be seen in the same figure, our viscosity measurements on the ready-made nanofluids show larger viscosities than the other measurements, which is attributed to the use of PVP as a dispersant, as already discussed. Our measurements without PVP (5 nm) agree well with the other measurements. In Figure 19, viscosity measurements performed with rotational viscometers together with our new measurements of Figure 19. Viscosity of ethylene glycol in the presence of TiO 2 nanoparticles as a function of the composition for nanoparticles with different diameters at K. Previous work:, 15 nm, Longo and Zilio; 31, 25 nm, Chen et al. 61 Present work:, 5 nm. nanofluids prepared in our laboratory without dispersant are shown. Those three systems seem to follow a previously mentioned statement that for a particular nanofluid the viscosity increases as the nanoparticle diameter decreases. It should be mentioned that no dispersant was added in the nanofluids examined by Longo and Zilio 31 and Chen et al Al 2 O 3 in Water or Ethylene Glycol. Figures 20 and 21 show the viscosities of water and ethylene glycol, respectively, with added Al 2 O 3 nanoparticles as functions of the composition for nanoparticles with different diameters. Because these fluids 501