Various synthesis procedures have been used for production of nanofluids. The PWE method is one approach to fabricate nanoparticles 37 . In this study we used the PWE method mainly because the process is simple to use, and it is not time consuming to produce nanofluids samples in enough quantity for the round-robin measurements.

Although the thermal conductivity of suspensions of ZnO nanoparticles in water or EG was studied, the previous studies 38 39 40 41 42 43 44 used nanofluids manufactured by the two-step method or commercial products with surfactants, as shown in Table 1. However, in this study, the EG-based ZnO nanofluids are manufactured by a one-step physical method using PWE 37 and do not contain any surfactant. Therefore, the ZnO nanofluids studied in this work are different from the previously studied ZnO nanofluids 38 39 40 41 42 43 44 .

As shown in Figure 1, the PWE system for synthesis of EG-based ZnO nanofluids consists of three main components which are the pulsed power generator, the control panel, and the evaporation chamber with continuous wire feeding and fluid nozzle subsystems. Pure Zn wire of 99.9% with a diameter of 0.5 mm was used as a starting material and the feeding length of the wire into the reaction chamber was 100 mm. When a pulsed high voltage of 25 kV is driven through a thin wire, non-equilibrium overheating induced in the wire makes the wire evaporate into plasma within several microseconds. Then the high-temperature plasma is cooled by an interaction with an argon-oxygen mixed gas, and evaporated Zn gas is condensed into small-sized particles and spontaneously immersed into EG-stained chamber. The Ar:O₂ atmosphere in the evaporation chamber facilitates formation of the zinc oxide phase. More details of the PWE method and system are given in 45 .

Using the one-step PWE process, three test samples were produced: EG-based ZnO nanofluids with nanoparticle concentrations of 1.0, 3.0, and 5.5 vol.%. A transmission electron microscopy (TEM) image of ZnO nanoparticles with an average diameter of 70 nm is shown in Figure 2.

In this study, four of the labs used a THWM developed in house to measure the thermal conductivity of EG-based ZnO nanofluids, and one of the five labs performed the thermal conductivity measurements using a commercial apparatus, LAMBDA (LAMBDA F5 Technology, Germany) with 1% error.

In order to obtain the accuracy of the transient hot wire apparatus, the measurement uncertainty analysis of the apparatus was performed by each laboratory as follows:

The thermal conductivity of fluids is calculated by Equation 1,

where k, q, ΔT and t are the thermal conductivity, the input power per unit length, the temperature rise of hot wire, and the measurement time, respectively. The thermal conductivity of fluids can be obtained if the input power unit length and temperature rise of hot wire are measured as a function of temperature. Therefore, the measurement uncertainty of the apparatus 46 is given by Equation 2,

where u_k, u_q , and uΔ _T are the measurement uncertainties of thermal conductivity, the input power per unit length, and the temperature rise of the hot wire, respectively. Equation 2 shows that the measurement uncertainty of the thermal conductivity using the transient hot wire apparatus consists of the measurement uncertainties of input power per unit length, q, and the temperature rise of hot wire, ΔT. Here the measurement uncertainties of q and ΔT in accordance with 95% confidence interval 47 48 are expressed by Equation 3,

where u_i, B, and t_λ,95%P are the measurement uncertainty of i, bias error, and estimate of the precision error in the repeated measurement data at 95% confidence. In addition, λ is the degree of freedom given by,

where N is the data size. Using this method, the measurement uncertainty of transient hot wire apparatus manufactured by each lab was determined to be less than 1.5%. In order to verify the accuracy and the reliability of this experimental system, the thermal conductivity was experimentally measured using deionized water and EG. As shown in Figure 3, a typical THW apparatus calibration with the reference fluids demonstrates that it is possible to measure thermal conductivities with less than 1.5% error, verifying the estimated measurement uncertainty of 1.5%. In Figure 3, the hollow symbols represent the calibration data and the solid symbols are the average value of the calibration data. The solid and dashed lines represent the thermal conductivity of water and EG, respectively 49 .

Figure 4a, b shows the thermal conductivity enhancements for the 3.0 and 5.5 vol.% ZnO nanofluids that were measured at each of the five participating labs. The thermal conductivity enhancement is defined as (k _eff - k _f)/k _f, where k _eff and k _f are the thermal conductivity of nanofluids and base fluids, respectively. Each data point represents the ratio of the mean of 10 measured enhancements to the thermal conductivity of base fluid. Error bars show measurement uncertainty determined by the participating labs as described in the previous section. Figure 4a, b indicates that the experimental thermal conductivity data show very little dependence on temperature in the 20 to 90°C range.

Following the statistical data analysis procedures used in the INPBE study 34 , we calculated the sample averages and the standard errors for all the thermal conductivity enhancement data. In Figure 4a, b, the sample average is shown as a solid line and the standard errors of the sample mean as dotted lines. As seen in Figure 4a, b, the experimental data obtained by the five participating labs lie within a narrow band about the sample average with only a few modest outliers. The data analysis shows that the standard errors of the sample mean for the 3.0 and 5.5 vol.% ZnO nanofluids samples are ±1.24 and ±3.95%, respectively.

Figure 5 shows the thermal conductivity enhancement of EG-based ZnO nanofluids at a temperature of 23°C as a function of nanoparticle volume fraction. Each data point represents the ratio of the ensemble average of enhancements measured by the participating labs at a given volume fraction to the thermal conductivity of base fluid. The error bars show the standard deviation from the ensemble average. The ZnO nanofluids show very significant increases in thermal conductivity, with a nearly 25% increase for 5.5 vol.% ZnO nanoparticles.

The Hashin and Shtrikman (H-S) bounds on the thermal conductivity of heterogeneous systems 30 have been used for nanofluids to show that the effective medium theory can explain the enhancement of nanofluids 27 29 . The H-S upper bound is given by Equation 5 and the H-S lower bound is the classical Maxwell model as given by Equation 6. Recently, Buongiorno et al. 34 used Equation 6, the classical Maxwell model with negligible interface resistance, for the upper bound for nanofluids and Equation 7, the Maxwell model with interface resistance, for the lower bound for nanofluids.

Upper bound of Hashin and Shtrikman 30

Upper bound of the Maxwell Model (no interfacial thermal resistance) 35

Lower bound of the Maxwell Model (with interfacial thermal resistance) 50

where k _f, k _p, r _p, R _b, and φ are the thermal conductivities of base fluids and nanoparticles, radius of nanoparticles, interfacial thermal resistance, and volume fraction of nanoparticles, respectively.

Figures 6 and 7 show comparisons of experimental thermal conductivity enhancements of 3.0 vol.% and 5.5 vol.% ZnO nanofluids with the three theoretical bounds of Hashin and Shtrikman and Maxwell models. The properties, such as the thermal conductivities of EG 49 and ZnO nanoparticles 51 , used for calculating the theoretical bounds are summarized in Table 2. The upper bound of Hashin and Shtrikman, which was used by Eapen et al. 27 and Kelbinski et al. 29 , dramatically overestimates the thermal conductivity of ZnO nanofluids. The H-S upper bound corresponds to large pockets of fluid separated by linked chain-forming or clustered nanoparticles 29 . The long wire-like structures made of perfectly aligned nanoparticles are not realizable with dilute nanofluids with well-dispersed nanoparticles. Furthermore, it is almost impossible to separate fluid by nanoparticle chains in nanofluids, although nanoparticles can be partially aggregated in nanofluids. Therefore, the upper bound given by the H-S model is not applicable to nanofluids. More realistic upper and lower bounds for nanofluids having low concentration of well-dispersed nanoparticles are given by Buongiorno et al. 34 . It is clear from Figures 6 and 7 that the thermal conductivity enhancements of EG-based ZnO nanofluids are larger than the upper bound of the Maxwell model.