Effect of CuO Nanolubricant on R134a 

Pool Boiling Heat Transfer with Extensive 

Measurement and Analysis Details

Mark A. Kedzierski

Maoqiong Gong

NISTIR 7454
2
3

NISTIR 7454

Effect of CuO Nanolubricant on R134a Pool 

Boiling Heat Transfer with Extensive 

Measurement and Analysis Details

Mark A. Kedzierski

U.S DEPARTMENT OF COMMERCE

National Institute of Standard and Technology

Building Environment Division

Building and Fire Research Laboratory

Gaithersburg, MD 20899-8631

Maoqiong Gong

Chinese Academy of Sciences

Beijing, China

September 2007

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology

James M. Turner, Acting Director
4

Effect of CuO Nanolubricant on R134a Pool Boiling Heat Transfer 

with Extensive Measurement and Analysis Details

M. A. Kedzierski

National Institute of Standards and Technology

Bldg. 226, Rm B114

Gaithersburg, MD 20899

Phone: (301) 975-5282

Fax: (301) 975-8973

M. Gong 

Chinese Academy of Sciences

Beijing, China

ABSTRACT

This paper quantifies the influence of CuO nanoparticles on the boiling performance of 

R134a/polyolester mixtures on a roughened, horizontal, flat surface. Nanofluids are liquids 

that contain dispersed nano-size particles. A lubricant based nanofluid (nanolubricant) was 

made with a synthetic ester and 30 nm diameter CuO particles stably suspended in the 

mixture to a 1 % volume fraction. For the 0.5 % nanolubricant mass fraction, the 

nanoparticles caused a heat transfer enhancement relative to the heat transfer of pure 

R134a/polyolester (99.5/0.5) of between 50 % and 275 %. A smaller enhancement was 

observed for the R134a/nanolubricant (99/1) mixture, which had a heat flux that was on 

average 19 % larger than that of the R134a/polyolester (99/1) mixture. Further increase in 

the nanolubricant mass fraction to 2 % resulted in a still smaller boiling heat transfer 

improvement of approximately 12 % on average. Consequently, significant 

refrigerant/lubricant boiling heat transfer enhancements are possible with nanoparticles. 

Thermal conductivity measurements and a refrigerant\lubricant mixture pool-boiling model 

were used to suggest that increased thermal conductivity is responsible for only a small 

portion of the heat transfer enhancement due to nanoparticles. Further research with 

nanolubricants and refrigerants are required to establish a fundamental understanding of the 

mechanisms that control nanofluid heat transfer.

Keywords: additives, boiling, copper (II) oxide, enhanced heat transfer, nanotechnology, 

refrigerants, refrigerant/lubricant mixtures
5

TABLE OF CONTENTS

ABSTRACT............................................................................................................................. 4

TABLE OF CONTENTS ....................................................................................................... 5

LIST OF FIGURES ................................................................................................................ 5

LIST OF TABLES.................................................................................................................. 6

INTRODUCTION................................................................................................................... 7

APPARATUS .......................................................................................................................... 8

TEST SURFACE .................................................................................................................... 8

MEASUREMENTS AND UNCERTAINTIES .................................................................... 8

EXPERIMENTAL RESULTS............................................................................................... 9

DISCUSSION........................................................................................................................ 12

CONCLUSIONS ................................................................................................................... 13

ACKNOWLEDGEMENTS ................................................................................................. 14

NOMENCLATURE.............................................................................................................. 15

English Symbols................................................................................................................ 15

Greek symbols................................................................................................................... 15

English Subscripts............................................................................................................. 15

REFERENCES...................................................................................................................... 16

APPENDIX A: UNCERTAINTIES................................................................38

APPENDIX B: LUBRICANT LIQUID DENSITY MEASUREMENTS ........................ 40

APPENDIX C: DILUTION OF 9 % VOLUME NANOLUBICANT ............................. 40

APPENDIX D: CAPILLARY RISE MEASUREMENTS ................................................ 44

APPENDIX E: LUBRICANT VISCOSITY MEASUREMENTS.................................... 45

LIST OF FIGURES

Fig. 1 Schematic of test apparatus...................................................................................... 29

Fig. 2 OFHC copper flat test plate with cross-hatched surface and thermocouple 

coordinate system...................................................................................................... 30

Fig. 3 Pure R134a boiling curve for plain surface ............................................................ 31

Fig. 4 R134a/RL68H mixtures boiling curves for plain surface ...................................... 32

Fig. 5 R134a/RL68H with 1 % volume CuO mixtures boiling curves for plain surface33

Fig. 6 R134a/RL68H mixture heat flux relative to that of pure R134a for a plain 

surface ........................................................................................................................ 34

Fig. 7 Boiling heat flux of R134a/RL68H1Cu mixtures relative to that of pure R134a 

for a plain surface ..................................................................................................... 35

Fig. 8 Measured thermal conductivity of RL68H/CuO nanoparticles mixtures as a 

function of volume fraction of CuO ........................................................................ 36

Fig. 9 Predicted heat flux ratio for RL68H1Cu (99.5/0.5) mixture using Kedzierski 

(2003b) model ............................................................................................................ 37

Fig. A.1 Expanded relative uncertainty in the heat flux of the surface at the 95 % 

confidence level.......................................................................................................... 38

Fig. A.2 Expanded uncertainty in the temperature of the surface at the 95 % confidence 

level............................................................................................................................. 39
6

LIST OF TABLES

Table 1 Conduction model choice....................................................................................... 18

Table 2 Pool boiling data..................................................................................................... 19

Table 3 Number of test days and data points.................................................................... 25

Table 4 Estimated parameters for cubic boiling curve fits for plain copper surface.... 26

Table 5 Residual standard deviation of ∆Ts ...................................................................... 27

Table 6 Average magnitude of 95 % multi-use confidence interval for mean Tw -Ts (K)

..................................................................................................................................... 28

Table B.1 RL68H liquid density measurements ............................................................... 41

Table D.1 Capillary rise measurements for RL68H......................................................... 44

Table E.1 Kinematic viscosity measurements for RL68H ............................................... 45
7

INTRODUCTION

The U.S. National Nanotechnology Initiative (NNI) has supported an explosion of research in 

recent years including the investigation of the heat transfer properties of liquids with

dispersed nano-size particles called nanofluids. Prior to the initiative, nanofluids research 

was mainly confined to thermal conductivity investigations. Eastman et al. (2001) found that 

the thermal conductivity of some nanofluids, with nanoparticles at a volume fraction of less 

than 0.4 % results in the nanofluid having a thermal conductivity that was more than 40 % 

greater than that of the pure base fluid. Herein lies what is believed to be a great potential for 

the enhancement of liquid heat transfer by the addition of nanoparticles to the base fluid.

Water, ethylene glycol, and lubricants have been successfully used as base fluids in making 

stable nanofluids where the particles remain suspended in the liquid. Although water based 

nanofluids are the least stable of the three liquids because of the relatively low viscosity of 

water, most of the boiling heat transfer studies have been conducted with water based 

nanofluids (Bang and Chang (2004), Wen and Ding (2005), and You et al. (2003)). 

Although, You et al. (2003) and Bang and Chang (2004) did not observe a pool-boiling 

enhancement with nanofluids, Wen and Ding (2005) did. Consequently, there is a potential 

for boiling heat transfer improvement with nanofluids even though the mechanisms that 

govern the improvement are not fully understood.

Currently, there are no published measurements to determine if nanoparticles can improve 

refrigerant/lubricant boiling heat transfer. One reason for this might be that although the 

nanoparticles are expected to form a stable suspension with the lubricant, once the 

nanolubricant is mixed with the refrigerant the nanoparticles will become unstable with 

respect to the refrigerant/lubricant mixture because the relatively low viscosity of the mixture 

discourages Brownian motion. This potential outcome, however, may not prohibit the 

application of nanoparticles to air-conditioning equipment because the mechanism of the 

boiling heat transfer of refrigerant/lubricant mixtures is strongly governed by the lubricant 

excess layer that resides at the boiling surface (Kedzierski, 2003a). There is reason to 

believe that the boiling will drive the nanoparticles to the heat transfer surface where they 

will become stable and remain within the lubricant excess layer. Some of the particles will 

also be entrained in the vigorous boiling of the fluid. If the nanoparticles significantly 

change the thermal conductivity of the lubricant excess layer, that may cause an enhancement 

or a degradation in heat transfer depending on whether the increased conduction causes a 

reduced available superheat or whether it increases the thermal boundary layer thickness. 

The potential for a boiling heat transfer enhancement is likely to depend on the material of 

the particles, their shape, size, distribution, and concentration. 

In order to investigate the influence of nanoparticles on refrigerant/lubricant pool boiling, the 

boiling heat transfer of three R134a/nanolubricant mixtures on a roughened, horizontal, flat 

(plain), copper surface was measured. A commercial polyolester lubricant (RL68H1

 1 Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the 

experimental procedure adequately. Such identification is not intended to imply recommendation or 

endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the 

materials or equipment identified are necessarily the best available for the purpose.

) with a 

nominal kinematic viscosity of 72.3 μm2

/s at 313.15 K was the base lubricant that was mixed 
8

with nominally 30 nm diameter copper (II) oxide (CuO) nanoparticles. Copper (II) oxide 

(79.55 g/mol) has many commercial applications including use as an optical glass-polishing 

agent. A manufacturer used a proprietary surfactant at a mass between 5 % and 15 % of the 

mass of the CuO as a dispersant for the RL68H/CuO mixture (nanolubricant). The 

manufacturer made the mixture such that 9 % of the volume was CuO particles. The mixture 

was diluted in-house to a 1 % volume fraction of CuO by adding neat RL68H (see Appendix 

C) and ultrasonically mixing the solution for approximately 24 h. The particle size and 

dispersion were verified by a light scattering technique and was found to be approximately 

35 nm and well dispersed with little particle agglomeration (Sung, 2006). The RL68H/CuO 

(99/1)2

APPARATUS

volume fraction mixture, a.k.a. RL68H1Cu, was mixed with pure R134a to obtain 

three R134a/RL68H1Cu mixtures at nominally 0.5 %, 1 %, and 2 % mass fractions for the

boiling tests. In addition, the boiling heat transfer of three R134a/RL68H mixtures (0.5 %, 

1 %, and 2 % mass fractions), without nanoparticles, was measured to serve as a baseline for 

comparison to the RL68H1Cu mixtures.

Figure 1 shows a schematic of the apparatus that was used to measure the pool boiling data 

of this study. More specifically, the apparatus was used to measure the liquid saturation 

temperature (Ts), the average pool-boiling heat flux (q"), and the wall temperature (Tw) of the

test surface. The three principal components of the apparatus were the test chamber, the 

condenser, and the purger. The internal dimensions of the test chamber were 25.4 mm × 

257 mm × 1.54 m. The test chamber was charged with approximately 7 kg of refrigerant, 

giving a liquid height of approximately 80 mm above the test surface. As shown in Fig. 1, the 

test section was visible through two opposing, flat 150 mm × 200 mm quartz windows. The 

bottom of the test surface was heated with high velocity (2.5 m/s) water flow. The vapor 

produced by liquid boiling on the test surface was condensed by the brine-cooled, shell-andtube condenser and returned as liquid to the pool by gravity. Further details of the test 

apparatus can be found in Kedzierski (2002) and Kedzierski (2001a). 

TEST SURFACE

Figure 2 shows the oxygen-free high-conductivity (OFHC) copper flat test plate used in this 

study. The test plate was machined out of a single piece of OFHC copper by electric 

discharge machining (EDM). A tub grinder was used to finish the heat transfer surface of the 

test plate with a crosshatch pattern. Average roughness measurements were used to estimate 

the range of average cavity radii for the surface to be between 12 μm and 35 μm. The 

relative standard uncertainty of the cavity measurements were approximately ± 12 %. 

Further information on the surface characterization can be found in Kedzierski (2001a).

MEASUREMENTS AND UNCERTAINTIES

The standard uncertainty (ui) is the positive square root of the estimated variance ui

2

. The 

individual standard uncertainties are combined to obtain the expanded uncertainty (U), which 

is calculated from the law of propagation of uncertainty with a coverage factor. All 

measurement uncertainties are reported at the 95 % confidence level except where specified 

otherwise. For the sake of brevity, only an outline of the basic measurements and 

 2 The equivalent mixture is RL68H/CuO (94.4/5.6) in terms of mass.
9

uncertainties is given below. Complete detail on the heat transfer measurement techniques 

and uncertainties can be found in Kedzierski (2000) and Appendix A, respectively.

All of the copper-constantan thermocouples and the data acquisition system were calibrated 

against a glass-rod standard platinum resistance thermometer (SPRT) and a reference voltage 

to a residual standard deviation of 0.005 K. Considering the fluctuations in the saturation 

temperature during the test and the standard uncertainties in the calibration, the expanded 

uncertainty of the average saturation temperature was no greater than 0.04 K. Consequently, 

it is believed that the expanded uncertainty of the temperature measurements was less than 

0.1 K. 

Twenty 0.5 mm diameter thermocouples were force fitted into the wells of the side of the test 

plate shown in Fig. 2. The heat flux and the wall temperature were obtained by regressing 

the measured temperature distribution of the block to the governing two-dimensional 

conduction equation (Laplace equation). In other words, rather than using the boundary 

conditions to solve for the interior temperatures, the interior temperatures were used to solve 

for the boundary conditions following a backward stepwise procedure given in Kedzierski 

(1995)3

EXPERIMENTAL RESULTS

. Fourier's law and the fitted constants from the Laplace equation were used to 

calculate the average heat flux (q") normal to and evaluated at the heat transfer surface based 

on its projected area. The average wall temperature (Tw) was calculated by integrating the 

local wall temperature (T). The wall superheat was calculated from Tw and the measured 

temperature of the saturated liquid (Ts). Considering this, the relative expanded uncertainty in 

the heat flux (Uq") was greatest at the lowest heat fluxes, approaching 10 % of the 

measurement near 10 kW/m2

. In general, the Uq" remained approximately within 3 % and 

6 % for heat fluxes greater than 30 kW/m2. The average random error in the wall superheat 

(UTw) was between 0.04 K and 0.1 K. Plots of Uq" and UTw versus heat flux can be found in 

Appendix A. 

The heat flux was varied approximately between 10 kW/m2 and 120 kW/m2 to simulate a 

range of possible operating conditions for R134a chillers. All pool-boiling tests were taken 

at 277.6 K saturated conditions. The data were recorded consecutively starting at the largest 

heat flux and descending in intervals of approximately 4 kW/m2. The descending heat flux 

procedure minimized the possibility of any hysteresis effects on the data, which would have 

made the data sensitive to the initial operating conditions. Table 2 presents the measured 

heat flux and wall superheat for all the data of this study. Table 3 gives the number of test 

days and data points for each fluid.

The mixtures were prepared by charging the test chamber (see Fig. 1) with pure R134a to a 

known mass. Next, a measured mass of nanolubricant or lubricant was injected with a 

syringe through a port in the test chamber. The refrigerant/lubricant solution was mixed by 

flushing pure refrigerant through the same port where the lubricant was injected. All 

compositions were determined from the masses of the charged components and are given on 

a mass fraction basis. The maximum uncertainty of the composition measurement is 

 3 For the record, Table 1 provides functional forms of the Laplace equation that were used in this study in the 

same way as was done in Kedzierski (1995) and in similar studies by this author.
10

approximately 0.02 %, e.g., the range of a 2.0 % composition is between 1.98 % and 2.02 %. 

Nominal or target mass compositions are used in the discussion. For example, the “actual” 

mass composition of the RL68H in the R134a/ RL68H (99.5/0.5) mixture was 0.53 % 

± 0.02 %. Likewise, the RL68H mass fractions for R134a/ RL68H (99/1) and the R134a/ 

RL68H (98/2) mixtures were 1.04 % ± 0.02 % and 2.10 % ± 0.02 %, respectively. Using the 

same uncertainties, the nanolubricant mass fractions as tested with R134a were 0.53 %, 

1.05 %, and 1.99 %. 

Figure 3 is a plot of the measured heat flux (q") versus the measured wall superheat (Tw - Ts) 

for pure R134a at a saturation temperature of 277.6 K. The closed circles represent 13 days 

of boiling measurements made over a period of approximately three weeks. The solid lines 

shown in Fig. 3 are cubic best-fit regressions or estimated means of the data. Five of the 145 

measurements were removed before fitting because they were identified as “outliers” based 

on having both high influence and high-leverage (Belsley et al., 1980). Table 4 gives the 

constants for the cubic regression of the superheat versus the heat flux for all of the fluids 

tested here. The residual standard deviation of the regressions - representing the proximity of 

the data to the mean - are given in Table 5. The dashed lines to either side of the mean 

represent the lower and upper 95 % simultaneous (multiple-use) confidence intervals for the 

mean. From the confidence intervals, the expanded uncertainty of the estimated mean wall 

superheat was 0.14 K and 0.06 K for superheats less than and greater than 7 K, respectively. 

Table 6 provides the average magnitude of 95 % multi-use confidence interval for the fitted 

wall superheat for all of the test data.

The effect of the pure lubricant mass fraction on R134a/lubricant pool boiling is shown in 

Fig. 4. Figure 4 plots the measured heat flux (q") versus the measured wall superheat (Tw -

Ts) at a saturation temperature of 277.6 K for the three R134a/RL68H mixtures. Comparison 

of the three mean boiling curves shows that the superheats are within approximately 1 K of 

each other for heat fluxes between approximately 30 kW/m2 and 90 kW/m2. For the same 

heat flux range, the superheat for the pure R134a is roughly 3 K less than that for the 

mixtures translating into a heat transfer degradation with respect to R134a. Kedzierski 

(2001b) has shown that, in general, degradations due to increased lubricant mass fractions 

occur when the concentration induced bubble size reduction, and its accompanying loss of 

vapor generation per bubble, is not compensated by an increase in site density. Once a heat 

transfer degradation has occurred, it has been observed to continue to degrade with respect to 

increasing lubricant mass fraction. All the measurements shown in Fig. 4 excluding those for 

the (98/2) mixture where the heat flux is greater than 30 kW/m2 are consistent with this trend. 

Consequently, the observation that the heat transfer degradation increases from the (99.5/0.5) 

mixture to the (99/1) mixture and then decreases from the (99/1) mixture to the (98/2) 

mixture, for heat fluxes greater than 30 kW/m2, is unusual and unexpected. In addition, 

Fig. 4 and Table 6 illustrate a second unusual characteristic of the measurements in that they 

become more repeatable for the larger lubricant concentrations. More specifically, the 

average magnitude of the 95 % multi-use confidence interval for the mean superheat 

decreases from 0.22 K, to 0.15 K, and to 0.09 K for increasing mixture compositions of 

(99.5/0.5), (99/1), and (98/2), respectively. This trend is contrary to what is typically 

observed for increasing lubricant mass fraction refrigerant/lubricant mixture boiling heat 

transfer measurements, which usually exhibit increasing data scatter. 
11

The effect of the nanolubricant mass fraction on R134a/nanolubricant pool boiling is shown 

in Fig. 5. Figure 5 is a plot of the measured heat flux (q") versus the measured wall 

superheat (Tw - Ts) for the R134a/RL68H1Cu mixtures at a saturation temperature of 

277.6 K. An average of 153 measurements were made for each mixture over the span of 

approximately a week. The means of the R134a/RL68H1Cu (99/1) and the 

R134a/RL68H1Cu (98/2) superheat measurements are within approximately 1 K for the 

entire heat flux range that was tested. For heat fluxes less than approximately 30 kW/m2 and 

greater than approximately 60 kW/m2, the R134a/RL68H1Cu (99/1) mixture mean superheat 

is less than that of the R134a/RL68H1Cu (98/2) mixture. For heat fluxes between these 

limits, the R134a/RL68H1Cu (98/2) mixture exhibits the unusual characteristic of having an 

enhanced boiling performance as compared to the R134a/RL68H1Cu (99/1) mixture. For 

most heat fluxes, the R134a/RL68H1Cu (99.5/0.5) superheat measurements, represented by 

the open triangles, are significantly less than those of the 99/1 and the 98/2 mixtures. For 

comparison, the mean of the pure R134a boiling curve is provided as a coarsely dashed line. 

The average expanded uncertainty of the estimated mean wall superheat for the three 

refrigerant/nanolubricant mixtures was 0.23 K.

A more precise comparison of the R134a/RL68H and the R134a/RL68H1Cu heat transfer 

performances relative to R134a and R134a/RL68H, respectively, is given in Figs. 6 and 7. 

Figure 6 plots the ratio of the R134a/RL68H mixture heat flux to the pure R134a heat flux 

(q"PL/q"p) versus the pure R134a heat flux (q"p) at the same wall superheat. Figure 6 

illustrates the influence of lubricant mass composition on the R134a/RL68H boiling curve 

with solid lines representing the mean heat flux ratios for each mixture. Overall, lubricant 

for all compositions has caused a heat transfer degradation relative to the heat transfer of 

pure R134a for all measured q"p. The degradation is shown to increase with lubricant mass 

fraction. For example, the average heat flux ratio for the R134a/RL68H (99.5/0.5), the 

R134a/RL68H (99/1), and the R134a/RL68H (98/2) mixture from approximately 15 kW/m2

to 120 kW/m2 was 0.43, 0.37, and 0.28, respectively.4

Figure 7 details the effect that the CuO nanoparticles had on the R134a/RL68H boiling 

curves. The figure plots the ratio of the R134a/RL68H1Cu heat flux to the R134a/RL68H 

heat flux (q"CuO/q"PL) versus the R134a/RL68H1Cu mixture heat flux (q"CuO) at the same 

wall superheat. The three different compositions are represented by three different lines 

where each R134a/nanolubricant mixture is compared to the R134a/pure-lubricant mixture at 

the same mass fraction. A heat transfer enhancement exists where the heat flux ratio is 

 The minimum heat transfer 

degradation for each mixture (or the maximum heat transfer) is shown on Fig. 6 to be at 

lowest measured heat fluxes. For 20 kW/m2, the heat flux ratio for the R134a/RL68H 

(99.5/0.5), the R134a/RL68H (99/1), and the R134a/RL68H (98/2) mixture is 0.62 ± 0.16, 

0.58 ± 0.16, and 0.47 ± 0.12, respectively. The lubricant effect becomes more pronounced as 

the heat flux increases from roughly 20 kW/m2 to 120 kW/m2 producing heat flux ratios of 

approximately 0.37, 0.3, and 0.25 at 100 kW/m2 for the R134a/RL68H (99.5/0.5), the 

R134a/RL68H (99/1), and the R134a/RL68H (98/2) mixtures, respectively.

 4 A heat transfer enhancement for the R134a/RL68H (98/2) mixture is not shown because this occurs for values 

of q"p larger than what was measured. Therefore, a comparison could not be made between the fluids at the 

larger heat flux. 
12

greater than one and the 95 % simultaneous confidence intervals (depicted by the shaded 

regions) do not include the value one. Figure 7 shows that the R134a/RL68H1Cu (99.5/0.5) 

mixture exhibits a significant boiling heat transfer enhancement over that of the 

R134a/RL68H (99.5/0.5) mixture. The heat flux ratio varies between roughly 1.5 and 3.75 

for the R134a/RL68H1Cu (99.5/0.5) mixture for heat fluxes between 10 kW/m2 and 

110 kW/m2. The R134a/RL68H1Cu (99/1) mixture shows a maximum heat flux ratio of 

approximately 1.54 and a region between 30 kW/m2 and 60 kW/m2 where no difference can 

be established between the two fluids because the confidence intervals include the value of 

one. Overall, the average heat flux ratio for the R134a/RL68H1Cu (99.5/0.5) mixture and 

the R134a/RL68H1Cu (99/1) mixture from approximately 10 kW/m2 to 110 kW/m2 was 2.4, 

and 1.19, respectively. The average heat flux ratio for the R134a/RL68H1Cu (98/2) mixture 

from approximately 10 kW/m2 to 65 kW/m2 was 1.12.

DISCUSSION

The heat transfer results summarized in Fig. 7 show that nanolubricants have a great potential 

for improving the pool boiling heat transfer of refrigerant/lubricant mixtures. However, 

Fig. 8 brings into question whether this enhancement is caused by an increase in thermal 

conductivity, as suggested in the Introduction, or some other mechanism(s). Figure 8 shows 

the thermal conductivity of several RL68H/CuO nanoparticle mixtures as measured with a 

transient line-source technique (Roder et al., 2000). Even though the thermal conductivity of 

CuO (20 W/m·K)5 is two orders of magnitude greater than that of neat RL68H 

(0.132 W/m·K ± 0.001 W/m·K6

 5 Kwak and Kim (2005)

6 This is a random uncertainty obtained solely from repeated measurements, which does not account for a 

possible bias error. The type B uncertainty obtained from the manufacturer was ± 0.01 W/m·K. 

), an improvement in the thermal conductivity significantly 

beyond that proportional to the volume fraction of the nanofluid was not obtained. For 

example, the volume fraction used in the boiling experiments (1 %) resulted in the nanofluid 

having a thermal conductivity that is roughly 5 % greater than that of the pure base fluid. 

This proportional improvement is disappointing compared to the 40 % improvement in 

thermal conductivity for a 0.4 % volume fraction achieved by Eastman et al. (2001). 

However, as shown in Fig. 8, the solid-liquid thermal conductivity model of Wasp (1977) 

confirms the measured thermal conductivity of the 1 % by volume mixture 

(0.139 W/m·K ± 0.001 W/m·K) to within approximately 4 %. 

The marginal increase in thermal conductivity of the refrigerant mixture as charged may not 

necessarily translate into marginal improvement of the thermal conductivity of the liquid at 

the heat transfer surface. The effective enhancement of the lubricant’s thermal conductivity 

may in fact be greater than what the bulk concentration suggests because of the accumulation 

of nanoparticles in the lubricant excess layer that exists on the heat transfer surface. The 

increase in nanoparticle concentration in the excess layer was supported by observing the 

darkened lubricant that remained on the test surface after testing and removing the charge 

from the test apparatus. As a result, the thermal conductivity of the lubricant that resides on 

the surface and governs the boiling process may be greater than what the bulk nanoparticles 

concentration would suggest.
13

In order to more closely examine the effect of thermal conductivity, Fig. 9 compares the 

enhancement ratio for the R134a/RL68H1Cu (99.5/0.5) mixture to those predicted by the 

refrigerant/lubricant mixture, pool-boiling model given in Kedzierski (2003b). The model is 

used to assess the effect of increased lubricant thermal conductivity on the boiling heat 

transfer. One prediction is presented for the charged 1 % volume fraction corresponding to a 

nanolubricant thermal conductivity of 0.139 W/m·K. The other prediction is presented to 

simulate the case where the nanoparticles accumulate to a 9 % volume fraction on the heat 

transfer surface giving a thermal conductivity of 0.206 W/m·K ± 0.002 W/m·K. Both 

predictions are at least 80 % less than the measured heat flux ratio. Consequently, the 

comparison demonstrates that the increased thermal conductivity of the nanofluid cannot be 

used to explain the entire enhancement associated with the refrigerant/nanolubricant boiling 

heat transfer. It appears that at most, 20 % of the enhancement may be due to increased 

thermal conductivity for a 9 % volume fraction excess layer. Other factors, are likely to 

contribute to the enhancement, for example, the particles may be inducing secondary 

nucleation on the bubbles and on the heat transfer surface. The particles may be 

agglomerating within the excess layer and acting similar to a porous surface in enhancing 

boiling. In addition, there may be particle-mixing effects that contribute to the heat transfer 

enhancement.

Future research is required to investigate the influence of the particle material, its shape, size, 

distribution, and concentration on refrigerant boiling performance. Not only should the bulk 

concentration be studied, the distribution of the concentration of the nanoparticles within a 

particular system should be investigated. Because of the instability of the nanoparticles in 

the low viscosity refrigerant, the balance between the entrainment of nanoparticles by fluid 

mixing (rather than Brownian motion) and the deposition of nanoparticles in the excess layer 

will, in part, determine the distribution of nanoparticles in a particular system. In addition, a 

smaller fraction of the nanoparticles may be held up in monolayers to the wetted adiabatic 

surfaces. Hence, several interacting mechanisms are likely to be responsible for the 

distribution of nanoparticles in the system and, in turn, the performance of the system. For 

this reason, the influence of refrigerant/nanolubricant charge, heat transfer area, and adiabatic 

surface area on the concentration of the nanoparticles in the lubricant excess layer should be 

investigated. The potential for nanoparticles to travel to the heat transfer surface by the act 

of boiling is dictated by the available mass of nanoparticles in the refrigerant mixture charge. 

Consequently, it may not be fair to compare studies at the same bulk nanoparticles 

concentration for two different systems because the relative refrigerant-charge-to-surfacearea may differ for the two systems. Considering this, a parameter more pertinent than the 

bulk nanoparticles concentration for investigation may be the concentration of nanoparticles in 

the nanolubricant excess layer that resides on the boiling surface. Further investigation into the 

above effects may lead to a theory that can be used to develop nanolubricants that improve 

boiling heat transfer for the benefit of the refrigeration and air-conditioning industry.

CONCLUSIONS

The effect of CuO nanoparticles on the boiling performance of R134a/polyolester mixtures 

on a roughened, horizontal flat surface was investigated. A nanolubricant containing CuO 

nanoparitcles at 1 % volume fraction with a polyolester lubricant was mixed with R134a at 

three different mass fractions. For the 0.5 % nanolubricant mass fraction, the nanoparticles 
14

caused a heat transfer enhancement relative to the heat transfer of pure R134a/polyolester 

(99.5/0.5) between 50 % and 275 %. A smaller enhancement was observed for the 

R134a/nanolubricant (99/1) mixture, which had a heat flux that was on average 19 % larger 

than that of the R134a/polyolester (99/1) mixture. Further increase in the nanolubricant mass 

fraction to 2 % resulted in a still smaller boiling heat transfer improvement of approximately 

12 % on average for the R134a/nanolubricant (98/2) mixture. The measurements illustrate 

that the performance improvement decreases with increasing lubricant concentration. In 

other words, nanoparticles are less likely to be of benefit where they are needed most. 

However, if a system can be designed to maintain a small lubricant concentration in the 

evaporator, significant performance improvements can be expected.

Although the nanoparticles increased the thermal conductivity of the lubricant, the increase 

in thermal conductivity appears to be responsible for only a small portion (potentially 20 %) 

of the boiling heat transfer enhancement. Other effects, in particular, secondary nucleation 

and particle mixing may contribute more significantly to the enhancement of the 

refrigerant/lubricant boiling heat transfer with nanoparticles.

ACKNOWLEDGEMENTS

This work was funded by NIST. Thanks go to the following NIST personnel for their 

constructive criticism of the first draft of the manuscript: Mr. B. Dougherty, and Dr. P. 

Domanski. Thanks go to Prof. A. Jacobi of the University of Illinois at Urbana-Champaign 

for his constructive criticism of the second draft of the manuscript. Furthermore, the authors 

extend appreciation to W. Guthrie and Mr. A. Heckert of the NIST Statistical Engineering 

Division for their consultations on the uncertainty analysis. Some boiling heat transfer 

measurements were taken by Mr. David Wilmering of KT Consultants. The RL68H 

(EMKARATE RL 68H) was donated by Dr. S. Randles of Uniqema. The RL68H1Cu was 

manufactured by Nanophase Technologies with a copper (II) oxide and dispersant in RL68H 

especially for NIST.
15

NOMENCLATURE

English Symbols

An regression constant in Table 4 n=0,1,2,3

Co viscometer calibration constant, μm

2

·s-1

g gravitational acceleration, m s-2

k thermal conductivity, W·K-1 m-1

l capillary rise height, m

Ly length of test surface (Fig. 2), m

M mass, kg

q" average wall heat flux, W·m-2

r radius of capillary tube, m

T temperature, K

Tw temperature at roughened surface, K

U expanded uncertainty

ui standard uncertainty

V volume, m3

X model terms given in Table 2

Greek symbols

∆T temperature difference, K

∆Ts wall superheat: Tw - Ts, K 

∆ρ difference between liquid and vapor density, kg·m-3

ν kinematic viscosity, m2·s-1

ρ liquid density, kg·m-3

σ surface tension, kg·s-2

φ volume fraction

English Subscripts

CuO R134a/RL68H1Cu mixture

i initial volume

l neat lubricant

L nanolubricant

np nanoparticles

p pure R134a

PL R134a/RL68H mixture

q" heat flux

s saturated state

t target volume

T total volume

Tw wall temperature

w wall, heat transfer surface 

+ added volume
16

REFERENCES

Adamson, A. W., and Gast, A. P., 1997, Physical Chemistry of Surfaces, Interscience Publ., 

New York, 6th Ed., p. 11.

Bang, I. C. and, Chang, S. H., 2004, “Boiling Heat Transfer Performance and Phenomena of 

Al2O3–Water Nanofluids From a Plain Surface in a Pool,” Proceedings of ICAPP, Pittsburgh, 

PA, pp. 1437-1443.

Belsley, D. A., Kuh, E., and Welsch, R. E., 1980, Regression Diagnostics: Identifying 

Influential Data and Sources of Collinearity, New York: Wiley.

Eastman, J. A, Choi, S. U. S., Li, S., Yu, W., and Thompson, L. J., 2001, “Anomalously 

Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing 

Copper Nanoparticles,” Appl. Phys. Lett. 78, p.718-720. 

Incropera, F. P., and DeWitt, D. P., 1985, Fundamentals of Heat and Mass Transfer, 2nd ed., 

John Wiley & Sons, New York.

Kedzierski, M. A., 2003a, “A Semi-Theoretical Model for Predicting R123/Lubricant Mixture 

Pool Boiling Heat Transfer,” Int. J. Refrigeration, Vol. 26, pp. 337-348.

Kedzierski, M. A., 2003b, “Improved Thermal Boundary Layer Parameter For Semi-Theoretical 

Refrigerant/Lubricant Pool Boiling Model,” Proceedings of Int. Congress of Refrigeration, 

ICR0504, Washington, DC.

Kedzierski, M. A., 2002, “Use of Fluorescence to Measure the Lubricant Excess Surface 

Density During Pool Boiling,” Int. J. Refrigeration, Vol. 25, pp.1110-1122.

Kedzierski, M. A., 2001a, “Use of Fluorescence to Measure the Lubricant Excess Surface 

Density During Pool Boiling,” NISTIR 6727, U.S. Department of Commerce, Washington, 

D.C.

Kedzierski, M. A., 2001b, “The Effect of Lubricant Concentration, Miscibility and Viscosity 

on R134a Pool Boiling” Int. J. Refrigeration, Vol. 24, No. 4., pp. 348-366.

Kedzierski, M. A., 2000, “Enhancement of R123 Pool Boiling by the Addition of 

Hydrocarbons,” Int. J. Refrigeration, Vol. 23, pp. 89-100.

Kedzierski, M. A., 1995, “Calorimetric and Visual Measurements of R123 Pool Boiling on 

Four Enhanced Surfaces,” NISTIR 5732, U.S. Department of Commerce, Washington. 

Kwak, K., and Kim, C., 2005, “Viscosity and Thermal Conductivity of Copper Oxide 

nanofluid Dispersed in Ethylene Glycol, Korea-Australia Rheology J., Vol. 17, No. 2, pp. 35-

40.
17

Reid, R. C., Prausnitz, J. M., and Sherwood, T. K., 1977, The Properties of Gases and 

Liquids, 3rd ed., McGraw-Hill, NY, p. 87.

Roder, H. M., Perkins, R. A., Laesecke, A., and Nieto de Castro, C. A., 2000, “Absolute 

Steady-State Thermal Conductivity Measurements by Use of a Transient Hot-Wire System,” 

J. Res. Natl. Inst. of Stand. and Technol., Vol. 105, No. 2, pp 221-253.

Sung, L., 2006, Private Communications, National Institute of Standards and Technology, 

Building and Fire Research Laboratory, Gaithersburg, MD.

Wasp, F. J., 1977, “Solid-Liquid Flow Slurry Pipeline Transportation, Trans., Tech. Pub., 

Berlin.

Wen, D, and Ding, Y., 2005, “Experimental Investigation into the Pool Boiling Heat Transfer 

of Aqueous Based γ-Alumina Nanofluids,” J. of Nanoparticle Research

You, S. M., Kim, J. H., and Kim, K. H., 2003, “Effect of Nanoparticles on Critical Heat Flux 

of Water in Pool Boiling Heat Transfer,” Applied Physics Letter, 83 (16) pp. 375-377.

, Vol. 7, pp. 265-274.
18

Table 1 Conduction model choice

X0= constant (all models) X1= x X2= y X3= xy 

X4=x

2

-y

2

X5= y(3x2-y

2

) X6= x(3y2-x

2

) X7= x

4

+y4-6(x2)y2

 X8= yx

3

-xy

3

Fluid Most frequent models

Pure R134a

(file: nan134.dat)

X1,X3 (73 of 145) 50 %

X1,X2 (61 of 145) 42 %

R134a/RL68H (99.5/0.5) 

(file: RL685.dat)

X1,X3 (70 of 186) 38 %

X1,X2 (53 of 186) 28 %

X1,X2,X3 (16 of 186) 9 %

X1,X2,X5 (15 of 186) 8 %

R134a/RL68H (99/1) 

(file: RL681.dat)

X1,X2 (48 of 68) 70 %

X1,X2,X4,X6 (11 of 68) 17 %

R134a/RL68H (98/2) 

(file: RL682.dat)

X1,X2,X3,X4,X6 (148 of 192) 77 %

X1,X2 (15 of 192) 8 %

X1,X2,X4 (12 of 192) 6 %

X1,X3,X4,X6 (12 of 192) 6 %

R134a/RL68H1Cu 

(99.5/0.5) 

(file: RL4Cu5.dat)

X1,X2,X4,X6 (66 of 132) 50 %

X1,X2,X4 (41 of 132) 31 %

X1,X2 (26 of 132) 19 %

R134a/RL68H1Cu (99/1) 

(file: RL4Cu1.dat)

X1,X2,X4 (61 of 157) 39 %

X1,X2,X4,X6 (54 of 157) 35 %

X1,X2 (31 of 157) 20 %

R134a/RL68H1Cu (98/2) 

(file: RL4Cu2.dat)

X1,X2,X3 (82 of 170) 48 %

X1,X2,X3,X5 (30 of 170) 18 %

X1,X3 (24 of 170) 14 %

X1,X2 (17 of 170) 10 %
19

Table 2 Pool boiling data

 Pure R134a

File: NAN134.dat ∆Ts (K) q" 

(W/m

2

)

 8.92 126104.

 8.79 119028.

 8.59 106475.

 8.43 99070.

 8.28 91217.

 8.01 82705.

 7.64 69801.

 7.28 60015.

 6.85 50199.

 6.50 44511.

 6.19 39901.

 5.67 31859.

 4.77 20893.

 4.25 15759.

 3.82 12669.

 8.73 130507.

 8.62 122030.

 8.51 114036.

 8.39 106353.

 8.24 98914.

 8.08 91180.

 7.91 84209.

 7.70 76344.

 7.46 68271.

 7.20 60806.

 6.84 51759.

 6.49 44281.

 6.05 36180.

 5.58 29364.

 5.03 22199.

 4.17 14172.

 3.34 9814.

 8.62 126906.

 8.47 116864.

 8.29 108305.

 8.09 97927.

 7.85 86807.

 7.71 81105.

 7.57 75561.

 7.27 65138.

 6.73 50435.

 8.92 127596.

 8.73 117731.

 8.50 105501.

 8.31 96894.

 8.14 88757.

 7.94 80277.

 7.29 57205.

 6.70 42432.

 5.87 27905.

 8.88 122952.

 8.58 109658.

 8.30 96066.

 8.04 84007.

 7.57 66907.

 7.03 50278.

 6.61 40074.

 5.94 27932.

 5.11 17791.

 9.04 130031.

 8.69 116715.

 8.15 91440.

 7.87 80278.

 7.39 63193.

 7.01 51846.

 6.49 38993.

 5.74 25263.

 4.99 16917.

 8.97 124136.

 8.67 111439.

 8.30 98564.

 7.95 84354.

 7.52 69117.

 6.97 52438.

 6.47 40246.

 5.71 26725.

 4.51 14899.

 8.95 126301.

 8.58 110232.

 8.22 95839.

 7.74 77856.

 7.34 64277.

 6.85 50734.

 6.33 38495.

 5.48 24416.

 4.27 13582.

 9.06 138038.

 8.50 113047.

 8.27 102662.

 8.04 92250.

 7.68 78416.

 7.18 61740.

 6.43 42351.

 5.90 32295.

 5.11 21158.

 9.08 125354.

 8.79 114612.

 8.58 107058.

 8.36 98699.

 8.21 92508.

 8.05 86679.

 7.86 78617.

 7.68 72797.

 7.35 61711.

 7.01 52569.

 6.65 43745.

 6.44 39244.

 6.12 33020.

 5.75 26675.

 5.10 19366.

 4.42 14315.

 9.23 129754.

 8.89 119950.

 8.65 111371.

 8.45 104257.

 8.20 95214.

 8.03 88745.

 7.76 78490.

 7.54 71987.

 7.34 65568.

 6.99 55133.

 6.74 48295.

 6.41 40600.

 6.04 33478.

 5.79 28819.

 5.32 22439.

 4.68 16512.

 4.02 12126.

 9.08 126898.

 8.89 119389.

 8.64 109873.

 8.44 102531.

 8.24 94776.

 8.01 86955.

 7.87 82399.

 7.66 75306.

 7.30 63501.

 7.02 54784.

 6.75 47883.

 6.42 40001.

 6.07 33381.

 5.62 26016.

 5.04 19027.

 4.41 14216.

 3.65 10334.

R134a/RL68H (99.5/0.5)

File: RL685.dat ∆Ts

(K)

q" 

(W/m

2

)

10.41 125461.

10.09 117289.

9.82 109225.

9.55 98358.

9.52 91624.

9.53 84267.

9.58 72981.

9.51 65377.

9.27 56853.

8.79 47343.

8.85 47278.

8.77 38900.

8.76 31930.

7.62 25182.

6.67 19668.

5.55 14154.

4.38 10401.

10.64 116069.

10.27 110599.

9.98 100115.

10.17 91232.

10.29 91094.

10.32 91375.
20

10.33 90476.

10.36 90320.

10.41 89728.

10.55 90939.

10.44 91270.

10.35 90233.

10.43 90408.

10.44 91518.

10.43 90661.

10.39 90783.

10.25 83003.

10.91 123338.

10.61 123991.

10.33 124434.

10.09 123731.

9.93 122460.

9.71 124093.

9.81 122523.

9.81 122964.

9.88 122758.

11.83 124963.

10.63 122392.

10.01 125262.

9.85 124800.

9.79 124447.

9.78 124857.

10.25 101381.

10.53 100100.

10.62 99685.

11.06 121789.

10.39 110647.

10.41 110453.

10.37 111313.

10.48 109214.

10.81 101046.

10.81 100335.

10.78 100504.

10.74 101889.

11.52 114620.

9.01 31346.

8.61 31682.

8.29 31432.

8.01 31367.

7.92 31200.

7.94 31877.

8.73 41245.

8.70 41025.

8.68 41310.

9.37 54189.

9.32 53486.

9.35 53874.

10.01 69882.

10.71 85442.

10.02 69569.

10.74 85289.

10.72 117490.

10.55 89892.

10.76 90368.

10.76 89757.

10.78 89430.

10.52 76064.

10.53 74333.

10.41 75353.

9.29 52566.

9.32 53737.

8.52 42095.

8.58 42005.

8.64 41953.

11.08 116281.

10.51 109510.

9.66 110884.

9.65 111548.

9.65 110644.

9.70 95978.

10.36 95059.

10.43 95029.

10.43 94190.

10.62 79303.

10.62 78988.

10.58 78967.

9.65 59256.

9.63 59493.

9.66 115942.

9.47 115817.

9.45 115446.

9.43 116102.

9.82 101375.

9.79 101447.

9.89 101632.

10.58 80370.

10.51 83137.

10.10 69612.

9.98 69519.

9.89 68735.

9.94 68481.

9.60 63125.

9.55 62877.

9.57 62833.

9.08 53290.

9.11 52372.

10.69 108075.

10.42 108081.

9.51 107191.

10.32 77311.

10.54 78551.

10.56 80934.

8.90 34451.

8.81 36837.

8.65 37225.

7.51 27878.

7.41 27849.

7.31 27864.

7.27 27338. 7.17 27023.

9.97 118979.

9.90 98160.

10.19 98735.

10.22 99564.

10.28 99233.

10.64 81195.

10.72 81282.

10.64 79004.

9.99 61334.

10.89 115820.

9.52 61465.

9.38 65648.

9.45 66079.

8.35 37041.

8.26 37629.

8.26 37613.

6.26 19940.

5.21 12965. 10.13 126231.

9.80 84883.

9.84 85440.

9.91 84946.

10.01 73115.

9.97 73398.

9.99 73437.

9.32 54567.

9.23 54394.

9.22 54900.

8.16 33901.

8.07 34073.

8.00 33965.

5.81 16579.

5.78 16880.

10.26 114713.

10.06 88189.

10.06 88985.

10.02 89430.

9.99 70106.

9.94 68598.

9.90 68983.

9.07 43312.

8.98 43557.

8.95 43212.

8.04 35039.

7.94 35399.

7.98 34504.

6.98 26646.

5.53 15057.

4.42 11080.

R134a/RL68H (99/1)

File: RL681.dat ∆Ts

(K)

q" 

(W/m

2

)

 11.45 114670.

 11.48 114253.

 11.37 101278.

 11.28 93385.

 11.06 84673.

 10.76 76916.

 10.39 69048.

 9.99 59964.

 9.74 53229.

 9.31 43447.

 9.02 36925.

 8.43 30041.

 7.79 24720.

 6.98 19617.

 6.19 15805.

 5.13 11493.

 11.61 117238.

 11.52 109067.

 11.55 101159.

 11.40 92569.

 11.14 85753.

 10.87 77917.

 10.65 72768.

 10.37 66045.

 10.13 59958.
21

 9.79 51877.

 9.47 43112.

 9.21 38451.

 8.65 31184.

 8.08 26866.

 7.45 22486.

 6.45 16995.

 5.38 12742.

 11.33 111594.

 11.38 104916.

 11.22 95263.

 11.09 88873.

 10.70 78358.

 10.35 72485.

 10.09 67134.

 9.76 59670.

 9.44 53291.

 9.17 46083.

 8.84 39211.

 8.43 32932.

 7.96 28150.

 7.43 23881.

 6.74 19409.

 5.85 14945.

 4.80 11088.

 11.39 116661.

 11.22 107363.

 11.18 98750.

 11.18 92532.

 11.07 85485.

 10.88 78025.

 10.66 71220.

 10.37 65212.

 10.11 60634.

 9.75 51898.

 9.30 42407.

 8.91 36174.

 8.35 29873.

 7.75 25073.

 6.82 19068.

 5.87 14832.

 4.92 11145.

 3.87 8484.

R134a/RL68H (98/2)

File: RL682.dat ∆Ts

(K)

q" 

(W/m

2

)

 10.46 120365.

 10.45 115838.

 10.41 111220.

 10.32 94618.

 10.39 97658.

 10.29 90814.

 10.32 92784.

 10.34 92810.

 10.18 79753.

 10.15 79841.

 10.16 81082.

 9.94 69921.

 9.94 70162.

 9.91 70304.

 9.67 59011.

 9.63 58948.

 9.61 59241.

 9.34 48700.

 9.29 48182.

 9.23 47451.

 8.88 35719.

 8.84 33420.

 8.78 33779.

 8.53 28958.

 8.52 28533.

 8.52 28117.

 7.97 20339.

 7.94 19897.

 7.90 19509.

 7.09 14308.

 6.79 13139.

 10.11 96882.

 10.21 101028.

 10.25 104081.

 10.16 96491.

 10.18 96990.

 10.22 98340.

 10.26 92205.

 10.31 93439.

 10.36 94510.

 10.18 80878.

 10.19 81197.

 10.21 81995.

 9.91 67986.

 9.89 67802.

 9.87 68453.

 9.59 56984.

 9.57 56757.

 9.56 57119.

 9.31 47737.

 9.27 47201.

 9.24 46919.

 8.90 37682.

 8.85 36516.

 8.73 32965.

 8.49 27176.

 8.46 26594.

 8.44 26820.

 8.03 20650.

 8.02 20603.

 8.01 20637.

 6.97 13807.

 6.91 13468.

 6.90 13458.

 4.37 7773.

 4.13 7814.

 10.38 116228.

 10.36 114533.

 10.32 112413.

 10.03 93005.

 10.03 90636.

 10.04 89940.

 9.91 79400.

 9.93 79285.

 9.97 79490.

 9.77 67901.

 9.73 67241.

 9.71 67796.

 9.53 58973.

 9.50 58434.

 9.50 58730.

 9.27 49772.

 9.25 49249.

 9.22 48154.

 8.97 40005.

 8.97 40118.

 8.97 40693.

 8.55 28219.

 8.52 27593.

 8.52 27297.

 7.97 19489.

 7.93 19342.

 7.95 19757.

 7.10 13514.

 7.07 13348.

 7.09 13330.

 5.12 9463.

 4.97 9221.

 10.35 113634.

 10.39 113879.

 10.38 113399.

 10.21 101492.

 10.20 100433.

 10.20 99352.

 10.08 86806.

 10.10 85998.

 10.13 85876.

 9.99 74165.

 9.99 73536.

 9.97 73612.

 9.67 59843.

 9.63 59155.

 9.60 58851.

 9.29 48030.

 9.24 48251.

 9.21 48237.

 8.91 38365.

 8.90 38280.

 8.90 38433.

 8.56 28864.

 8.54 28522.

 8.52 28082.

 8.03 20657.

 7.98 20000.

 7.98 20026.

 6.99 13522.

 6.88 13219.

 6.90 13323.

 4.75 8496.

 4.52 8336.

 10.39 113340.

 10.38 111810.

 10.36 109427.

 10.22 100505.

 10.19 98596.

 10.21 97769.

 10.08 83945.

 10.07 83114.

 10.10 83292.

 9.99 73887.

 9.99 74076.

 10.00 74565.

 9.69 62807.

 9.67 62988.
22

 9.65 63454.

 9.40 52781.

 9.37 52792.

 9.35 52793.

 9.12 44736.

 9.10 44631.

 9.10 44755.

 8.81 34764.

 8.76 34063.

 8.76 34093.

 8.33 24570.

 8.28 23925.

 8.27 23887.

 7.64 16725.

 7.60 16375.

 7.62 17454.

 5.90 10924.

 5.66 10706.

 10.33 96303.

 10.34 94383.

 10.31 93085.

 10.11 79719.

 10.11 78470.

 10.14 78057.

 9.91 67703.

 9.87 67670.

 9.83 67582.

 9.53 55465.

 9.50 55634.

 9.50 56202.

 9.23 45653.

 9.19 44948.

 9.14 45623.

 8.85 35942.

 8.86 36362.

 8.84 36780.

 8.34 24576.

 8.37 24673.

 8.39 24993.

 7.74 17522.

 7.70 17398.

 7.72 17517.

 6.49 11613.

 6.34 11481.

 6.29 11206.

 4.80 8877.

 4.67 8884.

 4.69 8920.

R134a/RL68H1Cu (99.5/0.5)

File: RL1Cu5.dat ∆Ts

(K)

q" 

(W/m

2

)

8.58 108670.

7.98 101295.

7.71 94268.

7.24 84389.

7.14 77994.

7.12 73189.

6.89 59731.

7.57 52222.

7.14 43333.

6.74 37432.

6.39 32012.

6.18 28581.

5.63 23208.

4.89 17594.

4.24 15345.

3.45 11017.

8.07 104134.

7.49 98239.

7.08 90736.

6.86 83594.

6.76 76379.

6.91 70628.

6.96 63820.

7.11 56794.

6.88 51101.

6.55 45204.

6.49 35966.

6.24 32460.

5.90 28561.

5.15 20877.

4.43 17539.

3.75 13200.

7.71 108174.

7.16 101751.

6.87 95097.

6.79 88910.

6.85 82367.

6.86 74585.

7.35 69317.

7.43 60356.

7.11 54639.

6.69 47786.

6.33 40530.

5.98 34347.

5.73 30130.

5.32 25229.

4.71 21116.

4.11 16094.

3.48 11974.

7.23 97257.

7.04 88884.

6.97 76461.

6.92 82271.

7.23 68989.

7.89 62465.

8.15 57984.

7.82 51489.

7.54 45596.

7.03 37402.

6.79 30262.

6.32 25728.

5.54 21812.

4.88 17308.

3.85 11820.

8.46 109658.

7.98 102696.

7.69 95626.

7.52 89791.

7.37 82639.

7.58 76129.

7.83 68624.

8.21 60228.

8.16 54231.

7.75 46416.

7.46 37082.

6.85 29355.

6.42 25715.

5.63 19775.

4.87 16983.

3.93 11987.

8.10 112782.

7.74 106076.

7.65 100674.

7.65 93818.

7.56 84705.

7.67 76848.

7.86 70397.

8.01 63698.

7.98 57635.

7.98 52079.

7.59 44632.

7.37 37876.

7.03 31737.

6.62 27346.

5.97 21934.

5.07 17898.

4.15 12991.

8.10 113418.

7.75 107131.

7.49 100701.

7.47 92226.

7.70 84174.

7.70 78430.

7.62 71396.

7.77 67305.

7.80 57584.

8.21 53149.

7.99 45743.

7.69 36808.

7.36 29231.

7.08 24901.

6.37 20541.

5.25 16369.

4.02 11383.

7.79 123100.

7.36 113999.

7.05 105138.

6.84 96025.

6.72 86175.

6.7679422.

6.90 72075.

7.18 64916.

7.55 60155.

7.60 49001.

7.56 42658.

7.40 35804.

7.33 27925.

6.73 22862.

5.92 20134.

4.91 15249.

3.99 11532.

3.22 9701.

R134a/RL68H1Cu (99/1)

File: RL1Cu1.dat ∆Ts q" 

(W/m

2

)
23

(K)

10.60 103166.

10.21 93530.

10.09 86311.

9.88 78804.

9.69 71499.

9.59 64194.

9.31 56611.

9.23 50457.

9.07 42082.

8.82 37123.

8.37 32224.

7.61 26896.

7.04 23433.

5.96 19523.

5.01 15069.

4.18 11702.

10.33 101030.

9.99 94207.

9.80 86567.

9.54 78575.

9.54 71329.

9.29 62666.

9.20 55782.

9.01 48927.

8.95 42343.

8.74 37814.

8.29 34129.

7.70 29346.

7.15 25624.

6.48 21547.

5.69 17369.

4.91 15376.

4.06 11667.

10.48 101465.

10.06 94378.

9.90 88678.

9.76 82513.

9.53 73434.

9.53 67989.

9.34 59422.

9.29 54735.

9.12 49853.

8.73 42361.

8.43 36045.

7.90 30783.

7.32 27021.

6.31 20422.

5.32 17538.

4.47 13486.

3.53 9817.

11.22 101906.

10.74 93607.

10.58 86294.

10.37 78433.

10.19 70480.

10.41 70114.

10.04 60758.

9.80 54318.

9.50 48886.

9.22 43934.

8.71 36869.

8.52 33927.

7.80 28512.

7.16 24330.

6.51 20635.

5.60 17757.

4.75 13868.

11.74 102607.

11.37 96498.

11.06 88918.

10.83 81607.

10.63 75313.

10.37 68995.

10.15 62096.

10.00 55724.

9.65 48422.

9.34 41191.

8.73 34270.

8.14 28910.

7.60 25166.

7.05 22071.

6.17 19254.

5.22 14892.

4.26 11183.

11.92 103832.

11.50 95600.

11.19 86633.

10.99 78660.

10.70 70602.

10.47 64027.

10.26 57898.

9.88 50591.

9.67 44603.

9.33 38714.

9.16 35229.

8.32 28781.

7.71 25031.

7.22 22212.

6.5620737.

5.48 15659.

4.38 11336.

12.11 103981.

11.80 104318.

11.64 100707.

11.36 93045.

11.31 84163.

11.10 78904.

10.94 73910.

10.75 68555.

10.51 63359.

10.20 55681.

10.04 49678.

9.67 43417.

9.11 34916.

8.52 29894.

7.71 24695.

6.91 22266. 6.30 19068.

5.37 14908.

4.43 11307.

8.58 35618.

7.89 29237.

10.28 104159.

9.85 97269.

9.68 89609.

9.80 84302.

9.39 73363.

9.40 67565.

9.70 60493.

9.55 54493.

9.48 47516.

9.21 42770.

7.16 25064.

6.56 21456.

5.71 17132.

4.87 15067.

4.20 12111.

10.44 102008.

10.11 101694.

10.20 102387.

9.77 94590.

9.47 87837.

9.42 81093.

9.34 73906.

9.31 65603.

9.21 56173.

9.13 49493.

9.00 43429.

8.56 36691.

8.11 31744.

7.47 27562.

6.77 23176.

6.90 23940.

6.32 20761.

5.48 18296.

4.66 14140.

3.36 9030.

R134a/RL68H1Cu (98/2)

File: RL1Cu2.dat ∆Ts

(K)

q" 

(W/m

2

)

 10.46 117375.

 10.72 116499.

 10.87 107367.

 10.87 107367.

 11.14 105427.

 11.03 98635.

 11.08 97650.

 11.13 97721.

 10.87 90341.

 10.87 90912.

 10.88 90957.

 10.70 84665.

 10.68 84396.

 10.63 83865.

 10.38 77812.

 10.35 77220.

 9.89 70267.

 9.66 71057.

 11.02 106456.

 9.75 71093.

 9.10 63377.

 9.16 63605.

 8.24 38542.

 8.24 38282.

 8.25 38343.

 8.09 33614.

 8.13 33300.

 8.14 33219.

 7.85 29422.

 7.84 29130.
24

 7.87 28847.

 7.40 24414.

 7.38 24237.

 7.38 24019.

 7.07 21693.

 7.07 21584.

 12.38 115121.

 12.41 114192.

 12.38 111421.

 12.11 100519.

 12.15 101108.

 12.19 100852.

 11.79 92992.

 11.72 92736.

 11.68 92689.

 11.28 82992.

 11.33 82498.

 11.34 82218.

 10.67 74378.

 10.49 73403.

 10.62 73787.

 10.13 67387.

 9.97 69014.

 9.95 69272.

 9.73 59182.

 9.52 60427.

 9.51 60576.

 9.52 60679.

 9.83 46661.

 12.66 108402.

 12.71 109366.

 12.70 109431.

 12.03 97660.

 11.99 97448.

 11.98 97568.

 11.46 88727.

 11.40 88896.

 11.42 89543.

 10.83 79243.

 10.80 78999.

 10.75 79352.

 10.07 70410.

 10.01 71980.

 10.16 72631.

 9.41 62404.

 9.38 62431.

 9.41 62499.

 8.83 50141.

 8.87 49166.

 8.87 48648.

 8.56 41777.

 8.59 41303.

 8.65 41110.

 8.09 30369.

 8.07 29521.

 7.98 28324.

 7.18 21028.

 7.21 20786.

 7.28 20909.

 4.09 7804.

 3.78 7242.

 3.64 6897.

 3.64 6897.

 3.64 6897.

 3.64 6897.

 3.64 6897.

 10.57 118327.

 11.08 117679.

 11.57 113229.

 11.36 101711.

 11.63 102424.

 11.79 103235.

 11.47 91806.

 11.55 91835.

 11.61 92244.

 11.24 84466.

 11.27 84462.

 11.30 84451.

 10.81 76156.

 10.79 76537.

 10.75 76372.

 10.11 67364.

 9.95 66474.

 9.87 66244.

 9.34 57958.

 9.14 57810.

 9.17 56532.

 8.90 50334.

 8.95 50320.

 8.96 50228.

 8.50 39834.

 8.55 39828.

 8.55 39438.

 8.05 28784.

 8.08 28331.

 7.31 21831.

 7.26 20580.

 7.22 20257.

 6.40 15790.

 6.41 15744.

 6.47 15812.

 4.52 8449.

 3.82 7355.

 3.65 6977.

 12.04 96718.

 12.23 98927.

 12.40 102452.

 11.94 89763.

 12.04 90371.

 12.13 91078.

 11.71 80889.

 11.70 81324.

 11.71 81709.

 11.13 71608.

 11.02 72162.

 11.03 72141.

 10.47 63398.

 10.29 63570.

 10.21 63573.

 9.66 54444.

 9.58 55300.

 9.65 56206.

 9.23 45690.

 9.35 44895.

 9.36 44622.

 8.73 33685.

 8.80 32253.

 8.86 31517.

 8.04 25273.

 7.98 24674.

 7.97 24231.

 6.84 17476.

 6.74 16696.

 6.79 16702.

 5.52 11747.

 5.35 11409.

 5.35 11352.

 4.17 7825.

 3.89 7495.

 3.83 7362.
25

Table 3 Number of test days and data points

Fluid (% mass fraction) Number of days Number of data points

Pure R134a

3 K ≤ ∆Ts ≤ 9 K

13 145

R134a/RL68H (99.5/0.5) 

4.3 K ≤ ∆Ts ≤ 10.2 K

14 186

R134a/RL68H (99/1) 

4.6 K ≤ ∆Ts ≤ 11.3 K

4 68

R134a/RL68H (98/2) 

4 K ≤ ∆Ts ≤ 10.5 K

6 192

R134a/RL68H1Cu (99.5/0.5) 

3.4 K ≤ ∆Ts ≤ 8.2 K

8 132

R134a/RL68H1Cu (99/1) 

3.5 K ≤ ∆Ts ≤ 10.7 K

9 157

R134a/RL68H1Cu (98/2) 

3.5 K ≤ ∆Ts ≤ 12 K

5 170
26

Table 4 Estimated parameters for cubic boiling curve fits for plain copper surface

∆Ts = A0 + A1 q” + A2 q”2 + A3 q”3

∆Ts in Kelvin and q” in W/m2

Fluid Ao A1 A2 A3

Pure R134a

3 K ≤ ∆Ts ≤ 7 K

7 K ≤ ∆Ts ≤ 9 K

1.41341

3.99702

2.70461x10-4

7.78356x10-5

-5.22703x10-9

-4.89337x10-10

3.94517x10-14

1.44222x10-15

R134a/RL68H (99.5/0.5) 

4.3 K ≤ ∆Ts ≤ 9.5 K

9.5 K ≤ ∆Ts ≤ 10.2 K

1.66769

1.04922

3.15055x10-4

2.64699x10-4

-4.19310x10-9

-2.48124x10-9

1.77327x10-14

7.59925x10-15

R134a/RL68H (99/1)

4.6 K ≤ ∆Ts ≤ 9.7 K

9.7 K ≤ ∆Ts ≤ 11.3 K

1.00155

9.14630

4.33942x10-4

-3.72774x10-5

-7.83196x10-9

1.28138x10-9

5.15712x10-14

-6.85804x10-15

R134a/RL68H (98/2)

4 K ≤ ∆Ts ≤ 8.5 K

8.5 K ≤ ∆Ts ≤ 10.5 K

-5.53159

7.09007

1.77713x10-3

5.83429x10-5

-7.97232x10-8

-2.74470x10-10

1.23223x10-12

1.13436x10-16

R134a/RL68H1Cu (99.5/0.5)

3.4 K ≤ ∆Ts ≤ 8.2 K 7.52004x10-1 3.15645x10-4 -4.69784x10-9 2.20673x10-14

R134a/RL68H1Cu (99/1)

3.5 K ≤ ∆Ts ≤ 9 K

9 K ≤ ∆Ts ≤ 10.7 K

6.0058x10-1

4.51615

3.28260x10-4

1.84658x10-4

-1.31501x10-9

-2.18782x10-9

-4.42454x10-14

9.58136x10-15

R134a/RL68H1Cu (99/2)

3.5 K ≤ ∆Ts ≤ 8.75 K

8.75 K ≤ ∆Ts ≤ 12 K

3.00385x10-2

7.65055

6.44828x10-4

-2.18447x10-5

-1.79772x10-8

1.37521x10-9

1.78650x10-13

-7.45213x10-15
27

Table 5 Residual standard deviation of ∆Ts

Fluid u (K)

Pure R134a

3 K ≤ ∆Ts ≤ 7 K

7 K ≤ ∆Ts ≤ 9 K

0.15

0.10

R134a/RL68H (99.5/0.5) 

4.3 K ≤ ∆Ts ≤ 9.5 K

9.5 K ≤ ∆Ts ≤ 10.2 K

0.28

0.41

R134a/RL68H (99/1)

4.6 K ≤ ∆Ts ≤ 9.7 K

9.7 K ≤ ∆Ts ≤ 11.3 K

0.13

0.12

R134a/RL68H (98/2)

4 K ≤ ∆Ts ≤ 8.5 K

8.5 K ≤ ∆Ts ≤ 10.5 K

0.09

0.07

R134a/RL68H1Cu (99.5/0.5)

3.4 K ≤ ∆Ts ≤ 8.2 K 0.45

R134a/RL68H1Cu (99/1)

3.5 K ≤ ∆Ts ≤ 9 K

9 K ≤ ∆Ts ≤ 10.7 K

0.23

0.51

R134a/RL68H1Cu (99/2)

3.5 K ≤ ∆Ts ≤ 8.75 K

8.75 K ≤ ∆Ts ≤ 12 K

0.16

0.43
28

Table 6 Average magnitude of 95 % multi-use confidence interval for mean Tw -Ts (K)

Fluid u (K)

Pure R134a

3 K ≤ ∆Ts ≤ 7 K

7 K ≤ ∆Ts ≤ 9 K

0.14

0.06

R134a/RL68H (99.5/0.5) 

4.3 K ≤ ∆Ts ≤ 9.5 K

9.5 K ≤ ∆Ts ≤ 10.2 K

0.22

0.22

R134a/RL68H (99/1)

4.6 K ≤ ∆Ts ≤ 9.7 K

9.7 K ≤ ∆Ts ≤ 11.3 K

0.15

0.14

R134a/RL68H (98/2)

4 K ≤ ∆Ts ≤ 8.5 K

8.5 K ≤ ∆Ts ≤ 10.5 K

0.09

0.04

R134a/RL68H1Cu (99.5/0.5)

3.4 K ≤ ∆Ts ≤ 8.2 K 0.26

R134a/RL68H1Cu (99/1)

3.5 K ≤ ∆Ts ≤ 9 K

9 K ≤ ∆Ts ≤ 10.7 K

0.18

0.34

R134a/RL68H1Cu (99/2)

3.5 K ≤ ∆Ts ≤ 8.75 K

8.75 K ≤ ∆Ts ≤ 12 K

0.15

0.24
29

Fig. 1 Schematic of test apparatus
30

Fig. 2 OFHC copper flat test plate with cross-hatched surface and thermocouple 

coordinate system
31

Fig. 3 Pure R134a boiling curve for plain surface
32

Fig. 4 R134a/RL68H mixtures boiling curves for plain surface
33

Fig. 5 R134a/RL68H with 1 % volume CuO mixtures boiling curves for plain surface
34

Fig. 6 R134a/RL68H mixture heat flux relative to that of pure R134a for a plain 

surface
35

Fig. 7 Boiling heat flux of R134a/RL68H1Cu mixtures relative to that of pure R134a 

for a plain surface
36

Fig. 8 Measured thermal conductivity of RL68H/CuO nanoparticles mixtures as a 

function of volume fraction of CuO
37

Fig. 9 Predicted heat flux ratio for RL68H1Cu (99.5/0.5) mixture using Kedzierski 

(2003b) model
38

APPENDIX A: UNCERTAINTIES

Figure A.1 shows the relative (percent) uncertainty of the heat flux (Uq") as a function of 

the heat flux. Figure A.2 shows the uncertainty of the wall temperature as a function of 

heat flux. The uncertainties shown in Figs. A.1 and A.2 are "within-run uncertainties." 

These do not include the uncertainties due to "between-run effects" or differences 

observed between tests taken on different days. The "within-run uncertainties" include 

only the random effects and uncertainties associated with one particular test. All other 

uncertainties reported in this study are "between-run uncertainties" which include all 

random effects such as surface past history or seeding. 

Fig. A.1 Expanded relative uncertainty in the heat flux of the surface at the 95 % 

confidence level
39

Fig. A.2 Expanded uncertainty in the temperature of the surface at the 95 % 

confidence level 
40

APPENDIX B: LUBRICANT LIQUID DENSITY MEASUREMENTS

This appendix presents the measurements and the correlation of the RL68H, and the 

RL68H with 9 % volume CuO nanoparticles liquid densities (ρ). The density of the 

liquid lubricant was measured as a function of temperature with a glass pycnometer. The 

pycnometer was factory instrumented with a glass mercury thermometer with a range of 

14 °C to 38 °C in 0.2 °C graduations, accurate to within ± 0.2 °C. The pycnometer was 

filled with distilled water and its volume was calculated from the known density of water. 

The volume was found with 29 trials to be 9.588 ml with a standard uncertainty of 

0.002 ml. The average mass of the pycnometer after nine trials was 28.794 g ± 0.001 g.

The pycnometer containing the RL68H lubricant was cooled in an ice bath and then 

removed from the bath and allowed to warm on the balance to room temperature over 

approximately one hour. The standard uncertainty of the balance was approximately 

1 mg. The outside of the pycnometer was wiped clean before each measurement to 

remove the lubricant that was expelled through the pipette due to volume expansion with 

temperature increase. 

The Biot number for the warming pycnometer was estimated to be approximately 0.5, 

which is greater than the recommended limit of 0.1 (Incropera and Dewitt, 1985) for a 

uniform temperature in fluid. It is difficult to estimate the error introduced in the 

measurements due to temperature gradients that existed in the lubricant. However, the 

data regression shows that the residuals are independent of temperature, which suggests 

that the error due to temperature gradients in the liquid had a negligible effect on the 

density measurements. 

Tables B.1 shows the recorded measurements for the RL68H lubricant. Equation B.1 

gives the fit of the liquid lubricant density (ρl) in kg/m3 versus temperature (T) in Kelvin:

l ρ = − 1146 0.6336T B.1

The expanded uncertainty of the fits were approximately ± 1 kg/m3 for 95 % confidence. 

The density of the RL68H with 9 % volume CuO nanoparticles (ρL) was measured at a 

single temperature (297.6 K) and found to be 1447.9 kg/m3 ± 0. 3 kg/m3

.

The density of the CuO particles at 297.6 K (ρnp) can be obtained from the mixture 

combination rule (Reid et al., 1977) between density and volume fraction for the 9 % 

volume nanolubricant solution: 

L np l ρρ ρ = +− 0.1 (1 0.1) B.2

Solving eq (B.2) for the density of the nanoparticles yields 5760 kg/m3

. The same form 

of eq (B.2) is obtained when the mass-fraction-based mixture density equation for 

suspensions given by Wasp (1977) is re-written interms of volume fraction.
41

Table B.1 RL68H liquid density measurements

T (°C) Lubricant mass (g) ρl (kg/m3)

16 9.241 963.80

17 9.234 963.07

17.8 9.228 962.44

18.4 9.223 961.92

19.2 9.217 961.29

20 9.212 960.77

20.6 9.207 960.25

21.2 9.201 959.62

22.2 9.197 959.21

22.8 9.191 958.58

23.8 9.184 957.85

24.2 9.182 957.64

14.2 9.235 963.17

15.4 9.229 962.54

17.8 9.222 961.82

18.6 9.214 960.98

19.4 9.21 960.56

20 9.207 960.25

21.2 9.2 959.52

21.8 9.197 959.21

22.8 9.19 958.48

23.4 9.184 957.85

24.2 9.181 957.54

14.4 9.236 963.28

15.8 9.226 962.23

17.2 9.221 961.71

18.4 9.211 960.69

19.4 9.206 960.15

20.6 9.201 959.62

21.6 9.195 959.00

22.6 9.189 958.37

23.4 9.182 957.64

24 9.175 956.91
42

APPENDIX C: DILUTION OF 9 % VOLUME NANOLUBICANT

This appendix presents the analysis that was used to dilute the 9 % copper (II) oxide 

volume fraction nanolubricant to a 1 % copper (II) oxide volume fraction. The 

uncertainty of the target (diluted) volume fraction is also discussed.

The volume fraction of the initial mixture (φi) is expressed in terms of the volume of the 

CuO particles (Vnp) and the volume of the initial neat lubricant (Vli):

np

np li

i

V

V V φ = + (C.1)

Likewise, the desired volume fraction of the target mixture (φt) is obtained by diluting the 

initial mixture with an additional volume of neat lubricant (Vl+):

np

np li l+

t

V

V VV φ = + +

(C.2)

Equations C.1 and C.2 can be simultaneously solved for the additional volume of neat 

lubricant required to dilute φi to φt:

i t

l+ li

t ti

V V φ φ

φ φφ

− = − (C.3)

Equation C.3 can be written in terms of the density of the initial nanolubricant mixture 

(ρL)

7

i

Ti i

l+

L t

1 M V

φ

φ

ρ φ

  = −    

and the mass of the initial nanolubricant sample to be diluted (MTi):

(C.4)

Equation C.4 can be written in terms of the mass of neat lubricant to be added to obtain 

the target dilution (Ml+) with use of the neat lubricant density (ρl):

i

Ti l i

l+ l+ l

L t

1 M M V

φ

ρ φ ρ ρ φ

  = = −    

(C.5)

 7 The ρm measurement was presented in Appendix B.
43

The total mass of the target mixture (MTt) is the sum of MTi and Ml+. This mass balance 

and eq (C.5) can be used to calculate the required Ml+ as: 

i

Tt

l+

L t

it l

1

M M

φ φ ρ

φφ ρ

=  

+     −

(C.6)

The volume fraction of the target mixture is expressed as:

i

i Ti

t

L

Ti l+

l

M

M Mφ

φ φ

ρ

ρ

=

+

(C.5)

where the dominant uncertainty of φt is the uncertainty of φi. All of the other eq (C.5) 

parameters combined cause only a 0.1 % uncertainty in φt for the dilution of the 9 % 

volume fraction solution to a 1 % volume fraction. The uncertainty in φi is a b-type 

uncertainty because it comes from the manufacturer as ± 1 %. Consequently, the total 

uncertainty in φt is approximately ± 1 %. 
44

APPENDIX D: CAPILLARY RISE MEASUREMENTS

This appendix presents capillary rise measurements for RL68H at approximately 25 oC. 

Table D.1 provides the capillary rise height measurements (l) that were used to calculate 

the surface tension for the lubricant. The standard deviation of the mean measurement 

for this method was approximately 0.5 % of the measurement. 

A force balance on the column of liquid in the capillary tube was used to calculate the 

surface tension (Adamson and Gast, 1997):

2 2

l r gl ρ r gl ρ σ

∆ = ≈ (D.1)

where the measured radius of the capillary tube (r) was 0.97 mm with a B-type estimated 

uncertainty of ± 0.03 mm. The liquid density (ρl) measurement is given in Appendix B. 

The uncertainty of the density measurements is approximately ± 1 kg/m3

.

The liquid-vapor (air) surface tensions as calculated from eq (D.1) for the RL68H was 

0.0277 N/m ± 0.0006 N/m at 297.97 K.

Table D.1 Capillary rise measurements for RL68H

T (oC) l (mm) ρ (kg·m-3

) σ (N·m-1)

24.813 23 957.18 0.0281

24.815 22.5 957.18 0.0275

24.816 22.5 957.18 0.0275

24.817 22.5 957.18 0.0275

24.817 22.5 957.18 0.0275

24.818 22.5 957.18 0.0275

24.818 22.5 957.18 0.0275

24.819 23 957.17 0.0281

24.819 23 957.17 0.0281

24.82 23 957.17 0.0281

24.82 22.5 957.17 0.0275

24.82 22.5 957.17 0.0275

24.82 22.5 957.17 0.0275
45

APPENDIX E: LUBRICANT VISCOSITY MEASUREMENTS

This appendix presents the liquid kinematic viscosity measurements for RL68H at 

approximately 25 oC in Table E.1. A glass viscometers at the appropriate viscosity range 

was used to measure the liquid viscosities of the lubricant. The B-type uncertainty of the 

viscometer was quoted by the manufacturer as 0.22 % of the measurement. The average 

measured viscosity of the lubricant, for the 95 % confidence level, was 85 μm

2

/s ± 1.5 

μm

2

/s. 

A model 300 viscometer with a viscosity range of 50 μm

2

/s to 250 μm

2

/s was used. The 

calibration constant (Co) for the viscosity was a function of viscometer/liquid 

temperature:

5 0.24317 1.6667 10 C T o− = −× (D.1)

where T is in Celsius and Co is in μm2/s.

The kinematic viscosity in μm

2

/s was obtained by multiplying the measured efflux time 

in seconds by Co. The averaged measured viscosity of RL68H at an average temperature 

of 297.74 K was 144 μm

2

/s ± 1.9 μm

2

/s. 

Table E.1 Kinematic viscosity measurements for RL68H

T (oC) Efflux time (s) Co (μm

2

/s) ν (μm

2

/s)

24.576 583.12 0.242757067 141.56

24.583 606.02 0.24275695 147.12

24.59 606.44 0.242756833 147.22

24.598 606.9 0.2427567 147.33

24.603 606.77 0.242756617 147.30

24.61 608.6 0.2427565 147.74