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Impact analysis of natural convection on thermal conductivity measurements of nanofluids using the transient hot-wire method
International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Impact analysis of natural convection on thermal conductivity measurements of nanofluids using the transient hot-wire method Sung Wook Hong a, Yong-Tae Kang a, Clement Kleinstreuer b, Junemo Koo a,⇑ a b
Mechanical Engineering Department, Kyung Hee University, Yongin 449-701, South Korea Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA
a r t i c l e
i n f o
Article history: Received 25 August 2010 Received in revised form 9 March 2011 Accepted 9 March 2011 Available online 21 April 2011 Keywords: Transient hot-wire method (THWM) Thermal conductivity Natural convection Nanofluids
a b s t r a c t Significant deviations between published results have been reported measuring the effective thermal conductivity of nanofluids with the transient hot-wire method (THWM). This may be attributed to a poor selection of the temperature data range, which should meet the following conditions. The start time should be chosen after the conductive heat flux delay time, while the end time should be selected before a crossover point when natural convection becomes significant. Considering an EG-based 1.06 vol.% ZnO nanofluid, the thermal conductivity was measured to increase by 5.4% over that of the base fluid. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluids, a dilute suspension of nanoparticles in liquids, have been considered as coolants because of their enhanced thermal conductivities. In general, the anomalous thermal conductivity enhancement of nanofluids, using typically metal or metal-oxide nanoparticles, has been attributed to nanoparticle Brownian motion, liquid molecule-layering, higher heat conduction, and/or clustering (see [1]; among others). Indeed, with some exceptions, thermal conductivity enhancement was generally observed; however, the magnitude of the increase varied among research groups [2]. A popular technique for measuring nanofluid properties is the transient hot-wire method (THWM) due to its simplicity, ease-of-use, and short measurement period which should not be affected by natural convection. For example, Nagasaka and Nagashima [3] developed a THWMset of 0.5% accuracy to measure the thermal conductivities of electrically conducting liquids (an aqueous NaCl solution) using a metallic wire coated with a thin electrical insulation layer. They analyzed the layer effect on the measurements, as again studied by Yu and Choi [4]. Castro et al. [5] re-assessed THWM as applied to thermal diffusivity measurements, where the effects of finite length of the wire, the diameter of the test section, variations in fluid properties and radiation heat transfer on measurement errors were analyzed. Richard and Shankland [6] used THWM to measure the thermal conductivities of both liquids and gases. Bleazard and ⇑ Corresponding author. Tel.: +82 31 201 3834; fax: +82 31 202 8106. E-mail address: [email protected] (J. Koo). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.03.041
Teja [7] developed a THWM apparatus to measure the thermal conductivities of electrically conducting liquids at high temperatures. Watanabe [8] analyzed the effect of radiation heat transfer on measurements and concluded that the impact is negligible at room temperature. Shi et al. [9] investigated the influence of natural convection and thermal radiation, where they showed the dependence of the measured thermal conductivity on the selection of the temperature data range. Most relevant is the paper by Hong et al. [10] who investigated the effects of the power supplier response delay, the thermal coefficient of resistors, the hot-wire type and the test section size on thermal conductivity measurements using THWM. They analyzed the impact of data range selection, response delay of power supply, thermal coefficients of the resistors, hot-wire type, and test section size. In this study, the effects of heat transfer delay time and natural convection on the proper selection of the temperature range when using THWM are discussed. The theoretical/experimental analysis of suitable data selection has been carried out with water and ethylene glycol (EG) and then applied to measure the thermal conductivity of a sample nanofluid, i.e., an EG-base containing ZnO nanoparticles of 1.06% in volume fraction.
2. Theory As the electric power is introduced into an electric wire, the temperature of the wire rises. The wire temperature depends on the rate of heat dissipated into the surrounding fluid. If the surrounding fluid is at rest, the heat is dissipated into the fluid
S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
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Nomenclature a c0, c1, c2 Cp g k L Q R t T q q000 z ur, uz z
Greek symbols temperature coefficient of resistance (TCR) [K1] thermal diffusivity [m2/s] b thermal expansion coefficient [K1] c Euler’s constant, 0.5772 m kinematic viscosity [m2/s] q density [kg/m3]
radius [m] constants specific heat [J/kg K] gravitational acceleration [m/s2] thermal conductivity [W/m K] length [m] heat transfer rate [W] resistance [X] time [s] temperature [K] heat generation per unit length [W/m] heat generation per unit volume [W/m3] coordinate [m] velocity components in r and z directions [m/s] coordinate [m]
a a
Subscripts 0 state at zero degree in Celsius 1 state at far field f fluid i insulation layer w wire
via conduction of which the magnitude is a function of the fluid’s thermal conductivity. The higher the thermal conductivity is, the lower the temperature rises due to increased thermal dissipation from the wire to the surrounding fluid. The relation between the hot-wire temperature rise and the thermal conductivity of the fluid is given by Carslaw and Jaeger [11] as:
Q d ln t 4pLw dT Rw ¼ R0 ð1 þ aT w Þ
kf ¼
ð1Þ ð2Þ
where Q is the heat transfer rate, Lw is the wire length, t is the time, and T is the temperature. Measuring the resistance change of the hot wire with time, and converting it to the wire temperature, Eq. (1) could be obtained to calculate the thermal conductivity of the fluid. Here, the temperature coefficient was set to be 0.00362 K1, which is the material property of platinum. Once the temperature data are obtained experimentally, the thermal conductivity can be determined with Eqs. (1) and (2). It should be noted that the linear relation in Eq. (2) is only valid for a small temperature range as in the case of this study, i.e., 298–318 K. For a wider temperature range a quadratic formula is typically used to capture the relation between resistance and temperature. Natural convection on a vertical surface, e.g., the surface of the hot wire in the THWM, originates from the buoyancy force caused by the temperature difference between the solid surface and the fluid. The axisymmetric momentum equation can be written as [12]:
" # @uz @uz @uz 1 @ @uz @ 2 uz þ 2 þ gbðT T 1 Þ; r þ ur þ uz ¼m r @r @t @r @z @r @z
Table 1 lists examples of recent effective thermal conductivity measurements of nanofluids using THWM. The data deviations in terms of linearity and slope of the thermal conductivity increase with particle volume concentration are significant. Although the deviations could be attributed to the differences in physicochemical properties, including nanoparticle size and volume concentration among nanofluids, part of the discrepancies between research groups is believed to be caused by the differences in selection of the temperature data range
1 @ðrur Þ @uz þ ¼0 r @r @z ! @T @T @T @ 2 T 1 @T @T þ q000 þ ur þ uz ¼k þ qC p þ @t @r @z @r2 r @r @z
ð4Þ ð5Þ
Eqs. (4) and (5) are the continuity and energy equations [12] which were solved, together with Eq. (3), by the commercial CFD package Fluent 6.3. The computational results were compared to experimental data sets. The no-slip condition was enforced on all walls including the top and bottom lids, wire, and test section shell surfaces. Heat generation in the wire and its propagation into the fluids were simulated as a conjugated heat transfer problem. The temporal mean temperature change of the hot-wire was monitored and the thermal conductivities of the fluids were estimated using Eqs. (1) and (2).
ð3Þ
where b is the thermal expansion coefficient of the fluid. The natural convection induced flow field is a function of the fluid properties such as the kinematic viscosity and the thermal expansion coefficient. The changes in thermal properties of water, i.e., dynamic viscosity and the thermal expansion coefficient, as a function of temperature are shown in Fig. 1. The thermal expansion coefficient is found to increase significantly with temperature, whereas the kinematic viscosity decreases slightly, i.e., it is basically negligible. As the thermal expansion coefficient increases, the buoyancy term in Eq. (3) increases for a given temperature difference between the surface and the fluid, affecting the flow field via natural convection. Hence, a change in thermal expansion coefficient may significantly impact the selection of a proper temperature data range.
Fig. 1. The effect of temperature change on the thermal property changes of water.
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S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456 Table 1 Examples of the effective thermal conductivities of nanofluids. Author
Particle material (size)
Base fluids
Temperature (K)
Duangthongsuka and Wongwises [13]
TiO2 (21 nm)
Water
298
Volume fraction (%)
Thermal conductivity enhancement (%)
0.2
2.5
0.6 1.0 1.6 2.0 0.5 0.8 1.0 2.0 3.0 4.0 5.0
3.6 4.2 6.1 6.8 4.5 9.5 18.4 23.8 25.6 27.3 29.8
Murshed et al. [14]
TiO2 (15 nm)
Water
298
Zhang et al. [15]
TiO2 (40 nm)
Water
303
1.2 2.5
3.5 5.4
Patel et al. [16]
CuO (31 nm)
Water
293
0.5 1.0 2.0 3.0
3.0 6.0 7.0 8.5
Karthikeyan et al. [17]
CuO (8.0 nm)
Water
298
0.1 0.3 0.8 1.0
13.0 18.0 25.0 31.0
Zhu et al. [18]
CuO (8.7 nm)
Water
298
0.5 1.0 2.0 3.0 4.0 5.0
13.0 18.0 25.0 28.0 30.0 31.0
Das et al. [19]
CuO (28.6 nm)
Water
298
1.0 2.0 3.0 4.0
6.4 10.0 12.0 14.0
Patel et al. [16]
Al2O3 (11 nm)
Water
293
0.5 1.0 2.0 3.0
6.0 7.0 8.5 11.0
Beck et al. [20]
Al2O3 (12 nm)
Water
297
2.0 3.0 4.0
2.0 3.0 5.0
Timofeeva et al. [21]
Al2O3 (11 nm)
Water
5.0 7.5 10.0
8.0 12.0 16.0
Das et al. [19]
Al2O3 (38.4 nm)
Water
1.0 2.0 3.0 4.0
2.4 5.2 7.0 9.5
3. Experimental set-up Fig. 2 shows the schematics of the transient hot-wire apparatus. A DC current electric power supplier (Array, model 3654A) imposed 4V across the Wheatstone bridge. The switching of the power supply was controlled by a relay circuit to avoid any power supply delay effect. The initial resistances of the resistors and the hot wires were measured by a low resistance meter (GOODWILL, model GOM-801G), which had a maximum reading error of 0.2%. The test section of 12 mm radius was fabricated with stainless steel. The length of the test section was 141 mm, and the top and bottom sides were covered by the lids. The hot-wire was made of 50 lm diameter platinum coated by a 25 lm electrically insulating Teflon layer. A thinner wire with anodic coating layer could be used to reduce the impacts of the initial delay, the insulation layer etc. However, a thicker, say, 50 lm, wire with 25 lm Teflon insulation layer was used for the ease of handling. No compensation wire was used for which Perkins et al. [24] claimed that end effects are
298
negligible when the wire is longer than 100 mm. The time variations of the voltage drop across the whole Wheatstone bridge and the voltage difference between the mid-points of the Wheatstone bridge circuit were stored in the computer using a data acquisition system (National Instrument, model USB-6210). The voltage history data were conditioned by the Butterworth low-pass filter to remove the signal noise. The viscosity and thermal expansion coefficient of a sample nanofluid were measured to investigate the effects of the two thermal properties on the thermal conductivity measurement using THWM. The viscosity was measured by an oscillatory type viscometer (AND, Model. SV-10). The definition of the thermal expansion coefficients is given in Eq. (6), where the specific gravities were measured at different temperatures using hydrometers
b¼
1 @q 2 q2 q1 q @T q1 þ q2 T 2 T 1
ð6Þ
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S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
Fig. 2. Schematics of the transient hot-wire apparatus.
The thermal expansion coefficients of water and EG were measured in the same way and the errors, when compared to literature values [12] were found to be 6.3% and 2.9%, respectively. The larger error for water can be attributed to the fact that the thermal expansion coefficient changes drastically with temperature. The effects of radiation heat transfer on the measurements were analyzed by Castro et al. [5], Watanabe [8], and Shi et al. [9]. Clearly, for ambient temperature conditions radiation effects are negligible. However, while the effect of natural convection can be successfully eliminated as shown, the radiation effect could not be eliminated, if present. 4. Results and discussion In this section, the simulation results are presented first to introduce the underlying idea. Then they are applied to select an adequate temperature data range, obtained from the temperature history using THWM, to evaluate the thermal conductivities of the test fluids. 4.1. Effect of wire heat conduction on measurements Fig. 3 shows the effect of actual heat conduction inside the wire. The values of thermal conductivity were obtained from the measured hot-wire temperature history data using Eqs. (1) and (2) in which the heat flux on the surface is set to be a constant. However, it takes a finite time for the heat, generated inside the wire, to reach the wire surface uniformly. The ‘ideal’ heat flux history, which neglects the time delay for the internally generated heat to arrive at the surface, and ‘real’ heat flux history which is obtained from the simulation results, are compared in Fig. 3. It takes around 1 s for the surface heat flux to reach steady state; thus, the thermal conductivity will be overestimated if the wire temperature history data before 1 s are used. In our case, platinum hot-wires of 50 lm in diameter coated by Teflon of 25 lm in thickness were used. Clearly, for thicker wires it will take longer for the surface heat flux to arrive at the steady value. As a result, the temperature history data affected by the surface heat flux time delay should be avoided when using THWM; otherwise, measurements would result in overestimation of the thermal conductivity.
Fig. 3. Conductive heat flux history for wire surface.
The influence of the insulation coating on thermal conductivity measurement by the transient hot-wire method was analytically investigated by Yu and Choi [22], expanding the theory outlined by Healy et al. [23] as shown in Eqs. (7)–(10)
T W ðtÞ ¼
4af t q c0 c1 1þ ln 2 c1 þ þ c2 ; 4pkf t t aw e
ð7Þ
where the coefficients c0, c1 and c2 are given as c0 ¼ c1 ¼
a2i kf ai ki af a2 ðki aw kw ai Þ þ w 2kf af ai 2kf ai aw a2i 2kf
a2i
a2w 2ki
a2w 4ki
þ
a2w ðkf
ki Þðai aw Þ þ 8kw ai aw
ð8Þ a2w lnðai =aw Þðki
a w kw a i Þ
ki ai aw
ð9Þ kf 2 lnðai =aw Þkf c2 ¼ þ 2kw ki
ð10Þ
They claimed that the effect of the insulation layer on the temperature-rise error is less than 0.2% or even less for t > 0.5 s if c0 and c1 are of the order 103, and c2 does not affect the thermal conductivity measurements. The constants c0 and c1 are estimated to be
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a
S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
0.62
b Start time 1.2 s Start time 1.6 s Start time 2.0 s Start time 2.4 s locally estimated value Crossover point Measure point
0.2528
1.0% error 0.616
0.5% error
0.614 Start time 1.0 s Start time 1.2 s Start time 1.4 s Start time 1.6 s locally estimated value Crossover point Measure point
0.612
0.61
0
1
2
3
4
7
5 6 End time (s)
8
Thermal conductivity (W/mK)
Thermal conductivity (W/mK)
0.618
0.2520
Reference
0.2516 -0.2% errir
0.2512
Reference
9
0.2524
0
10
1
2
3
4
5 6 End time (s)
7
8
9
10
Fig. 4. The simulation comparison of the heat flux delay and the natural convection effects on the thermal conductivity measurements for water and EG.
3.82 103 and 6.94 104, respectively, for the current case and hence the error becomes negligible after 0.5 s.
numerical simulation, they are scattered measurably with a couple of severe kinks with peaks and valleys, which may be attributed to the differentiation operation in Eq. (1). Due to the kinks, it is hard to read the thermal conductivities directly from the locally measured data. Since the data scattering becomes more severe for experimental measurements, the locally measured data cannot be used to estimate the thermal conductivity. It is proposed to estimate the thermal conductivity in a cumulative way, where a range of data should be properly selected to estimate the thermal conductivities so that the resulting values do not suffer much from data scattering. In Fig. 4(a) and (b), examples of thermal conductivity measurements, using various data ranges of different start
4.2. Effect of natural convection on measurements The effects of the induced natural convection on the measurements for water and EG are shown in Fig. 4. The locally measured thermal conductivities, which are measured using 100 neighboring points, decrease in the early phase when the wire-surface heat flux has not reached steady state. The data are shown every 10 points. They reach temporarily minimum values and start to increase due to natural convection. Although the data are taken from the
a 0.65
b Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Croosover point Measure point
Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.72
0.63
0.62 1.0% error 0.5% error
0.61
Thermal conductivity (W/mK)
Thermal conductivity (W/mK)
0.64
0.74
0.7
0.68
0.66
0.64 2.0% error 1.0% error Reference
Reference
0.62
0.6
0
1
2
3
4
7
5 6 End time (s)
8
9
0.6
10
0
1
2
3
4
5 6 End time (s)
7
8
9
10
c 0.82 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.8
Thermal conductivity (W/mK)
0.78 0.76 0.74 0.72 0.7 0.68 0.66
2.0% error 1.0% error Reference
0.64 0.62 0.6
0
1
2
3
4
5 6 End time (s)
7
8
9
10
Fig. 5. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of water at the temperature of (a) 298 K, (b) 308 K and (c) 318 K.
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S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456 0.26
b Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
Thermal conductivity (W/mK)
0.258
0.256
1.0% error
0.254 0.5% error
0.252
0.25
1
2
3
4
5
6
7 8 9 End time (s)
c
10
12
13
14
0.5% error
0.254
Reference
Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.25
15
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
0.27 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.268 0.266 Thermal conductivity (W/mK)
11
1.0% error
0.256
0.252
Reference
0
0.26
0.258 Thermal conductivity (W/mK)
a
0.264 0.262 0.26
1.0% error
0.258
0.5% error
0.256
Reference
0.254 0.252 0.25
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
Fig. 6. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of ethylene glycol at the temperature of (a) 298 K, (b) 308 K and (c) 318 K.
times, are shown. Since the thermal conductivity is overestimated in the early phase due to the heat flux delay and in the late phase due to natural convection, thermal conductivity values using the cumulative approach will first decrease then increase passing through points of minimum values. If the start time is selected in the region where the effect of the heat flux delay exists, the thermal conductivity estimation decreases initially at a given time as the start time of the data range increases. Then later in the phase when natural convection affects the measurement, the thermal conductivity estimation increases faster for the cases with the later start time. There should be a point where the thermal conductivity estimation of the later start time case exceeds that of the earlier start time case. The open red1 circles in the figures show the crossover points, beyond which the impact of the natural convection becomes significant. Hence, the thermal conductivity should be estimated before the crossover point to avoid the impact of natural convection. If the start time is selected in the region where the kinks exist, the thermal conductivity can either increase or decrease depending on the local scattering of the estimated values of the thermal conductivity. If the start time is selected too late, the thermal conductivity values do not go through the crossover point (see the cases of start time 1.6 s for water and 2.4 s for EG in Fig. 4). In summary, to choose the proper temperature data range for estimating the thermal conductivity, the following three conditions should be met. The start time should be selected after the heat flux delay time. The end time should be selected before the 1 For interpretation of color in Fig. 4, the reader is referred to the web version of this article.
crossover point among the lines which go through the crossover point. Lastly, the data range should be large enough not to be affected by local oscillations in the estimates. The open green diamonds in Fig. 4 are the points where the thermal conductivities are estimated for water and EG. Comparing the water and EG cases, it was found that natural convection occurs later for the case of EG due to its high viscosity and the selection of start-time and end-time of the temperature data range differs for each fluid. The proper temperature data ranges are 1.2–2.3 s and 1.6–3.3 s for water and EG, respectively. This implies that the temperature data range, which is usually predetermined before the measurement and kept fixed regardless of the test fluid type, should be selected after the temperature histories are obtained and analyzed considering the three listed conditions. It is found that the estimation error for EG is smaller than that for water, and this could be attributed to the fact that EG is less affected by natural convection due to its higher viscosity when compared to water. 4.3. Analysis of the experimental data Figs. 5 and 6 show the results of the thermal conductivity measurements of water and EG at different temperatures. The effect of selections of start-time and end-time of the data range used in the measurements is presented in the figures. As discussed, the earliest start-time is after 1 s to avoid the impact of surface heat flux time delay. All cases show similar behavior with the increase of the data range. The estimated thermal conductivity values oscillate near the start-time where the data range selected is short and the
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Table 2 The results of thermal conductivity measurements of water and EG. Trial no.
Water at 298 K (W/m K)
Water at 308 K (W/m K)
Water at 318 K (W/m K)
EG at 298 K (W/m K)
EG at 308 K (W/m K)
EG at 318 K (W/m K)
1 2 3 4 5 6 7 8 9 10
0.6140 0.6159 0.6168 0.6144 0.6033 0.6170 0.6117 0.6160 0.6105 0.6125
0.6649 0.6206 0.6347 0.6273 0.6753 0.6497 0.6536 0.6391 0.6411 0.6333
0.6542 0.6989 0.6606 0.6642 0.6656 0.6797 0.6411 0.6459 0.6577 0.6594
0.2537 0.2545 0.2543 0.2541 0.2539 0.2531 0.2532 0.2524 0.2538 0.2553
0.2541 0.2542 0.2548 0.2533 0.2554 0.2556 0.2557 0.2542 0.2552 0.2560
0.2574 0.2541 0.2567 0.2563 0.2582 0.2562 0.2584 0.2579 0.2581 0.2589
Average (W/m K) Bias error (%) Precision error (%) Total uncertainty (%)
0.613 0.04 0.44 0.48
0.6439 2.7 1.8 4.5
0.6627 4.1 1.7 5.8
0.2538 0.8 0.2 1.0
0.2548 0.3 0.23 0.53
0.2572 0.5 0.37 0.87
Table 3 Comparison of viscosity and thermal expansion coefficient of pure ethylene glycol [12] and EG-base 1.06 vol.% ZnO nanofluid at 299 K.
Viscosity (cP) Thermal expansion coefficient (1 K1)
Measured property
Reference (ethylene glycol)
Enhancement (%)
16.81 0.000459
16.7 0.00065
0.7 30
estimation is sensitive to the local noise. The oscillation originates from the noise signal, which vanishes or averages out with time. After the estimated thermal conductivity reaches a plateau or a local minimum, it starts to increase with the increase of the end-time or the data range due to the effect of natural convection. Comparing Fig. 5(a)–(c), it is apparent that the thermal conductivity is affected by natural convection early on as the water base temperature increases. The end-time of the properly selected data range decreases from 4 s to 3 s and 2.6 s as the water base temperature increases from 298 K to 308 K and 318 K. If the thermal conductivities are measured using a temperature data range of fixed start-time and end-time, e.g. tstart = 1 second and tend = 3 s, the estimation bias errors increase from 0.26% at 298 K to 1.8% at 308 K, and 4.6% at 318 K. As the water base temperature increases, the effect of natural convection increases due to the decrease of the fluid viscosity and the steep increase of the thermal expansion coefficient. Therefore, it is expected that there is a certain high
temperature at which the data range end-time is very close to the start-time, so that the thermal conductivity of water cannot be measured using THWM. In case of EG, the thermal expansion coefficient remains constant for a wide temperature range, whereas the viscosity decreases with temperature. Fig. 6 shows the effect of the data range selection on the thermal conductivity estimation of EG. As already observed, the thermal conductivities are less affected by natural convection than in the case of water due to the higher viscosity of EG. Although the thermal expansion coefficient remains constant for the test temperature range, the viscosity decrease causes the increase of the natural convection effect with temperature. As a result, the end-time of the data range decreases from 7.23 s to 7.2 and 3.74 s with the increase of the base temperature. From the analysis of the result, it can be expected that the limiting high temperature to measure the thermal conductivity of EG is higher than that of water. If the thermal conductivities are measured using a temperature data range of fixed start-time and end-time, e.g. tstart = 1 s and tend = 3 s, the estimation bias errors decrease from 1.8% at 298 K to 0.43% at 308 K and 0.42% at 318 K. Table 2 represents the examples of the measurement results together with an error analysis. In case of water, the error is below 1% for the low temperature of 298 K; but, it increases to around 5% at higher temperatures. In contrast, the errors for EG remain below 1% for the given test temperature range. This can be also attributed to the lower impact of natural convection for EG.
0.28
0.28
0.278
Thermal conductivity (W/mK)
0.276
Thermal conductivity (W/mK)
ZnO 1.0 vol.% + EG Mean(0.2657) EG reference
0.275
0.274 0.272 0.27 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.268 0.266 0.264
0.27
0.265
0.26
0.255
0.262 0.26
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
Fig. 7. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of a EG-base 1 vol.% ZnO nanofuid at 298 K.
0.25
0
1
2
3
4
5 6 Measurement set
7
8
9
10
11
Fig. 8. The results of 10 repeated thermal conductivity measurements for the EGbase ZnO nanofluid.
S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
In summary, the proper temperature data range selections are affected by both the fluid type, e.g., water or EG, and the base temperature. Since the proper temperature data range selection cannot be predetermined before taking measurements, it is recommended that the temperature history data is investigated carefully for each experiment. 4.4. Applications to a nanofluid The developed THWM technique is applied to measure the thermal conductivities of nanofluids. A sample of an EG-based nanofluid containing ZnO nanoparticles of 1.06% in volume fraction was prepared. The mean hydrodynamic diameter of the ZnO nanoparticles in EG was measured to be 10 nm using the dynamic light scattering method (OTSUKA, Japan, model ELS-Z). The measured physical properties, i.e., viscosity and thermal expansion coefficient which affect the incidence of the natural convection, are listed in Table 3. It was found that the viscosity increases by 0.7% while the thermal expansion coefficient decreases by 30% when comparing with the base fluid, EG. Therefore, it was expected that the thermal conductivity measurement would be less affected by natural convection (refer to Eq. (3)). Fig. 7 shows the effect of the temperature data range selection on the thermal conductivity measurements. In contrast to expectation, it was found that the THWM can be significantly influenced by natural convection, which cannot be explained relying on the natural convection theory for single phase fluids. The crossover point is shifted to about 5.5 s which was around 12 s for pure EG. It might be explained as a result of local motion of nanoparticles to invoke natural convection earlier, when compared to the cases of pure fluids. The proper selection of the temperature data should be between 1.2 and 3.2 s. The results of the 10 repeated thermal conductivity measurements of the EG-base ZnO nanofluid is represented in Fig. 8. The thermal conductivity of the EG-base 1.06 vol.% ZnO nanofluid is found to increase by 5.4% at 298 K over the pure EG case within a precision error of the measurements 0.53%.
5. Conclusions In this study, the effects of the temperature data range selection on thermal conductivity measurements using the transient hotwire method were investigated both theoretically and experimentally, taking transient conduction in the hot-wire as well as natural convection into account. The conclusions drawn from this theoretical/experimental study are as follows: It takes a finite time for the heat flux on the wire surface to reach steady state. It should be noted that the temperature data during the transient phase should not be included in the temperature data to estimate the thermal conductivity. In other words, the start-time of the selected temperature data range should be set after the transient phase. For the case of the 50 lm diameter platinum wire used, it was found that the delay time is about 1 s. In choosing the proper temperature data range to estimate the thermal conductivity, care must be taken to meet the following three conditions. First, the start time should be selected after the heat flux delay time. Secondly, the end time should be selected before the crossover point. Lastly, the data range should be large enough not to be affected local oscillation of the estimation. The proper temperature data range selections are affected by both the fluid type, e.g., water or EG, and the base temperature. Because the proper temperature data range selection cannot be
3455
predetermined, it is recommended that the temperature history is investigated for each experiment. Especially the thermal expansion coefficient of water increases drastically with temperature, so that the impact of natural convection on thermal conductivity measurements should be avoided by a proper selection of the temperature data range. While it was conjectured that the THWM applied to nanofluids would be negligibly affected by natural convection, due to the elevated value in viscosity and lower thermal expansion coefficient, it was found that the effect of natural convection can be significant. This might be a result of local motion of nanoparticles which induces natural convection early on. For the present test case of an EG-based 1.06 vol.% ZnO nanofluid, the thermal conductivity was measured to increase by 5.4% over pure EG within the precision error of 0.53%.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20458-0(2009)).
References [1] Y. Feng, C. Kleinstreuer, Nanofluid convective heat transfer in a parallel-disk system, Int. J. Heat Mass Transfer 53 (2010) 4619–4628. [2] S.K. Das, S.U.S. Choi, W. Yu, T. Pradeep, Nanofluids: Science and Technology, John Wiley & Sons, USA, 2008. [3] Y. Nagasaka, A. Nagashima, Absolute measurement of the thermal conductivity electrically conducting liquids by the transient hot-wire method, J. Phys. E: Sci. Instrum. 14 (1981) 1435–1440. [4] W. Yu, S.U.S. Choi, Influence of insulation coating on the thermal conductivity measurement by transient hot-wire method, Rev. Sci. Instrum. 77 (2006). 076102/1-3. [5] C.A.N. Castro, B. Taxis, H.M. Roder, W.M. Wakeham, Thermal diffusivity measurement by the transient hot-wire technique: a reappraisal, Int. J. Thermophys. 9 (1988) 293–316. [6] R.G. Richard, R. Shankland, A transient hot-wire method for measuring the thermal conductivity of gases and liquids, Int. J. Thermophys. 10 (1989) 673– 686. [7] J.G. Bleazard, A.S. Teja, Thermal conductivity of electrically conducting liquids by the transient hot-wire method, J. Chem. Eng. Data 40 (1995) 732–737. [8] H. Watanabe, Further examination of the transient hot-wire method for the simultaneous measurement of thermal conductivity and thermal diffusivity, Metrologia 39 (2002) 65–81. [9] Y. Shi, L. Sun, F. Tian, J.E.S. Venart, R.C. Prasad, Fluid radiation effects in the transient hot-wire technique, J. Therm. Anal. Calorim. 90 (2007) 693–698. [10] S.W. Hong, J. Jung, Y.T. Kang, J. Koo, Parametric study on transient hot-wire method to measure nanofluid conductivities, Int. J. Air-Cond. Refrig. 18 (2010) 191–199. [11] H.S. Carslaw, J.C. Jaeger, Conduction of Heat on Solids, Oxford University Press, USA, 1959. [12] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavin, Introduction to Heat Transfer, Fifth ed., John Wiley & Sons, Hoboken, NJ, USA, 2007. [13] W. Duangthongsuka, S. Wongwises, Measurement of temperature-dependent thermal conductivity and viscosity of TiO2–water nanofluids, Exp. Therm. Fluid Sci. 33 (2009) 706–714. [14] S.M.S. Murshed, K.C. Leong, C. Yang, Enhanced thermal conductivity of TiO2– water based nanofluids, Int. J. Therm. Sci. 44 (2005) 367–373. [15] X. Zhang, H. Gu, M. Fujii, Experimental study on the effective thermal conductivity and thermal diffusivity of nanofluids, Int. J. Thermophys. 27 (2006) 569–580. [16] H.E. Patel, T. Sundararajan, S.K. Das, An experimental investigation into the thermal conductivity enhancement in oxide and metallic nanofluids, J. Nanoparticle Res. 12 (2010) 1015–1031. [17] N.R. Karthikeyan, J. Philip, B. Raja, Effect of clustering on the thermal conductivity of nanofluids, Mater. Chem. Phys. 109 (2008) 50–55. [18] H.T. Zhu, C.Y. Zhang, Y.M. Tang, J.X. Wang, Novel synthesis and thermal conductivity of CuO nanofluid, J. Phys. Chem. C 111 (2007) 1646–1650. [19] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transfer 125 (2003) 567– 574. [20] M.P. Beck, Y. Yuan, P. Warrier, A.S. Teja, The effect of particle size on the thermal conductivity of alumina nanofluid, J. Nanoparticle Res. 5 (2008) 1129– 1136.
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[21] E.V. Timofeeva, A.N. Gavrilov, J.M. McCloskey, Y.V. Tolmachev, Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory, Phys. Rev. E 76 (2007). 061203/1–16. [22] W. Yu, S.U.S. Choi, Influence of insulation coating on thermal conductivity measurement by transient hot-wire method, Rev. Sci. Instrum. 77 (2006). 076102/1–3.
[23] J.J. Healy, J.J. de Groot, J. Kestin, The theory of the transient hot-wire method for measuring thermal conductivity, Physica 82C (1976) 392– 408. [24] R.A. Perkins, S.S. Mohammadi, R. McAllister, M.S. Graboski, E.D. Sloan, A new transient vertical hot-wire thermal conductivity instrument for fluids utilizing a ramp power input, J. Phys. E: Sci. Instrum. 14 (1981) 1279–1284.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Impact analysis of natural convection on thermal conductivity measurements of nanofluids using the transient hot-wire method Sung Wook Hong a, Yong-Tae Kang a, Clement Kleinstreuer b, Junemo Koo a,⇑ a b
Mechanical Engineering Department, Kyung Hee University, Yongin 449-701, South Korea Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA
a r t i c l e
i n f o
Article history: Received 25 August 2010 Received in revised form 9 March 2011 Accepted 9 March 2011 Available online 21 April 2011 Keywords: Transient hot-wire method (THWM) Thermal conductivity Natural convection Nanofluids
a b s t r a c t Significant deviations between published results have been reported measuring the effective thermal conductivity of nanofluids with the transient hot-wire method (THWM). This may be attributed to a poor selection of the temperature data range, which should meet the following conditions. The start time should be chosen after the conductive heat flux delay time, while the end time should be selected before a crossover point when natural convection becomes significant. Considering an EG-based 1.06 vol.% ZnO nanofluid, the thermal conductivity was measured to increase by 5.4% over that of the base fluid. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluids, a dilute suspension of nanoparticles in liquids, have been considered as coolants because of their enhanced thermal conductivities. In general, the anomalous thermal conductivity enhancement of nanofluids, using typically metal or metal-oxide nanoparticles, has been attributed to nanoparticle Brownian motion, liquid molecule-layering, higher heat conduction, and/or clustering (see [1]; among others). Indeed, with some exceptions, thermal conductivity enhancement was generally observed; however, the magnitude of the increase varied among research groups [2]. A popular technique for measuring nanofluid properties is the transient hot-wire method (THWM) due to its simplicity, ease-of-use, and short measurement period which should not be affected by natural convection. For example, Nagasaka and Nagashima [3] developed a THWMset of 0.5% accuracy to measure the thermal conductivities of electrically conducting liquids (an aqueous NaCl solution) using a metallic wire coated with a thin electrical insulation layer. They analyzed the layer effect on the measurements, as again studied by Yu and Choi [4]. Castro et al. [5] re-assessed THWM as applied to thermal diffusivity measurements, where the effects of finite length of the wire, the diameter of the test section, variations in fluid properties and radiation heat transfer on measurement errors were analyzed. Richard and Shankland [6] used THWM to measure the thermal conductivities of both liquids and gases. Bleazard and ⇑ Corresponding author. Tel.: +82 31 201 3834; fax: +82 31 202 8106. E-mail address: [email protected] (J. Koo). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.03.041
Teja [7] developed a THWM apparatus to measure the thermal conductivities of electrically conducting liquids at high temperatures. Watanabe [8] analyzed the effect of radiation heat transfer on measurements and concluded that the impact is negligible at room temperature. Shi et al. [9] investigated the influence of natural convection and thermal radiation, where they showed the dependence of the measured thermal conductivity on the selection of the temperature data range. Most relevant is the paper by Hong et al. [10] who investigated the effects of the power supplier response delay, the thermal coefficient of resistors, the hot-wire type and the test section size on thermal conductivity measurements using THWM. They analyzed the impact of data range selection, response delay of power supply, thermal coefficients of the resistors, hot-wire type, and test section size. In this study, the effects of heat transfer delay time and natural convection on the proper selection of the temperature range when using THWM are discussed. The theoretical/experimental analysis of suitable data selection has been carried out with water and ethylene glycol (EG) and then applied to measure the thermal conductivity of a sample nanofluid, i.e., an EG-base containing ZnO nanoparticles of 1.06% in volume fraction.
2. Theory As the electric power is introduced into an electric wire, the temperature of the wire rises. The wire temperature depends on the rate of heat dissipated into the surrounding fluid. If the surrounding fluid is at rest, the heat is dissipated into the fluid
S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
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Nomenclature a c0, c1, c2 Cp g k L Q R t T q q000 z ur, uz z
Greek symbols temperature coefficient of resistance (TCR) [K1] thermal diffusivity [m2/s] b thermal expansion coefficient [K1] c Euler’s constant, 0.5772 m kinematic viscosity [m2/s] q density [kg/m3]
radius [m] constants specific heat [J/kg K] gravitational acceleration [m/s2] thermal conductivity [W/m K] length [m] heat transfer rate [W] resistance [X] time [s] temperature [K] heat generation per unit length [W/m] heat generation per unit volume [W/m3] coordinate [m] velocity components in r and z directions [m/s] coordinate [m]
a a
Subscripts 0 state at zero degree in Celsius 1 state at far field f fluid i insulation layer w wire
via conduction of which the magnitude is a function of the fluid’s thermal conductivity. The higher the thermal conductivity is, the lower the temperature rises due to increased thermal dissipation from the wire to the surrounding fluid. The relation between the hot-wire temperature rise and the thermal conductivity of the fluid is given by Carslaw and Jaeger [11] as:
Q d ln t 4pLw dT Rw ¼ R0 ð1 þ aT w Þ
kf ¼
ð1Þ ð2Þ
where Q is the heat transfer rate, Lw is the wire length, t is the time, and T is the temperature. Measuring the resistance change of the hot wire with time, and converting it to the wire temperature, Eq. (1) could be obtained to calculate the thermal conductivity of the fluid. Here, the temperature coefficient was set to be 0.00362 K1, which is the material property of platinum. Once the temperature data are obtained experimentally, the thermal conductivity can be determined with Eqs. (1) and (2). It should be noted that the linear relation in Eq. (2) is only valid for a small temperature range as in the case of this study, i.e., 298–318 K. For a wider temperature range a quadratic formula is typically used to capture the relation between resistance and temperature. Natural convection on a vertical surface, e.g., the surface of the hot wire in the THWM, originates from the buoyancy force caused by the temperature difference between the solid surface and the fluid. The axisymmetric momentum equation can be written as [12]:
" # @uz @uz @uz 1 @ @uz @ 2 uz þ 2 þ gbðT T 1 Þ; r þ ur þ uz ¼m r @r @t @r @z @r @z
Table 1 lists examples of recent effective thermal conductivity measurements of nanofluids using THWM. The data deviations in terms of linearity and slope of the thermal conductivity increase with particle volume concentration are significant. Although the deviations could be attributed to the differences in physicochemical properties, including nanoparticle size and volume concentration among nanofluids, part of the discrepancies between research groups is believed to be caused by the differences in selection of the temperature data range
1 @ðrur Þ @uz þ ¼0 r @r @z ! @T @T @T @ 2 T 1 @T @T þ q000 þ ur þ uz ¼k þ qC p þ @t @r @z @r2 r @r @z
ð4Þ ð5Þ
Eqs. (4) and (5) are the continuity and energy equations [12] which were solved, together with Eq. (3), by the commercial CFD package Fluent 6.3. The computational results were compared to experimental data sets. The no-slip condition was enforced on all walls including the top and bottom lids, wire, and test section shell surfaces. Heat generation in the wire and its propagation into the fluids were simulated as a conjugated heat transfer problem. The temporal mean temperature change of the hot-wire was monitored and the thermal conductivities of the fluids were estimated using Eqs. (1) and (2).
ð3Þ
where b is the thermal expansion coefficient of the fluid. The natural convection induced flow field is a function of the fluid properties such as the kinematic viscosity and the thermal expansion coefficient. The changes in thermal properties of water, i.e., dynamic viscosity and the thermal expansion coefficient, as a function of temperature are shown in Fig. 1. The thermal expansion coefficient is found to increase significantly with temperature, whereas the kinematic viscosity decreases slightly, i.e., it is basically negligible. As the thermal expansion coefficient increases, the buoyancy term in Eq. (3) increases for a given temperature difference between the surface and the fluid, affecting the flow field via natural convection. Hence, a change in thermal expansion coefficient may significantly impact the selection of a proper temperature data range.
Fig. 1. The effect of temperature change on the thermal property changes of water.
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S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456 Table 1 Examples of the effective thermal conductivities of nanofluids. Author
Particle material (size)
Base fluids
Temperature (K)
Duangthongsuka and Wongwises [13]
TiO2 (21 nm)
Water
298
Volume fraction (%)
Thermal conductivity enhancement (%)
0.2
2.5
0.6 1.0 1.6 2.0 0.5 0.8 1.0 2.0 3.0 4.0 5.0
3.6 4.2 6.1 6.8 4.5 9.5 18.4 23.8 25.6 27.3 29.8
Murshed et al. [14]
TiO2 (15 nm)
Water
298
Zhang et al. [15]
TiO2 (40 nm)
Water
303
1.2 2.5
3.5 5.4
Patel et al. [16]
CuO (31 nm)
Water
293
0.5 1.0 2.0 3.0
3.0 6.0 7.0 8.5
Karthikeyan et al. [17]
CuO (8.0 nm)
Water
298
0.1 0.3 0.8 1.0
13.0 18.0 25.0 31.0
Zhu et al. [18]
CuO (8.7 nm)
Water
298
0.5 1.0 2.0 3.0 4.0 5.0
13.0 18.0 25.0 28.0 30.0 31.0
Das et al. [19]
CuO (28.6 nm)
Water
298
1.0 2.0 3.0 4.0
6.4 10.0 12.0 14.0
Patel et al. [16]
Al2O3 (11 nm)
Water
293
0.5 1.0 2.0 3.0
6.0 7.0 8.5 11.0
Beck et al. [20]
Al2O3 (12 nm)
Water
297
2.0 3.0 4.0
2.0 3.0 5.0
Timofeeva et al. [21]
Al2O3 (11 nm)
Water
5.0 7.5 10.0
8.0 12.0 16.0
Das et al. [19]
Al2O3 (38.4 nm)
Water
1.0 2.0 3.0 4.0
2.4 5.2 7.0 9.5
3. Experimental set-up Fig. 2 shows the schematics of the transient hot-wire apparatus. A DC current electric power supplier (Array, model 3654A) imposed 4V across the Wheatstone bridge. The switching of the power supply was controlled by a relay circuit to avoid any power supply delay effect. The initial resistances of the resistors and the hot wires were measured by a low resistance meter (GOODWILL, model GOM-801G), which had a maximum reading error of 0.2%. The test section of 12 mm radius was fabricated with stainless steel. The length of the test section was 141 mm, and the top and bottom sides were covered by the lids. The hot-wire was made of 50 lm diameter platinum coated by a 25 lm electrically insulating Teflon layer. A thinner wire with anodic coating layer could be used to reduce the impacts of the initial delay, the insulation layer etc. However, a thicker, say, 50 lm, wire with 25 lm Teflon insulation layer was used for the ease of handling. No compensation wire was used for which Perkins et al. [24] claimed that end effects are
298
negligible when the wire is longer than 100 mm. The time variations of the voltage drop across the whole Wheatstone bridge and the voltage difference between the mid-points of the Wheatstone bridge circuit were stored in the computer using a data acquisition system (National Instrument, model USB-6210). The voltage history data were conditioned by the Butterworth low-pass filter to remove the signal noise. The viscosity and thermal expansion coefficient of a sample nanofluid were measured to investigate the effects of the two thermal properties on the thermal conductivity measurement using THWM. The viscosity was measured by an oscillatory type viscometer (AND, Model. SV-10). The definition of the thermal expansion coefficients is given in Eq. (6), where the specific gravities were measured at different temperatures using hydrometers
b¼
1 @q 2 q2 q1 q @T q1 þ q2 T 2 T 1
ð6Þ
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Fig. 2. Schematics of the transient hot-wire apparatus.
The thermal expansion coefficients of water and EG were measured in the same way and the errors, when compared to literature values [12] were found to be 6.3% and 2.9%, respectively. The larger error for water can be attributed to the fact that the thermal expansion coefficient changes drastically with temperature. The effects of radiation heat transfer on the measurements were analyzed by Castro et al. [5], Watanabe [8], and Shi et al. [9]. Clearly, for ambient temperature conditions radiation effects are negligible. However, while the effect of natural convection can be successfully eliminated as shown, the radiation effect could not be eliminated, if present. 4. Results and discussion In this section, the simulation results are presented first to introduce the underlying idea. Then they are applied to select an adequate temperature data range, obtained from the temperature history using THWM, to evaluate the thermal conductivities of the test fluids. 4.1. Effect of wire heat conduction on measurements Fig. 3 shows the effect of actual heat conduction inside the wire. The values of thermal conductivity were obtained from the measured hot-wire temperature history data using Eqs. (1) and (2) in which the heat flux on the surface is set to be a constant. However, it takes a finite time for the heat, generated inside the wire, to reach the wire surface uniformly. The ‘ideal’ heat flux history, which neglects the time delay for the internally generated heat to arrive at the surface, and ‘real’ heat flux history which is obtained from the simulation results, are compared in Fig. 3. It takes around 1 s for the surface heat flux to reach steady state; thus, the thermal conductivity will be overestimated if the wire temperature history data before 1 s are used. In our case, platinum hot-wires of 50 lm in diameter coated by Teflon of 25 lm in thickness were used. Clearly, for thicker wires it will take longer for the surface heat flux to arrive at the steady value. As a result, the temperature history data affected by the surface heat flux time delay should be avoided when using THWM; otherwise, measurements would result in overestimation of the thermal conductivity.
Fig. 3. Conductive heat flux history for wire surface.
The influence of the insulation coating on thermal conductivity measurement by the transient hot-wire method was analytically investigated by Yu and Choi [22], expanding the theory outlined by Healy et al. [23] as shown in Eqs. (7)–(10)
T W ðtÞ ¼
4af t q c0 c1 1þ ln 2 c1 þ þ c2 ; 4pkf t t aw e
ð7Þ
where the coefficients c0, c1 and c2 are given as c0 ¼ c1 ¼
a2i kf ai ki af a2 ðki aw kw ai Þ þ w 2kf af ai 2kf ai aw a2i 2kf
a2i
a2w 2ki
a2w 4ki
þ
a2w ðkf
ki Þðai aw Þ þ 8kw ai aw
ð8Þ a2w lnðai =aw Þðki
a w kw a i Þ
ki ai aw
ð9Þ kf 2 lnðai =aw Þkf c2 ¼ þ 2kw ki
ð10Þ
They claimed that the effect of the insulation layer on the temperature-rise error is less than 0.2% or even less for t > 0.5 s if c0 and c1 are of the order 103, and c2 does not affect the thermal conductivity measurements. The constants c0 and c1 are estimated to be
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a
S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456
0.62
b Start time 1.2 s Start time 1.6 s Start time 2.0 s Start time 2.4 s locally estimated value Crossover point Measure point
0.2528
1.0% error 0.616
0.5% error
0.614 Start time 1.0 s Start time 1.2 s Start time 1.4 s Start time 1.6 s locally estimated value Crossover point Measure point
0.612
0.61
0
1
2
3
4
7
5 6 End time (s)
8
Thermal conductivity (W/mK)
Thermal conductivity (W/mK)
0.618
0.2520
Reference
0.2516 -0.2% errir
0.2512
Reference
9
0.2524
0
10
1
2
3
4
5 6 End time (s)
7
8
9
10
Fig. 4. The simulation comparison of the heat flux delay and the natural convection effects on the thermal conductivity measurements for water and EG.
3.82 103 and 6.94 104, respectively, for the current case and hence the error becomes negligible after 0.5 s.
numerical simulation, they are scattered measurably with a couple of severe kinks with peaks and valleys, which may be attributed to the differentiation operation in Eq. (1). Due to the kinks, it is hard to read the thermal conductivities directly from the locally measured data. Since the data scattering becomes more severe for experimental measurements, the locally measured data cannot be used to estimate the thermal conductivity. It is proposed to estimate the thermal conductivity in a cumulative way, where a range of data should be properly selected to estimate the thermal conductivities so that the resulting values do not suffer much from data scattering. In Fig. 4(a) and (b), examples of thermal conductivity measurements, using various data ranges of different start
4.2. Effect of natural convection on measurements The effects of the induced natural convection on the measurements for water and EG are shown in Fig. 4. The locally measured thermal conductivities, which are measured using 100 neighboring points, decrease in the early phase when the wire-surface heat flux has not reached steady state. The data are shown every 10 points. They reach temporarily minimum values and start to increase due to natural convection. Although the data are taken from the
a 0.65
b Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Croosover point Measure point
Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.72
0.63
0.62 1.0% error 0.5% error
0.61
Thermal conductivity (W/mK)
Thermal conductivity (W/mK)
0.64
0.74
0.7
0.68
0.66
0.64 2.0% error 1.0% error Reference
Reference
0.62
0.6
0
1
2
3
4
7
5 6 End time (s)
8
9
0.6
10
0
1
2
3
4
5 6 End time (s)
7
8
9
10
c 0.82 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.8
Thermal conductivity (W/mK)
0.78 0.76 0.74 0.72 0.7 0.68 0.66
2.0% error 1.0% error Reference
0.64 0.62 0.6
0
1
2
3
4
5 6 End time (s)
7
8
9
10
Fig. 5. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of water at the temperature of (a) 298 K, (b) 308 K and (c) 318 K.
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S.W. Hong et al. / International Journal of Heat and Mass Transfer 54 (2011) 3448–3456 0.26
b Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
Thermal conductivity (W/mK)
0.258
0.256
1.0% error
0.254 0.5% error
0.252
0.25
1
2
3
4
5
6
7 8 9 End time (s)
c
10
12
13
14
0.5% error
0.254
Reference
Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.25
15
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
0.27 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.268 0.266 Thermal conductivity (W/mK)
11
1.0% error
0.256
0.252
Reference
0
0.26
0.258 Thermal conductivity (W/mK)
a
0.264 0.262 0.26
1.0% error
0.258
0.5% error
0.256
Reference
0.254 0.252 0.25
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
Fig. 6. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of ethylene glycol at the temperature of (a) 298 K, (b) 308 K and (c) 318 K.
times, are shown. Since the thermal conductivity is overestimated in the early phase due to the heat flux delay and in the late phase due to natural convection, thermal conductivity values using the cumulative approach will first decrease then increase passing through points of minimum values. If the start time is selected in the region where the effect of the heat flux delay exists, the thermal conductivity estimation decreases initially at a given time as the start time of the data range increases. Then later in the phase when natural convection affects the measurement, the thermal conductivity estimation increases faster for the cases with the later start time. There should be a point where the thermal conductivity estimation of the later start time case exceeds that of the earlier start time case. The open red1 circles in the figures show the crossover points, beyond which the impact of the natural convection becomes significant. Hence, the thermal conductivity should be estimated before the crossover point to avoid the impact of natural convection. If the start time is selected in the region where the kinks exist, the thermal conductivity can either increase or decrease depending on the local scattering of the estimated values of the thermal conductivity. If the start time is selected too late, the thermal conductivity values do not go through the crossover point (see the cases of start time 1.6 s for water and 2.4 s for EG in Fig. 4). In summary, to choose the proper temperature data range for estimating the thermal conductivity, the following three conditions should be met. The start time should be selected after the heat flux delay time. The end time should be selected before the 1 For interpretation of color in Fig. 4, the reader is referred to the web version of this article.
crossover point among the lines which go through the crossover point. Lastly, the data range should be large enough not to be affected by local oscillations in the estimates. The open green diamonds in Fig. 4 are the points where the thermal conductivities are estimated for water and EG. Comparing the water and EG cases, it was found that natural convection occurs later for the case of EG due to its high viscosity and the selection of start-time and end-time of the temperature data range differs for each fluid. The proper temperature data ranges are 1.2–2.3 s and 1.6–3.3 s for water and EG, respectively. This implies that the temperature data range, which is usually predetermined before the measurement and kept fixed regardless of the test fluid type, should be selected after the temperature histories are obtained and analyzed considering the three listed conditions. It is found that the estimation error for EG is smaller than that for water, and this could be attributed to the fact that EG is less affected by natural convection due to its higher viscosity when compared to water. 4.3. Analysis of the experimental data Figs. 5 and 6 show the results of the thermal conductivity measurements of water and EG at different temperatures. The effect of selections of start-time and end-time of the data range used in the measurements is presented in the figures. As discussed, the earliest start-time is after 1 s to avoid the impact of surface heat flux time delay. All cases show similar behavior with the increase of the data range. The estimated thermal conductivity values oscillate near the start-time where the data range selected is short and the
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Table 2 The results of thermal conductivity measurements of water and EG. Trial no.
Water at 298 K (W/m K)
Water at 308 K (W/m K)
Water at 318 K (W/m K)
EG at 298 K (W/m K)
EG at 308 K (W/m K)
EG at 318 K (W/m K)
1 2 3 4 5 6 7 8 9 10
0.6140 0.6159 0.6168 0.6144 0.6033 0.6170 0.6117 0.6160 0.6105 0.6125
0.6649 0.6206 0.6347 0.6273 0.6753 0.6497 0.6536 0.6391 0.6411 0.6333
0.6542 0.6989 0.6606 0.6642 0.6656 0.6797 0.6411 0.6459 0.6577 0.6594
0.2537 0.2545 0.2543 0.2541 0.2539 0.2531 0.2532 0.2524 0.2538 0.2553
0.2541 0.2542 0.2548 0.2533 0.2554 0.2556 0.2557 0.2542 0.2552 0.2560
0.2574 0.2541 0.2567 0.2563 0.2582 0.2562 0.2584 0.2579 0.2581 0.2589
Average (W/m K) Bias error (%) Precision error (%) Total uncertainty (%)
0.613 0.04 0.44 0.48
0.6439 2.7 1.8 4.5
0.6627 4.1 1.7 5.8
0.2538 0.8 0.2 1.0
0.2548 0.3 0.23 0.53
0.2572 0.5 0.37 0.87
Table 3 Comparison of viscosity and thermal expansion coefficient of pure ethylene glycol [12] and EG-base 1.06 vol.% ZnO nanofluid at 299 K.
Viscosity (cP) Thermal expansion coefficient (1 K1)
Measured property
Reference (ethylene glycol)
Enhancement (%)
16.81 0.000459
16.7 0.00065
0.7 30
estimation is sensitive to the local noise. The oscillation originates from the noise signal, which vanishes or averages out with time. After the estimated thermal conductivity reaches a plateau or a local minimum, it starts to increase with the increase of the end-time or the data range due to the effect of natural convection. Comparing Fig. 5(a)–(c), it is apparent that the thermal conductivity is affected by natural convection early on as the water base temperature increases. The end-time of the properly selected data range decreases from 4 s to 3 s and 2.6 s as the water base temperature increases from 298 K to 308 K and 318 K. If the thermal conductivities are measured using a temperature data range of fixed start-time and end-time, e.g. tstart = 1 second and tend = 3 s, the estimation bias errors increase from 0.26% at 298 K to 1.8% at 308 K, and 4.6% at 318 K. As the water base temperature increases, the effect of natural convection increases due to the decrease of the fluid viscosity and the steep increase of the thermal expansion coefficient. Therefore, it is expected that there is a certain high
temperature at which the data range end-time is very close to the start-time, so that the thermal conductivity of water cannot be measured using THWM. In case of EG, the thermal expansion coefficient remains constant for a wide temperature range, whereas the viscosity decreases with temperature. Fig. 6 shows the effect of the data range selection on the thermal conductivity estimation of EG. As already observed, the thermal conductivities are less affected by natural convection than in the case of water due to the higher viscosity of EG. Although the thermal expansion coefficient remains constant for the test temperature range, the viscosity decrease causes the increase of the natural convection effect with temperature. As a result, the end-time of the data range decreases from 7.23 s to 7.2 and 3.74 s with the increase of the base temperature. From the analysis of the result, it can be expected that the limiting high temperature to measure the thermal conductivity of EG is higher than that of water. If the thermal conductivities are measured using a temperature data range of fixed start-time and end-time, e.g. tstart = 1 s and tend = 3 s, the estimation bias errors decrease from 1.8% at 298 K to 0.43% at 308 K and 0.42% at 318 K. Table 2 represents the examples of the measurement results together with an error analysis. In case of water, the error is below 1% for the low temperature of 298 K; but, it increases to around 5% at higher temperatures. In contrast, the errors for EG remain below 1% for the given test temperature range. This can be also attributed to the lower impact of natural convection for EG.
0.28
0.28
0.278
Thermal conductivity (W/mK)
0.276
Thermal conductivity (W/mK)
ZnO 1.0 vol.% + EG Mean(0.2657) EG reference
0.275
0.274 0.272 0.27 Start time 1.1 s Start time 1.2 s Start time 1.3 s Start time 1.4 s Crossover point Measure point
0.268 0.266 0.264
0.27
0.265
0.26
0.255
0.262 0.26
0
1
2
3
4
5
6
7 8 9 End time (s)
10
11
12
13
14
15
Fig. 7. The effect of the start- and end-time of the temperature data range used to evaluate the thermal conductivity of a EG-base 1 vol.% ZnO nanofuid at 298 K.
0.25
0
1
2
3
4
5 6 Measurement set
7
8
9
10
11
Fig. 8. The results of 10 repeated thermal conductivity measurements for the EGbase ZnO nanofluid.
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In summary, the proper temperature data range selections are affected by both the fluid type, e.g., water or EG, and the base temperature. Since the proper temperature data range selection cannot be predetermined before taking measurements, it is recommended that the temperature history data is investigated carefully for each experiment. 4.4. Applications to a nanofluid The developed THWM technique is applied to measure the thermal conductivities of nanofluids. A sample of an EG-based nanofluid containing ZnO nanoparticles of 1.06% in volume fraction was prepared. The mean hydrodynamic diameter of the ZnO nanoparticles in EG was measured to be 10 nm using the dynamic light scattering method (OTSUKA, Japan, model ELS-Z). The measured physical properties, i.e., viscosity and thermal expansion coefficient which affect the incidence of the natural convection, are listed in Table 3. It was found that the viscosity increases by 0.7% while the thermal expansion coefficient decreases by 30% when comparing with the base fluid, EG. Therefore, it was expected that the thermal conductivity measurement would be less affected by natural convection (refer to Eq. (3)). Fig. 7 shows the effect of the temperature data range selection on the thermal conductivity measurements. In contrast to expectation, it was found that the THWM can be significantly influenced by natural convection, which cannot be explained relying on the natural convection theory for single phase fluids. The crossover point is shifted to about 5.5 s which was around 12 s for pure EG. It might be explained as a result of local motion of nanoparticles to invoke natural convection earlier, when compared to the cases of pure fluids. The proper selection of the temperature data should be between 1.2 and 3.2 s. The results of the 10 repeated thermal conductivity measurements of the EG-base ZnO nanofluid is represented in Fig. 8. The thermal conductivity of the EG-base 1.06 vol.% ZnO nanofluid is found to increase by 5.4% at 298 K over the pure EG case within a precision error of the measurements 0.53%.
5. Conclusions In this study, the effects of the temperature data range selection on thermal conductivity measurements using the transient hotwire method were investigated both theoretically and experimentally, taking transient conduction in the hot-wire as well as natural convection into account. The conclusions drawn from this theoretical/experimental study are as follows: It takes a finite time for the heat flux on the wire surface to reach steady state. It should be noted that the temperature data during the transient phase should not be included in the temperature data to estimate the thermal conductivity. In other words, the start-time of the selected temperature data range should be set after the transient phase. For the case of the 50 lm diameter platinum wire used, it was found that the delay time is about 1 s. In choosing the proper temperature data range to estimate the thermal conductivity, care must be taken to meet the following three conditions. First, the start time should be selected after the heat flux delay time. Secondly, the end time should be selected before the crossover point. Lastly, the data range should be large enough not to be affected local oscillation of the estimation. The proper temperature data range selections are affected by both the fluid type, e.g., water or EG, and the base temperature. Because the proper temperature data range selection cannot be
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predetermined, it is recommended that the temperature history is investigated for each experiment. Especially the thermal expansion coefficient of water increases drastically with temperature, so that the impact of natural convection on thermal conductivity measurements should be avoided by a proper selection of the temperature data range. While it was conjectured that the THWM applied to nanofluids would be negligibly affected by natural convection, due to the elevated value in viscosity and lower thermal expansion coefficient, it was found that the effect of natural convection can be significant. This might be a result of local motion of nanoparticles which induces natural convection early on. For the present test case of an EG-based 1.06 vol.% ZnO nanofluid, the thermal conductivity was measured to increase by 5.4% over pure EG within the precision error of 0.53%.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20458-0(2009)).
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