Introduction
The new reference material for Conductivité ThermiqueThermal conductivity (λ with the unit W/(m•K)) describes the transport of energy – in the form of heat – through a body of mass as the result of a temperature gradient (see fig. 1). According to the second law of thermodynamics, heat always flows in the direction of the lower temperature.thermal conductivity, ERM-FC440, is the successor to the well-known IRMM- 440 reference material, which is no longer available. ERM-FC440 was certified by the Institute of European Reference Materials, ERM®, located in Belgium [1]. The material is intended for quality control and assessment of the method performance of guarded hot plate (GHP) measurements as well as for calibration of heat flow meter (HFM) instruments [2].
Properties of ERM-FC440
ERM-FC440 resin-bonded glass fiber boards are available in three different sizes:
- 30 cm x 30 cm (ERM-FC440a)
- 50 cm x 50 cm (ERM-FC440b)
- 60 cm x 60 cm (ERM-FC440c)
The mean thickness of ERM-FC440 is (28.65 ± 0.15) mm under a load of 0.25 kPa and (28.27 ± 0.19) mm under a load of 1.5 kPa. The densities of all ERM-FC440 samples are in the range of 130 and 148 kg/m3 [2]. The thickness and density of each individual sample plate at 0.25 kPa are stated on each reference material certificate. ERM-FC440 is certified for its Conductivité ThermiqueThermal conductivity (λ with the unit W/(m•K)) describes the transport of energy – in the form of heat – through a body of mass as the result of a temperature gradient (see fig. 1). According to the second law of thermodynamics, heat always flows in the direction of the lower temperature.thermal conductivity in the temperature range from -10°C to 70°C [2]. In addition, indicative thermal conductivity values are given in the range from -150°C to -10°C. The temperature-dependent thermal conductivity λ of ERM-FC440, as stated in the certificate, is expressed as
λ [W/(m·K)] = 0.03104 + 1.1 · 10-4 · T [°C] (1)
for the entire temperature range from -150°C to 70°C.
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The expanded uncertainty is 1.1 % in the range from -10°C to 70°C and 1.9% to 1.1% in the range from -150°C to -10°C. Figure 2 displays the nominal thermal conductivity λ of ERM-FC440 according to equation 1 as well as the uncertainty budget.
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Thermal Conductivity Results
1. Results Obtained with the GHP 456
The guarded hot plate (GHP) technique is an absolute method without any calibration of the thermal conductivity. In the two-plate mode, the thermal conductivity λ is calculated from the power Q flowing into the hot plate with metering area A, the temperature gradient across the two samples ΔT as well as the mean sample thickness d as follows:
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GHP measurements on ERM-FC440 samples were carried out using a NETZSCH GHP 456 HT Titan® equipped with liquid nitrogen cooling. ERM-FC440a specimens with serial numbers 001, 002, 003, and 005 were used for the GHP tests. The pair of specimens 001+002 and the pair 003+005 were each measured simultaneously in the two-plate mode. The temperature gradient across the samples was 30 K at temperatures below -10°C, and 20 K at 10°C and higher temperatures. The specimens had rigid spacers in their corners with a length identical to the nominal sample thickness in order to ensure a defined sample thickness.
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Figure 3 depicts the GHP measurement results: In the temperature range between -150°C and 70°C, the relative deviation from the nominal thermal conductivity values calculated from equation 1 is less than ± 1.3% for all measurement data except for one point at -150°C which deviates by -2.2%. These results are in accordance with the expected accuracy of the GHP 456.
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2. Results Obtained with the HFM 446
The heat flow meter (HFM) technique is a relative method based on calibration of the heat-flux sensors using a reference material with known thermal conductivity. The unknown thermal conductivity λ of a sample is calculated from the heat flux per area Q/A and the temperature gradient ΔT across the sample with mean thickness d according to the Fourier‘s equation for onedimensional heat flow as follows:
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The HFM measurements on the ERM-FC440 samples were carried out using the NETZSCH HFM 446 Lambda Eco-Line Small, Medium and Large instruments. Two HFM 446 Large devices with serial numbers 0009 and 0010 at different locations were used to test the ERM-FC440c specimens with serial numbers 004 and 005. Two HFM 446 Medium devices with serial number 0007 and 0009 were used to test the ERM-FC440a specimens with serial numbers 001, 002, 003 and 005. Three HFM 446 Small devices with serial numbers 0086, 0087 and SOA-002 were used to test ERM-FC440 specimens with the size 20 cm x 20 cm cut out of the ERM-FC440c board with serial number 005 after the measurements in the HFM 446 Large were completed. For documentation purposes, each 20-cm board was assigned an identification number with five digits, which was lasered on the front face (see also figure 1 on the right). All devices were calibrated with either NIST SRM 1450d or IRMM440. The measurements were performed at mean temperatures between -10°C and 70°C with a temperature gradient across the samples of 20 K and a contact pressure of maximum 2 kPa.
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Figures 4 to 6 depict the measurement results from all HFM instruments. Across the entire temperature range, the relative deviation from the nominal thermal conductivity values calculated using equation 1 is within ± 1.5% for most measurement results, except for some measurement points at the highest temperature of 70°C. All results are in accordance with the expected accuracy of ± 2% for the HFM 446 heat flow meters.
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Summary
The thermal conductivity of the new reference material for thermal conductivity, ERM-FC440, was investigated in the temperature range between -150°C and 70°C applying one GHP 456 and several HFM 446 devices. Almost all results were in agreement within ± 1.5% with the nominal values, reflecting the accuracy of GHP 456 Titan® and HFM 446 Lambda instruments by NETZSCH.