Enhancing the Thermal Gradient of Thermometer Calibration Systems with an Assembly of Water Heat Pipes

To improve the temperature gradient of an electric furnace for the calibration of thermometers, a heat pipe assembly that uses a number of commercial water heat pipes, sealed in a cylindrical copper tube, was designed and tested. Twenty heat pipe tubes were arranged around the circumference of a cylindrical Cu or Al pillar well and attached to the pillar surface using a high-thermal-conductivity epoxy. This heat pipe assembly was installed in an electric furnace with a single heater, and its thermal characteristics were examined by measuring the temperature gradient using a PT100 resistance thermometer. Without any inserts in the single-zone electric furnace, the temperature gradient was disappointing at 0.6 °C·cm−1 at 225 °C and cannot be used for any purposes. However, the heat pipe assembly could enable a very uniform temperature gradient of 0.02 cm·°C−1 or better inside the Sn fixed-point cell, leading to a realization of the Sn fixed point with a flat melting and freezing plateau. From the experimental results, it was verified that this inexpensive heat pipe assembly gives improved thermal uniformity and thus is adequate for the calibration of thermometers, even for the realization of Sn and possibly in fixed points, without using an expensive multi-zone furnace or liquid bath.


Introduction
For the precise calibration of thermometers, it is generally required to prepare appropriate thermal media such as stirred liquid baths or electric furnaces. Liquid baths are useful from − 70 °C up to 650 °C by changing the liquid medium. Many comparison calibrations for industrial thermometers such as platinum resistance thermometers (PRTs), thermistors, and liquid-in-glass thermometers have been done in liquid baths because of their usefulness and stability. They can also be used for the realization of In freezing points (156.5985 °C) because of their good thermal homogeneity [1]. However, even though the liquid bath system is convenient for the calibration of many thermometers, it is bulky, expensive, and takes a long time to stabilize thermally. In addition, environmental safety systems such as fume hoods are required, and liquid droplets may spill over the laboratory floor.
For much faster calibration in dry conditions, electric furnaces have been used with wide temperature ranges and temperatures reaching more than 1000 °C. A weak point of electric furnaces is the steep temperature gradient through the working volume, which is caused by natural heat conduction from hot (inside) to cold (outside). To overcome these issues and obtain better thermal uniformity, furnaces with two or three multi-heating zones are recommended for metrological calibration purposes [2,3]. Moreover, by introducing heat pipe tubes, it is possible to improve the temperature uniformity even further. Depending on the temperature range, many kinds of working fluids are used in the heat pipes, such as ammonia (213 K ~ 373 K), alcohol (methanol (283 K ~ 403 K) or ethanol (273 K ~ 403 K)), water (298 K ~ 573 K), mercury (523 K ~ 923 K), cesium (673 K ~ 1073 K), and sodium (873 K ~ 1473 K) [4]. Sodium heat pipes have frequently been used for the realization of Al and Ag fixed points of the International Temperature Scale of 1990 [5].
However, one critical disadvantage of heat pipe systems is their high cost. For efficient and economic calibration work, it is required to develop much cheaper systems; the present study was initiated from this perspective. For example, electric furnaces with a single water heat pipe are available on the market for the realization of In or Sn (231.928 °C) freezing points [6]. These furnaces can also be used for comparison calibration of industrial thermometers below 250 °C. The performance characteristics would be good for precise calibration, but at a high cost. The key and expensive part of these furnaces is the water heat pipe tube surrounded by the electric heater. If it can be replaced with a cheaper option, it would be beneficial for every calibration laboratory and national metrology institute.
A water-filled heat pipe enveloped in a Cu tube, as shown in Fig. 1, is commercially available. The example shown in the figure, at a cost of a few tens of dollars, is 350 mm long with a diameter of 8 mm, and can be operated up to 250 °C. There are many Fig. 1 Single water heat pipe sealed in a Cu tube inexpensive heat pipe products with various materials, shapes, and sizes. By applying these heat pipes to a single-zone furnace, significantly improved temperature uniformity can be anticipated. If it works properly, it is expected that an inexpensive and simple heat pipe can be made for the calibration of PRTs and other thermometers. Moreover, it can be extended to a fixed-point calibration system for In and Sn. This paper presents the preparation of a water-filled heat pipe assembly and experimental results to realize the Sn fixed point. One important thing to notice is that water heat pipe(s) in Cu tube could be de-sealed at elevated temperatures near the freezing temperature of tin due to the volume expansion inside the pipe. In some extreme cases, it can be de-sealed or busted, causing damage to the furnace system. Therefore, one should be careful in selecting heat pipes in the market. It is recommended that the maximum usable temperature should be higher than 250 °C. Figure 2 shows the three-dimensional design of the heat pipe assembly. Figure 2a gives a cross-sectional view, (b) gives a view of the internal arrangement, and (c) shows the outer Cu cover of the heat pipe assembly. The container is composed of two commercial Cu pipes, the inner pillar well (Type 50 A, OD: 53.98 mm, ID: 50.42 mm, L: 370 mm) and an outer cover (Type 80A, OD: 79.38 mm, ID: 74.8 mm, L: 386 mm). The maximum usable temperature of the prepared heat pipes was 250 °C. As shown in the figure, heat pipe tubes were mounted vertically around the Fig. 2 Three-dimensional images of the heat pipe assembly: (a) cross-sectional view, (b) view of the internal arrangement, and (c) the outer Cu cover of the heat pipe assembly circumference of the inner pillar well. To join the heat pipes, a base plate and top tube holder were machined using brass. Figure 3a and b shows the outer cover and inner pillar well, (b) shows the assembly with only one heat pipe installed, and (c) shows the assembly with all heat pipes installed. Each heat pipe can be vertically placed into holes in the base plate and top tube holder. The outer cover is joined to the base plate and tube holder using bolts. A maximum of 20 heat pipes were attached to the surface of the tube with an outer diameter of 54 mm, between the tube holder and base plate. For better thermal contact between the heat pipes and inner pillar well, heat conductive epoxy (AREMCO Bond 805A and B) was used. This assembly was placed into the well (500 mm in depth and 85 mm in opening aperture) of a vertical electric furnace. The home-made furnace has a single heating zone from the bottom of the well of approximately 150 mm in height.

Experimental Details
The temperature uniformity inside the furnace with and without the heat pipe assembly was measured using a PRT sensor (PT100 resistance thermometer) and WIKA CTR5000 display. The results of the uniformity assessment are given in Section III. The PT100 was calibrated from the ice point to 650 °C with a calibration uncertainty of 0.05 °C (k = 2) at the Korea Research Institute of Standards and Science (KRISS).
To examine the possibility of using the heat pipe assembly for the realization of the In or Sn freezing points, which have transition temperatures lower than 250 °C, the melting and freezing behavior of a sealed-type Sn cell was investigated with and without the heat pipe assembly. The test Sn cell was a sealed type made by KRISS in In these studies, a standard platinum resistance thermometer was not used because the PT100 was found to be sufficient to examine the operational features of the heat pipe assembly. As the PT100 sensor has a resolution of 0.01 °C, it was capable of distinguishing the effects of the heat pipe assembly on the temperature uniformity as well as on the melting and freezing behavior of an Sn fixed-point cell.

Results and Discussion
To assess the effect of the heat pipe assembly on the performance of the furnace, the temperature profile inside the furnace was compared before and after insertion of the heat pipe assembly. The temperature gradient inside the furnace was measured while maintaining the temperature of the furnace at a constant 225 °C. The results are shown in Fig. 3. The black circles and blue triangles denote the inside temperature gradient of the furnace without and with the heat pipe assembly, respectively. To block the heat loss through the furnace entrance, it was mounted with ceramic thermal insulator wool with about 5-cm depth, except for the small hole for a measuring thermometer. At each immersion depth, the furnace was at thermal equilibrium when the measurements were carried out.
The temperature measurement uncertainty at each immersion point was estimated to be about 0.06 °C with k = 2. As uncertainty factors, two major factors were considered. The first one was the calibration uncertainty of the thermometer with an uncertainty of 0.05 °C (k = 2), and the other was the temporal thermal stability of the electric furnace for 10 min under thermal equilibrium. A standard deviation value of 0.055 °C for 10 min was used for thermal stability. Other minor factors such as the resolution limit of the thermometer display and heat loss through the thermometer stem were neglected because of their tiny contribution to the combined uncertainty.
Without the assembly, the temperature gradient was quite steep and the temperature difference was as large as 9.5 °C at 15 cm from the furnace bottom. This difference is too large to be acceptable for the fixed-point realization, even for the usual comparison calibration of thermometers. However, by introducing the heat pipe assembly into the furnace, the temperature gradient was improved six-fold. The temperature drop decreased to as small as a 1.6 °C difference at 15 cm from the bottom with a slope of 0.11 °C·cm −1 . This demonstrated that the assembly can dramatically improve the uniformity of the temperature gradient because of the excellent heat conduction of the individual heat pipe tubes.
The red squares and green rhombuses in Fig. 3, respectively, denote the inside temperature gradient of the Sn cell installed in this furnace and in the commercial three-zone metrology furnace (ISOTECH Model ITL-M-17703). In these cases, a measuring thermometer was located in the thermometer well of the fixed-point cell. The test cell was also thermally insulated with ceramic wool by packing the wool on the top of the cell. It can be seen that incorporating the test Sn cell into the heat pipe assembly, the temperature gradient was further improved by more than four times. At 15 cm from the cell bottom, the temperature difference was very small, at only 0.38 °C (gradient of 0.025 °C·cm −1 ). This result is comparable to results obtained from the commercial three-zone furnace (green rhombus in Fig. 4). The maximum temperature variation along the Sn cell of the ISOTECH furnace was measured to be 0.12 °C from 0 to 14 cm from the bottom (gradient of 0.009 °C·cm −1 ). Commercial furnaces do perform better, but it is considered that this heat pipe assembly can be applied in a practical manner for metrological purposes.
In order to study the effects of the heat pipe assembly on the phase transition behavior of the Sn fixed point, the test Sn cell was realized before and after the installation of the heat pipe assembly at melting and freezing offset temperatures of 238 °C and 229 °C, respectively. Figure 5 shows the melting and freezing curves for the results. Without the heat pipe assembly, the melting and freezing behavior of the Sn greatly deteriorated, as shown in Fig. 5a. At the initial stage, the melting plateau temperature is uniform and looks like a conventional melting plateau of fixed-point cells, which means that the melting transition progressed as expected.
As the temperature at the bottom is highest and relatively uniform along the cell, the ingot in this area may start to melt. After this flat region, the temperature gradually increased. This increase may be caused by the nonuniform melting from the middle to the top section of the ingot inside the cell as a result of the large temperature gradient, as shown in Fig. 4. Finally, the temperature rapidly rose to the melting offset temperature. When considering the freezing curve, it was observed to be steeply declined, which means that the temperature of the inside molten liquid was severely affected by the outside temperature profile of the cell. The small supercool peak was observed at a much higher temperature than the expected melting and freezing Fig. 4 Temperature gradient profiles measured at 225 °C. Blue triangles and black circles denote the temperature gradient profiles of the furnace without and with the heat pipe assembly, respectively. Red squares and green rhombuses denote the profiles inside the Sn cell installed in the heat pipe furnace and in the commercial three-zone metrology furnace, respectively (Color figure online) temperatures indicated by the red broken line. All these abnormal and unnecessary melting and freezing behaviors might be caused by the worst temperature gradient along the fixed-point cell.
However, after the installation of the heat pipe assembly, the melting and freezing curves were recovered as normal, as shown in Fig. 5b. The melting plateau lasted for about 8 h with a stable and flat plateau within ± 1.5 mK. The freezing plateau was initiated, followed by a short period of supercooling of only 0.3 °C, below the guiding red broken line. This small amount of supercooling is abnormal when compared with the commonly known deep supercooling of 20-30 °C [5,7]. Later it was found to be ascribed to the oxidation of Sn caused from the sealed cell undergoing fabrication of the cell [8], and it could be restored by high-temperature carbothermal reduction at 750 °C. The Sn cell was also tested in the three-zone furnace under the same melting and freezing offset temperature as Fig. 5. The freezing curve having a tiny supercool was the same as the case in the single-zone furnace with the heat pipe assembly. It means that the small supercooling is not caused by the thermal effects. At the freezing offset temperature of − 3 °C, the freezing plateau lasted longer than 10 h within ± 4 mK, enabling the calibration of several secondary-class thermometers, such as thermocouples and industrial PRTs, during one realization. It was therefore found that the heat pipe assembly could enhance the thermal uniformity of a single-zone electric furnace suitable for the realization of the Sn fixed point. At this point, it was shown that a heat pipe assembly made of several water heat pipes sealed in a Cu tube is economical and useful for the calibration of thermometers, and can even be applied for the realization of an Sn fixed point. To improve this approach, it was suggested that the weight of the heat pipe assembly be reduced for easy and convenient handling. The heat pipe assembly used was made of Cu or Cu alloy. Therefore, it was somewhat heavy, and it also took a long time to reach the target temperature of the furnace. To avoid this, it was thought that Al alloy could be an alternative, sacrificing 10% of thermal diffusivity (α Al = 102.0 mm 2 ·s −1 , α Cu = 115.4 mm 2 ·s −1 at 25 °C) [9]. More specifically, the inner tube, base plate, and tube holder could be replaced by an Al alloy such as Al 6061. Another possible step for improvement would be eliminating the Cu outer cover pipe and tube holder, which was designed to protect and fix the heat pipes. However, after the heat pipe assembly was installed into the furnace, it was found that there was no opportunity for it to be damaged mechanically. The outer cover and tube holder are therefore not considered to be necessary components of the assembly. Eliminating these parts would also be helpful to increase the thermal reaction kinetics. From this consideration, an attempt was made to make an Al-base heat pipe container. Figure 6 shows the three-dimensional schematic diagram of the container and the constructed heat pipe assembly, respectively. As shown in the figure, the container is composed of two parts, a commercial Al 6061 pillar tube well (outer diameter 58 mm, inner diameter 52 mm, and length 370 mm) and a base plate (outer diameter 80 mm, inner diameter 51.9 mm, and step 10 mm). These two parts were joined using four screw bolts. Finally, 20 heat pipes were attached to the surrounding outer surface of the pillar based on the grooves formed on the base plate, and fixed using an O-shaped clamp. A high-temperature Fig. 6 Three-dimensional diagram of the Al-base container and the resultant manufactured heat pipe assembly heat-conductive ceramic epoxy from Cotronics (Resbond 920 powder), which can be activated by mixing 14 parts of water into 100 parts of powder by weight, was used to increase the thermal contact between the heat pipes and the pillar well. As a result, this Al-base container was considerably simpler and substantially lighter than the Cu-base container. The number of main parts was reduced to only two and the weight was decreased from 4.0 to 1.4 kg, including the 20 heat pipe tubes. In addition, the manufacturing cost was less than a third of that for the Cubase container. However, without the outer case, one should be careful that there will be unexpected damage to the furnace due to de-sealing the heat pipe(s) at elevated temperatures.
To examine the heat-conducting performance of the Al-base heat pipe assembly, it was loaded into the furnace, and then the Sn test cell was installed into the heat pipe assembly. Figure 7 shows the result of the temperature gradient profile at 225 °C, represented by red triangles. For comparison, data from the Cu-base holder (black circles) is also presented. Up to 15 cm from the bottom, the gradient was measured to be as small as 0.015 °C·cm −1 , which seemed slightly less than that of the Cu-base, compared with the measurement uncertainty at each point. However, when it comes to considering that both liners used the same heat pipes, which did the temperature homogenization, it could not say that the Al-base holder was superior to Cu-base. The difference in gradient in Fig. 7 might come from the difference in the external setup conditions of heat pipe assembly into the furnace such as insulating wool packing. Above 15 cm from the bottom, however, the gradient became much steeper than for the Cu-base system, owing to the increased heat loss because the thermometer is moved closer to the ambient temperature as the distance from the bottom is increased. From the gradient tests, it was found that the heat pipe assembly with Al-base holder also showed good thermal uniformity with lighter weight than Cu-base holder, which was more comparable to the commercial three-zone furnace. Fig. 7 Temperature gradient profiles inside the Sn fixed-point cell at 225 °C installed in the Al-base and Cu-base heat pipe assembly, respectively. The lines were calculated using only the results from 0 to 15 cm. Error bars denote for the expanded uncertainty at each point Figure 8 shows the three repeated melting and freezing transitions of the Sn fixed point in the Al-base heat pipe assembly. The melting and freezing offset temperatures were the same as for the case of Fig. 5, i.e., 238 °C for melting and 229 °C for freezing, respectively. As shown in the figure, it was reproducible and showed typical phase transition behaviors of the metal fixed points in thermometry. In order to check the reproducibility of the melting temperature, the melting temperature of each realization was considered as the average value of 10 h in the middle of the freezing plateau as indicated by the arrow in Fig. 8. The resultant reproducibility (one standard deviation) was calculated to 4 mK. Its variation may come mainly from the instability of the Pt100 thermometer and the measuring device. Because the purpose of this work is not the exact determination of the Sn fixed-point temperature, but rather investigating the suitability of the assembly as a good uniform thermal enclosure, this level of standard deviation was considered as a successful result.
From the studies, it was found that using Al alloy as a heat pipe container was practical and useful. It is possible to also make a Cu-base container similar to the Al-base, but it is recommended that Al alloy be used because of the raw material price and weight. Conclusively, the heat pipe assembly manufactured in this study, regardless of raw materials, was demonstrated as a successful alternative for the expensive three-zone furnace or complicated liquid bath as a uniform thermal enclosure for the calibration of thermometers. In addition, further studies can also investigate the application of the heat pipe assembly to an In fixed-point cell for which a dry system would be efficient and more convenient than a liquid bath.