Thermocouples are widely used for temperature measurements. They are particularly useful in lab testing, due to their relatively low cost and the ability to easily fabricate thermocouples of specific lengths for a given test. This Tech Brief discusses issues related to the size of a thermocouple that may be considered when using them.
A thermocouple consists of two wires made of different metals. The wires are welded together at one end and, due to the Seebeck Effect, this junction of dissimilar metals generates a small voltage (typically of only a few millivolts). Since the voltage is a function of the junction temperature, the thermocouple produces a temperature response that can be measured relatively easily, which led to their being adopted for temperature measurements more than a century ago [1].
Originally, thermocouple circuits were typically comprised of three wires in series (such as copper – constantan – copper) that included two junctions of dissimilar metals. One junction would be attached to the location where the temperature was to be measured and the other junction held at a reference temperature (typically ice water). Each junction generated a voltage, but with opposite polarity so that the net voltage generated by the circuit corresponded to the temperature difference between the two junctions. The actual measurement does not directly determine the voltage generated by the thermocouple junctions but instead determines the voltage that must be applied to the circuit to produce zero current flow. The magnitude of this voltage is equal to that generated by the thermocouple junction, but with the opposite sign. Since the applied voltage results in no current flow, there is no electrically resistive loss in the thermocouple wires. Thus, the length of the thermocouple does not affect the measurement. In practice today, thermocouple meters include circuitry that provides this voltage balance, converts the voltage to a temperature measurement, and applies an internal reference temperature that eliminates the need for an ice bath1.
Basic information on thermocouples is available from many resources, such as references [2, 3, 4]. These provide information on topics including the materials used in different thermocouple types, their measurement sensitivity, temperature limits, etc. However, these introductory overviews don’t necessarily discuss details such as the impact of the size of thermocouple wires on measurements.
For example, one of the cited references stated that “(thermocouples) do not conduct much heat away from a contact point” [2]. This is generally correct, but it depends on one’s definition of ‘much.’ This Tech Brief gives quantified answers as to what ‘much’ may be for a thermocouple heat sinking effect.
When attached to a heat source, such as an electronic component, thermocouple wires can be described as thin metal structures that extend into the surrounding air. This is also an appropriate description of cooling fins, i.e., thermocouple wires can act as fins that dissipate power. They therefore somewhat cool the component being measured and reduce its temperature.
For example, Figure 1 shows images of a circuit board in a thermal test. The top image shows an infrared (IR) image of the entire board while the bottom image shows a close-up of two components that dissipated the same power. Two sizes of Type-T thermocouples2 were attached to the two components: the top thermocouple had 30 gauge wire (0.254mm / 10 mil diameter) while the bottom thermocouple had 40 gauge wire (0.0787mm / 3.1 mil diameter).
The top of Figure 2 shows a close-up of the IR image of the two thermocouple components (the image has been rotated 90°C counterclockwise) and the bottom image in the figure shows a temperature scan along the horizontal slice depicted with the blue/ red line. This image shows ‘dips’ on the two components; these dips are caused by the two thermocouples that locally cool the components by acting as fins. The larger (30 gauge) wires cause a much larger temperature dip of ~3°C while the smaller (40 gauge) wires only caused a temperature dip of ~0.9°C. The relative thermal loss in the thermocouples is also illustrated by the larger length of the 30 gauge wire that is yellow and green while the 40 gauge wire is primarily blue in the IR images of Figure 2. Note that the temperature profile shows two apparent temperature dips between the components; these are due to the low emissivity of the electrical leads on the components.
The test results shown in the previous figures indicates that thermocouple size can affect the temperature being measured. This is certainly not a new finding: other researchers have pointed out that larger thermocouples will cause a temperature drop [5] and that the effect also depends on thermocouple type [6].
To quantify the heat loss from a thermocouple, we can use fin equations to estimate the thermal loss from it. The thermal dissipation (Q) from an insulated tip fin is calculated as Q=M*tanh(mL), where:
M = (hPkAc)1/2 * ΔT and m = (hP/kAc)1/2.
In these equations, L is the length of the fin, h is the convection coefficient, P is the perimeter of the wire (πD), where D is the wire
diameter, k is the wire thermal conductivity, and Ac is the wire cross sectional area (πD2/4).
For a 30 gauge thermocouple (0.254mm diameter) that is 4” long (10cm) and in contact with a surface at 100°C while exposed to 25°C ambient air with free convection (assuming the convection coefficient is 10 W/m2K), the heat transfer from a copper (k=390 W/mK) wire would be 28.7mW and 6.91mW from a constantan (k = 21 W/mK) wire. The actual thermocouple length has little impact on the results – the wire is essentially at ambient temperature within 1-2 cm. The total thermal loss from the two wires that make up a type-T, 30 gauge thermocouple is then ~35.6mW. In comparison, the smaller 40 gauge wire would only lose ~6.3mW to the ambient temperature. If the thermocouple wires are exposed to fan cooling that increases the convection coefficient to 40 W/m2K, the thermal losses for the 30 and 40 gauge thermocouples are calculated to be 73.4 and 12.7mW, respectively.
Careful readers may point out that thermocouples generally are not bare wires, but are insulated. One would think that this electrical insulation thermally insulates them and reduces thermal loss. Somewhat surprisingly, analyses (both one-dimensional radial conduction and finite element modeling) indicate that the insulation around the bare wires actually increases the thermal loss by 30-50% compared to bare wires. This is a result of the larger surface area, due to the insulation, reducing the convective resistance more than conduction through the insulation adds resistance3.
In summary, attaching a thermocouple to a power-dissipating component will lead to some thermal loss into the thermocouple wires, which reduces the local temperatures. The size and type of thermocouple will impact the magnitude of the temperature drop. Type-T thermocouples, which have a copper wire, will have more thermal loss than other types. Using smaller thermocouples, such as 40 gauge instead of 30 gauge, will reduce the amount of thermocouple ‘dip’. However, these smaller thermocouples are more delicate, so their non-junction ends are typically soldered to larger thermocouple wires for routing to the data acquisition system.
Figure 3 compares the expected thermal losses for different thermocouple types and sizes when used to measure a temperature 100°C above the surrounding air. These estimates were based on calculations for bare wires; as mentioned previously, insulation will likely increase the loss. The thermal loss due to thermocouples is generally a few tens of mW or less, so it can be ignored for parts that dissipate a few W. But if thermocouples are used on small parts that dissipate a few hundred mW, a large thermocouple can have a noticeable effect on the measured temperature.
100°C above ambient
1 30+ years ago, the University of Minnesota Mechanical Engineering department had an ice machine to make ice for thermocouple reference temperature baths. Ice from this machine was also occasionally used for chilling beer during unofficial Friday afternoon graduate student ‘colloquia’. Presumably, today’s grad students no longer have this perk.
2 Type-T thermocouples are made of a set of copper and constantan wires.
3 This critical radius of insulation [7] effect is interesting enough that it could be a topic of a future Tech Brief.
Note – The images used in Figures 1 and 2 were produced by staff in the Rockwell Collins (now Collins Aerospace) Heat Transfer Lab: Dave Dlouhy (retired) and Doug Twedt.
References
[1] L.B. Hunt, “The Early History of the Thermocouple”, Platinum Metals Rev. 1964, 8, (1), 23; https://technology.matthey.com/ article/8/1/23-28
[2] Steve Roberts, “Thermocouple Basics Part 1: Advantages to Multi-Channel Isolated Thermocouples”, Electronics Cooling Magazine Blog, July 18, 2023; https://www.electronics-cooling.com/2023/07/advantages-to-multi-channel-isolated-thermocouples/
[3] Steve Roberts, “Thermocouples Basics Part 2: How They Are Made and Its Measurement System”, Electronics Cooling Magazine Blog, July 26, 2023; https://www.electronics-cooling.com/2023/07/35284/
[4] “Thermocouple Probes”, Omega Engineering, https://www.omega.com/en-us/resources/thermocouple-hub
[5] Q. He, S. Smith and G. Xiong, “Thermocouple attachment using epoxy in electronic system thermal measurements — A numerical experiment,” 2011 27th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, San Jose, CA, USA, 2011, pp. 280-291
[6] W. Tian, M. Berktold, C. Carte and E. Tan, “Investigation on Reading Discrepancy of Type T and Type J Thermocouples,” 2020 19th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Orlando, FL, USA, 2020, pp. 905-908
[7] Frank White, “Heat Transfer”, Addison-Wesley, (1984), pp. 61-63
