Characterization method of the Joule heating efficiency of electric textiles and influence of boundary conditions

Joule heating textiles are available on the market for a variety of applications. However, their market growth is limited by challenges in terms of quality, for instance with the need to provide a reliable account of the heating to be expected, prevent the occurrence of overheating leading to burns and fires, and ensure the long-term performance when exposed to use conditions such as abrasion and laundering. Standard test methods are a key component to solve these issues of efficiency, safety, and durability. Yet, they mostly remain to be established. In this research, a test method was developed for the characterization of the Joule heating efficiency of electric textiles. It involves measuring the temperature of a heating textile using a thermocouple affixed to its surface while it is powered for an hour. The value of the surface temperature that would ultimately be reached by the heating textile after an infinite heating time and the time for the temperature to enter a slow increase regime are determined by fitting an equation to the temperature-time data. These two parameters provide a quantitative mean of comparison between different heating textiles/conditions. This test method was used to analyze the effect of different experimental conditions on the heating efficiency of four heaters corresponding to different technologies of Joule heating textiles and make recommendations in terms of conditions for a standardized test protocol. These results give some insights towards the development of a robust and universal test method for the quantitative assessment of the Joule heating efficiency of electrical textiles that will ultimately be proposed for standardization to help support the growth of the e-textile industry.


Introduction
Joule heating is also known as Ohmic or resistive heating. It is based on Ohm's law and involves the generation of heat by applying a voltage between two points on an electric conductor (Harlin and Ferenets 2006). The loss of power (P) corresponding to the heat being generated depends on the current and electric resistance of the conductor; it is given by P = I 2 R. Conductive materials used in Joule heating systems include metals/metal alloys, carbonaceous materials, and conductive polymers. When embedded into a fabric structure, the resistance of the resulting circuit component depends on the linear resistance of the conductive yarns or tracks (Bahadir and Sahin 2018).
Joule heating textiles are currently used for a variety of applications including car seats, de-icing blankets, winter boots, wearable jackets, and therapeutic heating pads (figure 1) Sahin 2018, Lederer et al 2019). The inherent flexibility and diverse form factors of textile heating elements have contributed toward the large adoption of these smart textiles (Mbise et al 2015). However, the market growth for heating textile products is limited by challenges in terms of quality, including variation in response time and uniformity of surface heat distribution (Hao et al 2018, Xiao et al 2019. Standard test methods are a key component to solve these issues of efficiency, safety, and durability (Shuvo et al 2021). Yet, to our knowledge, only one standard test method for thermal applications of smart textiles has been published so far. CEN EN 16806-1 (2016) relates to products based on phase-change materials. Two other documents relative to phase change materials are also in preparation. Another document, IEC 63203-406-1 (2021), was recently published to characterize the surface temperature of wearable electronic devices worn on the wrist while in contact with the skin. However, no standard test method is available yet to assess the efficiency of products based on the Joule heating principle.
On the other hand, researchers have taken various approaches to characterize the efficiency of flexible Joule heaters. Table 1 provides an overview of these studies. A total of eight different parameters used by researchers to characterize the efficiency of Joule heating textiles have been identified: (i) the maximum steady-state temperature (T Max ), (ii) the response time (R90) (time to reach 90% of T Max ), (iii) the heat time constant (H TIME ) (time to reach 63.2% of T Max ), (iv) the cooling time, (v) the heat flux, (vi) the thermal stability, (vii) the uniformity of heating, and (viii) the average max min −1 temperature. However, many of these parameters, including T Max , are determined visually. This leads to a lack of precision in the value of T Max , as well as of the other parameters that are based on T Max such as R90 and H TIME . The problem is amplified by the fact that the heating curve does not reach a plateau but rather keeps on increasing at a slow pace.
To overcome these challenges, this study aims at providing a precise and reliable test method for the characterization of the efficiency of Joule heating textiles by modelling the heating-cooling curve.
The robustness of the model is validated by applying it to different technologies of Joule heating textiles. The test method is used to analyze the effect of the boundary conditions provided by the material in contact on each side of the heating textile, ambient temperature and relative humidity (RH), and ambient air flow velocity, on the heating efficiency.

Materials
The study involves four different types of heating textiles (figure 2). They were selected to cover different commercially available heating textile technologies. The first one (labelled C-heater) is a commercial product (Yinhing, China) composed of an embroidered serpentine pattern of carbon fibers sandwiched between two layers of polyester (PET) nonwoven fabrics (figure 2(A)). A second commercial product (labelled Si-heater) is manufactured by Signswise (China). A copper wire disposed in a serpentine pattern is embedded within a silicone rubber pad ( figure 2(B)). The two other heating textiles were produced by CTT Group (Quebec, Canada) using an electrically conductive nonwoven fabric composed of PET and silver-coated nylon fibers. The first conductive nonwoven-based heating textile model (labelled Ag-heater) comprised a piece of the conductive nonwoven with a copper Tinsel yarn electrode stitched at each end (figure 2(C)). For the second conductive nonwoven-based heating textile model (labelled polyurethane (PU)-heater), the conductive nonwoven fabric with the two electrodes is encapsulated by a PU film (figure 2(D)). The dimensions and resistance   For the tests, different boundary materials were used on the top and bottom sides of the heating textiles. The bottom boundary is the material on top of which the heater was laid on and the top boundary was the material used to cover the heater. For the bottom boundary conditions, four different materials were used to simulate the skin: (i) hydrogel pads (Tender Care Hydrogel, Medela, Canada), (ii) neoprene sheets used for the Surgery and Laparoscopy Torso simulator (neoprene skin, Erler Zimmer, Germany), (iii) flexible low density polyethylene (LDPE) sheets (McMaster Carr, USA), and (iv) a polyvinyl chloride pouch filled with water (PVC-H 2 O). These materials were covered with a thin silk liner to simulate the liner present in a heating jacket that would separate the heating textile from the skin. Some experiments also used a wooden board as the bottom boundary. Five different fabrics were used as top boundary conditions to simulate typical configurations in which heating textiles may be used: (i) cotton felt; (ii) PET felt; (iii) wool felt; (iv) texturized nylon knit fabric; and (v) nylon woven fabric. They were obtained from Testfabrics Inc. (USA).
Relevant characteristics of these different boundary materials are given in table S1 (in supplementary information). The thickness was measured using a C&R CS-55 thickness tester (Custom Scientific Instruments Inc., USA) according to the standard test method CAN/CGSB-4.2 No. 37-2002 at five different locations using a 1 kPa pressure. The measurement of the thermal conductivity was conducted at 21 • C and 65% RH under a pressure of 10.7 kPa using a modified transient plane source Instrument (TCi, C-Therm Technologies, Canada) according to the standard test method ASTM D7984-16.

Test protocol
During the experiment, the heating textile was sandwiched between different materials used as bottom and top boundaries. Two K-type thermocouples were positioned in the middle and at the periphery of the heating zone (figure 3(A)). They were affixed to the surface of the heating textiles, and were covered by the top boundary material when one was used for the test. The heating textile was powered for one hour and the temperature was recorded using the two thermocouples connected to a data acquisition system (DAQ, DATAQ Instruments, USA). The power was then turned off and the experiment was extended for 1 h or until the heating textile reached room temperature. The same DAQ system also continuously recorded the voltage and the current in the heating textile (figure 3(B)).
Depending on the case, the tests were conducted inside an environmental chamber (Lunaire Environmental, USA) at different conditions of temperature and RH as well as in a conditioning room at 20 • C and 65% RH. When the air circulation was on in the environmental chamber, the air velocity was 0.18 m s −1 . Experiments without air flow were also conducted with the environmental chamber: after the temperature and RH conditions had stabilized, the chamber was turned off and the test was initiated without opening the door of the chamber. Over the course of a 2 h test (1 h of heating and 1 h of cooling), the temperature would increase by 0.8 • C-0.9 • C and the RH drop from 65% to 50%. In the case of the conditioning room, a cardboard screen was installed around the heating textile assembly to avoid air drafts while making sure that heat could be evacuated from the top. Before the tests, the boundary materials were conditioned at 20 • C and 65% RH for at least 24 h.

Experimental design
During the study, the effect of a series of parameters was investigated: the ambient temperature and RH, the presence of air flow, and the heating textile top and boundary conditions. The heating behavior of the four different heating textiles was also compared. For this comparison, the power supplied to each heating textile was adjusted to generate a similar temperature increase upon heating.
The experiments are organized in seven categories (table 3). Category 1 tests looked at different heating textiles and different top boundary conditions in the environmental chamber at 20 • C and 65% RH in the presence of air flow. Category 2 tests measured the four heating textiles in the conditioning room with air as the top boundary condition. Category 3 tests compared different standard environmental conditions (temperature and humidity) with the C-heater. Category 4 tests investigated the effect of the environment temperature with the C-heater. Category 5 tests compared the effect of different top and bottom boundary conditions with the C-heater in the conditioning room at 20 • C and 65% RH. Category 6A tests looked at the effect of different top boundary conditions on the performance of the C-heater with the silk liner over the neoprene skin as the bottom boundary condition. Category 6B tests compared the effect of two top boundary conditions (air and PET felt) on the performance of the C-heater with the silk liner over the LDPE sheet as the bottom boundary condition in the conditioning room. Finally, Category 7 tests compared the effect of air and PET felt top boundary conditions on the performance of the C-heater in the environmental chamber without air flow. Table 3 also mentions the power applied to the heating textile during each test. Figure 4 shows the heating/cooling curve recorded with the middle thermocouple for each conditionin each of the seven test categories. In each case, the conditions at which the measurements were conducted are provided.

Results
For the Category 1 results, the PU-heater, Agheater, and C-heater displayed a similar shape of the heating and cooling temperature-time profile in a presence of a 0.18 m s −1 air flow when laying over a wooden board and without being covered (figure 4(i.A)). It is to be noted that, in order to achieve a similar level of heating (about 40 • C), the three heaters had to be powered at different levels: 18 W for Ag-heater (voltage: 8 V; current: 2.25 A), 8.8 W for PU-heater (voltage: 8.3 V; current: 1.06 A), and 1.6 W for C-heater (voltage: 5 V; current: 0.32 A). Therefore, about half of the power was needed to reach a similar level of heating in the conductive nonwoven fabric when it was encapsulated in the PU film compared to the bare nonwoven fabric. Figure 4(i.B) shows that a slightly lower temperature, by about 4 • C, was achieved when the C-heater was covered with a PET felt compared to the cotton and wool felt.
When the top boundary condition was still air (Category 2, figure 4(ii)), a much larger difference in the temperature reached at the end of the heating cycle was observed between the C-heater, Ag-heater, and PU-heater compared to the condition with air flow (figure 4(i.A)), even though they were supplied with the same power in both cases. After 1 h of heating, the Ag-heater reached 80 • C while the surface of the PU-heater was at around 60 • C and the C-heater levelled off at about 55 • C. The shapes of the heating curves also exhibit some differences between the four heaters shown in figure 4(ii), with the C-heater's temperature reaching a plateau after about 5 min while the Ag-and PU-heater was still increasing after 1 h. In the case of the Si-heater, the heating was much more gradual compared to the three other heating textiles. Differences in the cooling curves are also visible between the four heating textiles.
A comparison of the heating/cooling profile while the C-heater was covered with the PET felt in an environmental chamber at different values of temperature and RH corresponding to the ASTM D1776 standard conditions (21 • C, 65% RH) and ISO 139 standard conditions for the alternative atmosphere (23 • C, 50% RH) showed no effect either on the shape of  the curves or on the heating produced (Category 3, figure 4(iii)). When the temperature of the environmental chamber was varied between 10 • C and 30 • C while keeping all the other parameters the same (including the use of C-heater, PET felt as top boundary, 65%RH, and air flow of 0.18 m s −1 ), an increase in the temperature reached after 1 h of heating was obtained (Category 4, figure 4(iv)). However, the heating and cooling rates remained similar.  Figure 4(v.A) (Category 5) shows the difference produced in the heating and cooling curves when the C-heater was covered by felts with different fiber content while in still air. Wool felt produced the lowest heating, then PET felt, and finally cotton felt. Figure 4(v.B) (Category 5) compares the heating and cooling produced with the C-heater covered with PET felt in still air while different materials were used as the bottom boundary condition. A thin liner was positioned between the heating textile and the boundary condition material. With the exception of the water-containing pouch, the different bottom liner materials produced similar shapes of the heating/cooling curve, with the temperature still slowly increasing after 1 h. However, the temperatures reached after one hour of heating were all different: the neoprene skin led to the highest temperature and the LDPE to the lowest. On the other hand, with the water-containing pouch, the temperature stabilized after a few minutes of heating.
Category 6A tests (figure 4(vi.A)) compared the effect of different top boundary materials on the performance of the C-heater in still air with the silk liner over the neoprene skin as the bottom boundary condition. The PET, cotton and wool felt led to similar heating performance of the C-heater while the nylon knitted and woven fabrics were associated with a lower heating produced by the C-heater. Figure 4(vi.B) shows the results of the Category 6B tests, which compared the effect of air and PET felt as top boundary conditions on the performance of the C-heater in still air with the silk liner over the LDPE sheet as the bottom boundary condition. The temperature stabilized rapidly when the C-heater was left uncovered (i.e. with air as the top boundary condition) both during the heating and cooling cycles while, with the PET felt top layer, the surface temperature of the C-heater kept on increasing during the heating cycle and decreased more gradually during the cooling cycle.
Finally, Category 7 tests (figure 4(vii)) compared the effect of air and PET felt top boundary conditions on the performance of the C-heater in the environmental chamber without air flow. A similar trend as the result of the Category 6B tests is observed, with a more rapid stabilization of the temperature for the uncovered C-heater compared to the C-heater covered with the PET felt.
To assess the reproducibility of the results, the experiment in which the C-heater was laid over the wooden board and covered with the PET felt in still air was performed three times. Between each replication, the thermocouples were removed so that the assessment included the variability in their positioning on the heater surface relative to the location of the carbon fiber's serpentine pattern. The heating and cooling curves for the three replicate measurements are shown in figure 5 for both thermocouples (in the middle and at the periphery of the heating textile). For the middle thermocouple, the curves for the three replications perfectly superimposed. On the other hand, for the thermocouple located close to the power electrodes, a difference of up to 5.85 • C is observed between the different replications after 1 h of heating. A comparison of the curves corresponding to the two thermocouples in figure 5 also shows that the temperature in the middle of the heating textile after one hour of heating is lower compared to the edges, i.e. closer to the power electrodes. The same behavior was observed for all four heating textiles.
In order to allow a quantitative comparison of the heating behaviors observed under the different conditions tested, the heating curves were fitted using the following equation: where, x is the time (s); y is the temperature of the heating textile ( • C); a is a constant with the unit of a temperature; and b and c are constants with the unit of time. Figures 6(A) and (B) display an example of fitting of a heating curve recorded for the C-heater. A good agreement between the measurement and the fitting can be observed. Similar values of R 2 were obtained for the other conditions and the other heating textiles, indicating the robustness of the fitting equation to describe the heating behavior of the heating textile.
In equation (1), constant a corresponds to the asymptote of the heating curve, i.e. the ultimate temperature (UT) of the heater. The time to reach the set temperature can be assessed by computing the second derivative of the fitting curve to determine the inflexion point (IP) corresponding to the transition between the rapid heating phase and the slow increase (figures 6(C) and (D)). It is given by equation (2). The details of the calculations are presented in SN1 (supplementary information), In the case of the data shown on figure 6(A), the calculation of the IP gave x = 88.8 s. The values of the IP and UT corresponding to the different conditions in each category of experiments for both thermocouples are provided in table S2 (supplementary information).

Assessment of the precision in the determination of the heating textile UT and time to stabilization
Some of the heating textiles are manufactured using discrete conductive materials such as serpentine patterns of carbon fibers for the C-heater and copper wire for the Si-heater. In this case, a small variation in the positioning of the thermocouple on the heater surface may greatly affect the result of the temperature measurement as the distance between the thermocouple and the source of heat would be different. Figure 7 shows the values of UT and IP for the three replications of the measurements using the middle and peripheral thermocouples for the C-heater inside the conditioning room with the wood board as bottom layer and PET felt as top layer (corresponding to the heating and cooling curves in figure 5). The mean UT value is 64.1 ± 0.7 • C for the middle  thermocouple and 75 ± 3 • C for the peripheral thermocouple. The variability is lower than 5%, which indicates that, even for heating textiles with discrete conductive materials, a good repeatability in the positioning of the thermocouple on the heating textiles can be obtained, leading to a good precision in the determination of UT with point thermocouples. On the other hand, the variability in the determination of IP is much higher for both thermocouples, with 21% for the middle thermocouple and 30% for the peripheral thermocouple.

Effect of the environmental conditions on the heater performance
Tests were conducted using the C-heater in two series of standard environmental conditions: 21 • C-65% RH corresponding to the ASTM D1776 standard for general textiles and 23 • C-50% RH specified as the alternative atmosphere in ISO 139. The other conditions were kept the same: 1.3 W applied power, wood board as bottom layer, PET felt as top layer, and air flow of 0.18 m s −1 . Figure 8(A) shows the UT and IP values for the middle thermocouple. The UT values are similar when the ASTM D1776 or the ISO 139 conditions are used. On the other hand, the IP values show a difference of 15% between the two series of conditions. However, as this difference is lower than the variability of up to 30% recorded during the replication study, it is not possible to conclude on the effect of differences in the standard conditions on the stabilization time of the heating textiles.
A systematic study of the effect of temperature on UT and IP values was carried out with the C-heater. The temperature in the environmental chamber was varied between 10 • C and 30 • C while the other conditions were kept the same: 1.3 W applied power, wood board as bottom layer, PET felt as top layer, RH of 65%, and air flow of 0.18 m s −1 . The values are displayed in figure 8(B). Both the IP and UT values appear to display an increasing trend. The effect on UT can be attributed in the lower ability for the heating textile to dissipate heat due to the higher ambient temperature. The effect of the temperature on IP may eventually be a result of the increased UT.

Effect of air flow on the heater performance
The effect of air flow on IP and UT values can be deduced from tests performed with the C-heater in the environmental chamber with and without air flow and in the conditioning room. Figures 9(A) and (B)  show the IP and UT values extracted from the middle thermocouple data when air and PET felt were used as the top boundary, respectively. The other conditions were 20 • C and 65% RH with the wood board as the bottom boundary.
When the C-heater was left uncovered (figure 9(A)), the presence of air flow in the environmental chamber led to a 15% reduction in the UT value by comparison with the values provided with the environmental chamber without air flow. The UT value of 56.7 • C measured in the conditioning room was slightly higher compared to the value of 50.2 • C in the environmental chamber without air flow. This could eventually be attributed to the use of a cardboard screen around the heating textile to limit the influence of occasional air drafts in the conditioning room. This cardboard screen may have restricted the dissipation of heat from the heating textile, and thus caused a slightly higher temperature at the surface of the heating textile. The heating textile stabilization is observed to take the same time in the environmental chamber with air flow and in the conditioning room, and be longer in the environmental chamber without air flow.
When the C-heater was covered by a layer of PET felt ( figure 9(B)), the UT values increased because the PET felt restricted the transfer of heat between the heating textile and the ambient air. On the other hand, even if the lowest UT value was still observed for the measurement performed in the environmental chamber with air flow, the difference between the UT values corresponding to the different air flow conditions strongly decreased compared to the uncovered heater case as the PET layer limited the ability of the air flow to increase the heat transfer from the heating textile. The IP values also increased when the Cheater was covered with a layer of PET felt. However, in this case, the difference between the different airflow conditions increased compared to the uncovered situation.   Figure 10 shows a comparison of the values of UT and IP when air and different felt materials were used as the top boundary materials, both with and without air flow. The results were obtained with the C-heater using the middle thermocouple at 20 • C and 65% RH, using the wood board as the bottom boundary.

Effect of the top boundary material on the heater performance
Both with and without air flow, a large difference in the UT value can be observed when air is the top boundary condition and when one of the PET, cotton and wool felt is covering the heating textile. This observation can be directly related to the barrier created by the felt materials, which prevent the proper evacuation of heat from the heating material to the ambient air. A strong increase in the IP value is also observed between the air and felt boundary conditions. On the other hand, the UT values are quite similar for the different felt materials. This may be attributed to the fact that they have quite similar values of thermal conductivity (table S1, in supplementary information).
In figure 11, a nylon knitted fabric and a nylon woven fabric are compared with the PET, cotton and wool felts as top boundary materials. In this series of experiments, the heating textile is still the C-heater but the bottom boundary condition is made of a neoprene skin and a silk liner on top of the usual wooden board. The measurements were made in the conditioning room at 20 • C and 65% RH. The UT values are similar for the three felt materials. On the other hand, the UT values are about 20% lower with the nylon knit and woven fabrics. This result can be attributed to their higher value of thermal conductivity, almost double that of the felts (table S1, in supplementary information). These fabrics are also much thinner and their open structure may allow heat to better circulate by convection between the heating textile and the ambient air. Lower IP values were also obtained for the nylon knit and woven fabrics.

Effect of the bottom boundary material on the heater performance
The effect of the bottom boundary material was studied with the C-heater using the PET felt as the top boundary. The measurement was made in the conditioning room at 20 • C and 65% RH. Figure 12 shows the results in terms of measured UT and IP when the bottom boundary was the wooden board (wood in figure 12), the wooden board covered with a silk liner (liner in figure 12), the wooden board covered with an hydrogel pad and the silk liner (hydrogel in figure 12), the wooden board covered with a neoprene sheet and the silk liner (neoprene in figure 12), the wooden board covered with a LDPE sheet and the silk liner (LDPE in figure 12), and the wooden board covered with a PVC pouch filled with water and the silk liner (H 2 O in figure 12).
Despite the very large range of thermal conductivity values of the different materials used, ranging from 0.05 W m −1 K for the neoprene sheet to 0.5 W m −1 K for the hydrogel pads (table S1, in supplementary information) to 0.6 W m −1 K for the water contained in the PVC pouch, the UT values only showed a limited variation, without any obvious relation with the thermal conductivity values. This may have been due to the presence of the solid wooden board, and the laboratory countertop beneath it, preventing any evacuation of the heat on that side of the heating textile. On the other hand, the IP values displayed a large difference between the water-filled pouch and the rest of the materials. Since the values of thermal conductivity of the hydrogel pads are close to that of water, the much shorter time to stabilization with the waterfilled PVC pouch, which had been recorded both for the heating and cooling phase (figure 4, Cat 5.B), can possibly be attributed to the efficient transfer of heat away from the surface of the heating textile by convection by the water contained in the pouch. However, this more efficient heat transfer by the waterfilled PVC pouch did not translate into a reduction in the UT as the heat could not be evacuated further away due to the presence of the wooden board below the water-filled PVC pouch.

Comparison between the different heaters
To compare the heating behavior of the different heating textiles, the supplied power was adjusted to produce a similar UT. Figures 13(A) and (B) show the results for the condition with and without air flow, respectively. The rest of the conditions were the same, i.e. 20 • C, 65% RH, air as top boundary, and wooden board as bottom boundary. The value of the power density for each heater is mentioned in the figure.
A first observation regards the power needed for heating the different heaters. While it took 947.4 W m −2 to reach a UT of 41 • C with the conductive non-woven Ag-heater in the environmental chamber with air flow (figure 13(A)), 23% less power density was necessary to achieve the same UT with the PU-heater, which is made of the same conductive non-woven but has an additional PU encapsulation. This result can be attributed to the presence of the PU encapsulation, which prevents the rapid dissipation of heat in the ambient air. When the same respective values of powder densities were used to power the Ag-and PU-heater in still air ( figure 13(B)), the UT reached by the Ag-heater was slightly higher than the UT reached by the PU-heater; in this case, the PU layer had a more limited effect in reducing the heat loss from the surface of the heating textile.
The most efficient heating was obtained with the C-heater, with only 228.6 W m −2 consumed to produce a similar UT as the two non-woven-based heaters (figure 13(A)). A much shorter time to stabilization IP was also observed for the C-heater compared to the Ag-and PU-heater. However, this may be due to the fact that, in the case of the C-heater, the thermocouple was positioned directly above the heating carbon fiber yarn ( figure 5(C)). The result may have been different if the thermocouple was positioned in the space between two segments of the heating serpentine.
Finally, for the silicone heater, which is made with a copper wire serpentine embedded in a silicone rubber pad, the power density needed to achieve the same UT as the C-heater was about 3.5 times higher ( figure 13(B)). The IP was almost 15 times longer too. This may be attributed to the presence of the silicone rubber, which provided a thick thermal insulation layer between the heating copper wire and the thermocouple.

Proposed test protocol for the characterization of the Joule heating efficiency of electric textiles
Based on the results of the analysis of the effect of the different boundary conditions on the measurement of the heating efficiency of the four different heating textiles investigated in this study, some recommendations can be made toward the development of a standardized test protocol for the characterization of the Joule heating efficiency of electric textiles.
In terms of the environmental conditions, the measurements were found to be sensitive to a variation in the ambient air temperature. However, no difference in UT was measured between the two standard conditions corresponding to 21 • C-65% RH (ASTM D1776 standard for general textiles) and 23 • C-50% RH (alternative atmosphere in ISO 139). In addition, a linear fit of the variation of the UT with temperature ( figure 8(B)) gave a slope of 1.145 • C • C −1 . It is thus recommended to specify a temperature of 21 ± 2 • C for the conditioning of the specimens and the test, which would cover the standard conditions in different jurisdictions and would lead to a variability in the UT that is with the measurement variability recorded with the peripheral thermocouple. In terms of the RH, no effect on the UT has been recorded between the two standard atmospheres tested. A value of 57.5 ± 7.5% RH could be recommended, which covers the standard conditions in different jurisdictions.
Regarding the boundary conditions, the recommendation is to specify a reference PET felt as a material for the top boundary as it was shown to limit the effect of air flow on the measurements and would be less sensitive to the influence of differences in RH in the environment compared to cotton, wool or nylon. In addition, due to the heating textile being covered by a PET felt during the test, the use of a screen aimed at preventing the effect of air drafts in the conditioning room can be avoided, which is an advantage as it was shown to hinder the proper evacuation of heat from the heating textile. In terms of the bottom boundary, a wooden board is recommended to provide a standardized material.
In terms of the test protocol itself, the use of a point thermocouple was observed to provide repeatable results as long as care is taken in positioning the thermocouple at the same location on the heater surface each time in the case of heating textiles involving discrete conductive materials. However, it may be noted that, in the case of these non-homogeneous heating textiles, the selection of the location of the thermocouple relative to the heating element will affect the result of the UT measurement. Finally, a 1 h duration for the heating period combined with the fitting model allowed extracting the UT from the data in a way that permits a quantitative comparison between different heating textile products.

Conclusion
In this research, a test method has been developed for the characterization of the efficiency of Joule heating textiles. It involves measuring the temperature of a heating textile using a thermocouple affixed to its surface while it is powered for an hour. The value of the temperature that would ultimately be reached by the heating textile after an infinite heating time as well as the time for the temperature to enter a slow increase regime are determined by fitting an equation to the temperature-time data. These two parameters provide a quantitative mean of comparison between different heating textiles/conditions. This test method with its associated fitting model was successfully used to measure the heating efficiency of four different textile heaters corresponding to different Joule heating technologies. It was also successfully used to analyze the effect of different experimental conditions on their heating efficiency. For instance, similar results were obtained when the measurements were performed at 21 • C and 65% RH, which corresponds to the ASTM D1776 standard for general textiles, and 23 • C and 50% RH, which is the alternative atmosphere in ISO 139. This indicates the robustness of the test method towards small variations in the environmental conditions. On the other hand, both the UT and the stabilization time increased when the ambient temperature was varied between 10 • C and 30 • C.
The presence of a 0.18 m s −1 air flow affected the heating efficiency results when the heating textile was left uncovered. On the other hand, covering it with a layer of felt limited the effect of the presence of air flow, which provides a strategy for decreasing the sensitivity of the measurements to the presence of air drafts in the testing area. Felts made of different types of fibers provided similar results as top boundary materials while the differences observed with a nylon knit and a nylon woven fabric used as the top boundary were attributed to the difference in their thermal conductivity, thickness, and openness of structure. In terms of the bottom boundary, no effect on the UT was observed for the series of materials that covered a wide range of thermal conductivity values. On the other hand, the use of a water-filled PVC pouch as the bottom boundary provided a much shorter time to stabilization, which was attributed to convective heat transport through the liquid.
These results give some insights toward the development of a robust and universal test method for the quantitative assessment of the Joule heating efficiency of electric textiles and allowed making recommendations in terms of the conditions for a standardized test protocol. They will contribute to the development of standardized quality control methods for heating textiles and help support the growth of the e-textile industry.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).