Research on the Heating of Woven Carbon Fiber Fabrics Using Thin-Film Solar Cells

An amorphous silicon thin-film solar cell was purchased from Dongguan Xinliangguang New Energy Technology Co., Ltd., with a voltage of 2 V, electrical current of 330 mA, and dimensions of 194×60 ×0.8 mm. 12k Teflon flame-retardant carbon fiber was purchased from Jiangsu Maisiyang Cable Co., Ltd., with a resistance of 0.33 Ω/cm. 2.5 mm copper wire was purchased from Guangdong Guide Wire and Cable Co., Ltd., with a resistivity of 0.001 Ω/cm. 100% cotton yarn was purchased from Fujian Minhou Huada Textile Co., Ltd., with a size of 15.2 tex×32. A GU101A sample loom was purchased from Jiangyin Longda Textile Machinery Co., Ltd, a VC890c multimeter from Shenzhen Shengli High Electronic Technology Co., Ltd., and an NTC (10K/3435) temperature sensor from Zhaoqing Sendor Electronic Technology Co., Ltd.

The heating fabric was formed on the GU101A sample loom. The fabric structure was plain, and the four-page heald was worn by the pass-through method. The warp yarn was a cotton thread. The warp density of the fabric was 64 ends/10 cm and the weft density 40 ends/10 cm. The weft yarn was a cotton thread and a heating carbon fiber line, and the number of the two kinds of lines woven was matched according to design requirements. The heating line weaving density was designed to be 3, 4, ... 10 and 11 ends/10 cm. For a blank control group, the fabric was not woven into the heating line fabric, and the weft yarn was not cut when it was woven to ensure a continuous heating line. Five samples of each fabric were prepared. Figure 1 shows the heating fabric, where the red yarns are heating carbon fiber lines, and the grey are cotton threads.

Fig. 1

The voltage across a series circuit is equal to the sum of the supply voltages. The total current of the parallel circuit is equal to the sum of the currents of the branches. Since the minimum current required for carbon fiber heating is 0.6 A, to increase the current, two solar panels must be connected in parallel. Then, the panels are connected in parallel to the required voltage, and the design voltages were 6, 8, 10, ..., 18 V, as shown in Figure 2.

Fig. 2

Solar radiation intensity can greatly vary throughout the day, and at sunrise, sunset, and on rainy days, solar cells cannot produce voltage. To test the heating effect of the heating fabric and reduce experimental error, tests were conducted between 11:00 and 13:00 on a sunny day in May 2020 in Fuzhou University Town. Due to the long span of the experiment, the study found that even at the same time on different days, the output current of the thin-film solar cells measured was different, and the current varied even at the same time on days before and after a rainy day.

The temperature change of the heating fabric was different under the same test conditions; however, to ensure accuracy, all experimental data from the same group were tested at noon on one day. Such an experimental treatment minimises the error and provides a reference value for future experimental research. The temperature sensor was placed in the middle of two heating wires and did not directly contact the heating wire. Figure 3 shows the experimental test. To ensure the accuracy of the temperature measurements of the heating fabric, a control group was used. The temperature increases at 5 different positions were selected for each test fabric, and the test results were reported as the average of 10 measurements.

Fig. 3

The density of the heating carbon fiber woven by the GU101A sample loom was 5 ends/10 cm, and the voltage of the thin-film solar cell was 12 V. The temperature of the heating fabric was tested as a function of time and recorded every 20 seconds. A graph of the temperature of the fabric versus time is shown in Figure 4. During the 420 s test, the temperature of the heating fabric increased. Figure 4 shows that the curve increased, but the slope decreased, i.e., the temperature of the fabric increased more slowly over time. After 420 s, the temperature did not increase any further and remained constant. Throughout the test, the fabric temperature increased by 5.3 °C, at an average rate of 0.8 °C per minute.

Fig. 4

According to Joule’s law (Q=Pt), the curve of the fabric temperature versus time in Figure 4 should increase linearly with time, but it changes regularly. Thin-film solar cells produce a current in sunlight, forming a loop. The heating line uses the Joule effect of current to convert electrical energy into heat, which increases the temperature of the heating fabric. Since the carbon fiber heating line has thermal resistance, it requires time to conduct heat in the fabric. Since the resistance R of the heating line gradually increased with the temperature, the heating efficiency P=U₂/R will decrease at a constant voltage, causing the heating rate to become smaller. When the carbon fiber line is heated, the heating line and the fabric will also transfer the heat it has generated to the air, causing heat dissipation, and the temperature will remain unchanged when the heating and heat dissipation are balanced.

The voltage of the thin-film solar cell is 12 V, and the curve of the temperature of the heating fabric at 480 s as a function of the heating carbon fiber density change is shown in Figure 5. When the heating line density in the latitudinal direction of the fabric increased from 3 ends/10 cm to 5 ends/10 cm, the fabric temperature sharply increased to 9.1 °C. When the density of the heating carbon fiber line increased from 5 ends/10 cm to 8 ends/10 cm, the temperature sharply decreased. However, when the density was greater than 8 ends/10 cm, the temperature increase was more gradual. When the density was 11 ends/10 cm, the temperature rise was only 4.4 °C. It can be predicted from the trend shown in Figure 5 that as the density of the heating carbon fiber line increases, the temperature increase will gradually plateau.

Fig. 5

A higher density of the heating carbon fiber line increased the length of the heating carbon fiber line in the circuit, which increased the resistance according to the resistance formula R=ρL/S. At a constant voltage U, the resistance R increased, and the current I became smaller. When the current I was small, the internal voltage of the power source was reduced, and when the loop voltage was constant, the external voltage of the power source increased. P=UI increases and decreases individually, but their product increases continuously, causing the heating power to increase. When the power reaches the maximum P_max, the resistance continues to increase, and the power will decrease. Due to the greater power, more heat is generated, and maximum power is generated. This corresponds to an optimal resistance, i.e., the heating line density is 5 ends/10 cm. As the carbon fiber heating line density continued to increase, the resistance increased, and the cell voltage remained at 12 V, causing the heating power to decrease. Theoretically, when the resistance tends to infinity, the heating power of the fabric will tend to 0; but considering the actual weaving process, the weft of the fabric is composed of the heating carbon fiber line, and the resistance is largest when they do not overlap. At this time, the heating line density is unlikely to be infinite but 10D {{10} \over D} ends/10 cm (D is the diameter of the heating carbon fiber line in cm), and hence the heating power of the fabric infinitely tends to a positive value.

When the density of the heating carbon fiber line was 5 ends/10 cm, the energisation time was 480 s, and the temperature of the heating fabric changed with the voltage to form the curve shown in Figure 6. As the voltage of the thin-film solar cell increased, the temperature of the fabric also increased, but at an increasingly slower rate. When the voltage increased from 16 V to 18 V, the temperature increased by only 0.2 °C. According to the power formula P=U²/R, when the voltage of the thin-film solar cell increased continuously, the heating law of the fabric per unit time did not follow the curve of the quadratic function. The reason is that the resistance of the heating carbon fiber line increased with the temperature, which slowed the heating power increase rate. Increasing the voltage can significantly increase the power to rapidly heat the fabric, but this also requires more thin-film solar panels. This will lead to a cumbersome and uneconomical heating system, which is not conducive to the practical application of heating fabrics.

Fig. 6

According to the conclusion of the single-factor experiments, the voltages of three kinds of thin-film solar cells were selected as 10 V, 12 V, and 14 V; three time periods : 240 s, 360 s, and 480 s; and three kinds of heating line densities : 4 ends/10 cm, 5 ends/10 cm, and 6 ends/10 cm. Regardless of the interaction between the factors, L₉3⁴ is the smallest orthogonal table that satisfies the condition. The design header is shown in Table 1, and the experimental scheme and results in Table 2.

The first number corresponding to the row of K₁ indicates the sum of the index values corresponding to factor 1 at the level of 1, and is recorded as K₁₁. The first number in the subscript is the horizontal number, and the second number represents the factor. The first number corresponds to the row of K_1(一) is K_11(一), K_11(一)=K₁₁/3, and so on; the range R_j = max{K_ji(一)}-min{K_ji(一)}, where K_ji(一) is the average value of the index of factor i at level j.

For factor 1 (voltage), K_31(三)＞K_21(二) ＞K_11(一), thus a voltage of 14 V was the best level; for factor 2 (time), K_32(三)＞K_22(二)＞K_12(一), the optimal time was 480 s; for factor 3 (heating line density), K_24(二)＞K_34(三)＞K_14(一), thus the density of 5 ends/10 cm was the best level. It can be seen from the extremely poor result R₂>R₁>R₃ that time is the most influential factor among all parameters, followed by voltage, and then heating line density. Therefore, the comprehensive analysis shows that the best combination of the fabric heating process is A₃ B₃ C₂, that is, a voltage of 14 V, a time of 480 s, and a heating line density of 5 ends/10 cm. It was experimentally verified that under the optimal heating conditions, the maximum temperature increase of the heating fabric was 7.9 °C, which demonstrates the accuracy of the optimal heating process.

The variance test for the orthogonal table is shown in Table 4. After calculation and analysis, it was found that the influence of each factor on the experiment is significant.