Investigation of the Thermal Transfer Behavior of Single Layer Woven Fabrics at Different Temperatures Xiaoxia Liu, Tingting Wang, Mingyu Zhuang, Binjie Xin, Wei Liu Shanghai University of Engineering Science, Shanghai CHINA Correspondence to: Xiaoxia Liu email: liuxiaoxialucky@126.com ABSTRACT The thermal conductivity of several high performance woven fabrics at temperatures ranging from -50 to 200 was measured using the hot wire method to explore the relationship between the thermal conductivity and temperature. Data regression of the least squares was used to obtain curves of the thermal conductivity of various fabrics vs. temperature. Results show that the thermal transfer process in woven fabrics is mainly thermal conduction consisting of phonon and molecular conduction. Thermal conductivity as a function of temperature varies as temperature range changes, and is significantly affected by fiber type. Keywords: thermal conductivity, high temperature, high-performance fabrics, thermal transfer mechanism. INTRODUCTION High performance fibers are widely used in various industries including aerospace, metallurgy, petrochemical, transportation, firefighting and sports, due to their excellent mechanical properties, high temperature resistance and other characteristics. The main applications of high performance fibers are technical fields which demand excellent heat resistance and mechanical properties. In addition, good insulation properties are also required in some special cases, such as heat shield used in the spacecraft re-entry, fire protection apparel, high performance inorganic fiber lining used in the metallurgical industry, and insulating material used in the transportation and storage of liquid nitrogen and liquid oxygen. Consideration of fabrics for these applications requires investigation and characterization of the insulation properties at high and low temperatures. Thermal conductivity is the key factor influencing the insulation properties of materials. The thermal conductivity of fabric is not only related to its composition, structure, moisture and other factors, but is also a function of the ambient temperature. As the temperature increases, different types of fabric show different rates of thermal conductivity. Currently, the thermal conductivity tests are usually carried out at room temperature. Few studies concerning thermal conductivity testing of of fabrics at low and high temperature have been reported. Lin et al. [1] simulated the temperature-rise period of the ZrO2 fiber laminate and predicted its effective thermal conductivity by using finite difference numerical simulation methods. Gallego et al. [2] documented thermal conductivity changes as a function temperature for various types of carbon fibers. Hofmann [3] studied the thermal conductivity of insulation material at low temperature as well as the effect of the temperature on thermal conductivity. However, the mechanism of heat transfer has not been clearly explained. Moreover, the trend of thermal conductivity tested using the hot wire method at temperatures ranging from -50 to 200 has not been reported. In order develop a better understanding of the practical performance of a given fabric, it is necessary to understand how the fabric conducts heat over a wide range of temperatures. This study addresses that concept. EXPERIMENTAL Samples Plain woven fabrics consisting of aramid fiber, glass fiber (Figure 1), basalt fiber and carbon fiber were cut into 5 4 cm size. The fabrics were placed between two blocks of borosilicate glasses and a 500g weight for testing as shown in Figure 2. The experiments were conducted in a laboratory which remained at 20 temperature and65% humidity. Journal of Engineered Fibers and Fabrics 9 http://www.jeffjournal.org
FIGURE 1. Sample of glass fabric. FIGURE 2. Photograph of the experimental setup. Hot Wire Method The thermal conductivity of the four types of fabric was measured using a transient hot wire instrument (TC3000, Xi an Xiatech Electronic Technology Co., Ltd, China). Thermal conductivity of the fabrics was measured at the following temperatures: -50,-25, 0, 50, 100, 150, and 200. Fabric samples were placed on each side of the sensor and stabilized between the two blocks of borosilicate glass. The 500g placed on top to insure close contact between the samples and sensor as shown in Figure 2. A software program was used to control the temperature. Thermal conductivity was measured when stable temperatures were the fabric samples were tested at five minute intervals and five tests were conducted at each temperature. Thermal conductivity values reported are the averages of the five data points. In recent years, the hot wire method has been used to measure the thermal conductivity and the thermal diffusivity of non-conductive in unsteady states. The hot wire method is the only international standard method used to measure the thermal conductivity at elevated temperatures [4]. This method can measure not only the thermal conductivity of fabric but also thermal diffusivity, heat capacity and other indices. In the hot wire testing method, it is assumed that there is an ideal infinitely thin and long linear heat source (hotline) in the solid medium. The temperature of the hotline itself as well as the ambient temperature will rise under the influence of the hotline. The heating rate of the hotline depends on the thermal conductivity of the surrounding medium. The higher the thermal conductivity the fabric being tested, the faster results the heat generated is removed and smaller the temperature rise of the hotline. Thus, the thermal conductivity of fabrics be obtained by measuring the heating rate of the hotline [5]. THERMAL TRANSFER MECHANISM OF WOVEN FABRICS At the microscopic level, the mechanism of the thermal conductivity of different materials is different. For metals, free electrons are the main mechanism of thermal transfer. The thermal transfer within crystals mainly depends on vibrations of phonons within the lattice. The thermal transfer mechanism for non-crystalline materials is the thermal vibration around a point for molecules and atoms disorderly arranged, and subsequent transfer of energy to adjacent molecules or atoms. Because non-crystalline materials can be considered as extremely fine crystals, the thermal transfer mechanism can be described through phonons. For some transparent and translucent solids, electromagnetic wave spectra with high frequency can be generated; this is known as photon transmission. In gases, thermal transfer occurs through the collision between gas molecules; this is known as molecular thermal conductivity [6]. The fabrics in this study are translucent materials consisting of air and fibers, so thermal transfer within woven fabrics will occur mainly through molecules, phonons and photons. Journal of Engineered Fibers and Fabrics 10 http://www.jeffjournal.org
Fabric is porous material with lots of tiny voids. The thermal transfer process includes thermal conduction, thermal convection, thermal radiation and latent thermal transfer accompanied by water vapor transmission [7]. Data [8, 9] indicates that when the temperature of porous material is less than 300 the influence of radiation can be neglected. When external pressure is lower than 10 5 N/m 2 and temperature is less than 1000K, with the porosity of material below 0.95 and the thickness below 5cm, thermal convection inside porous material can be ignored [10,11]. With a stable heat source and a low heat flow rate, sample temperature increases slowly by the hotline method. Therefore, the influences of heat convection and heat radiation are reduced. This method excludes heat transfer as a result of non-heat conduction caused by other non-steady-state test methods which can send strong or transient pulses of thermal disturbance. Thus, it is a preferable pure process of heat conduction. In addition, the test time is very short. This can reduce errors caused by the evaporation of water or natural convection of air during testing. In this paper, only the influence of thermal conduction on the thermal conductivity is considered. This includes thermal conduction between fibers, air as well as fiber and air. Since the yarn twist is very low, it can be assumed that fibers arrange closely in a hexagonal area as cylinder in the yarn. The porosity of the yarn is considered to be uniform as shown in Figure 3. Based on the principle of the hot wire method, it is assumed that heating flow is transferred along the fabric thickness direction. Besides, the hotline stays parallel with warp yarns. The diameter of hotline is much lower than that of yarn and the length of hotline is larger than the length of a single cell of the fabric (Figure 4, Figure 5). FIGURE 3. Diagram of the yarn structure. FIGURE 4. Diagram of the hot wire method. FIGURE 5. Principle diagram of the hot wire method. When the hotline is placed in the yarn, it can be regarded as parallel with a proportion of air and fiber. The thermal conductivity k e of yarn is [12]: ( f ) k f k e f1k a + 1 1 = (1) When the hotline is laid in between two yarns, the contacting area is composed a combination of yarns air. It can be considered that the thermal channel is the interphase between air and fiber. According to the harmonic mean method, the thermal conductivity k e ' can be calculated as follows: k = e f k 1 2 1 + e f k a 2 (2) Where, ka and k f are the thermal conductivity of air and fiber respectively, f 1 is the ratio of air in the yarn, f 2 is the porosity of fabric. In this case, it is assumed that the fibers are arranged closely, thus f 1 =0. Therefore, Eq. (1) and (2) can be simplified as: k = k (3) e f Journal of Engineered Fibers and Fabrics 11 http://www.jeffjournal.org
k = e f k k a f 2ka + ( 1 f 2 ) k f (4) From Eq. (3) and Eq. (4), the thermal conductivity of fabrics changes with thermal the conductivity of the fibers. The thermal conductivity is closely related to the thermal conductivity of fiber and air. EXPERIMEMTAL DATA AND PROCESSING The thermal conductivity of fabrics in the high and low temperatures was tested in separate test chambers, so the position of the hotline in the fabric changed during the two ranges of temperature testing. Experimental data shows that varying the position results in 5 to 10 percent variation in the data. In order to improve the accuracy of the analysis, results obtained from the high temperature testing and low temperature testing were handled separately. In an attempt to clarify the relationship between the thermal conductivity and the environmental temperature, the data from high temperature tests were processed by the least squares method. Fitting curves of thermal conductivity of various fabrics as a function of temperature were obtained. Considering that the thermal transfer process of fabric may include any combination of thermal conduction, thermal convection, the data was fitted to a one-dimensional linear regression equation, power function and exponential regression equation. The curve of one-dimensional linear regression equation is close to the curve of exponential regression equation. However, the correlation coefficient of one-dimensional linear regression equation is greater, which can reflect the variation of the data better. Therefore, the curves of one-dimensional linear regression equation (linear) and power function regression equation (dotted line) are shown in Figure 6. Figure 6(1) shows the relationship between the thermal conductivity of aramid fabric and the temperature. The regression equation and correlation coefficient r of two curves are given. (a)one-dimensional linear regression equation (linear):λ=0.1234+0.0001t,r=0.9925;(b)power function regression equation (dotted line) λ=0.0843 T 0.1092,r=0.9908;Figure 6(2) shows the relationship between the thermal conductivity of glass fabric and the temperature. The regression equation and correlation coefficient r of two curves are given. (a)one-dimensional linear regression equation(linear):λ=0.1321+0.00008t,r=0.9665; (b) power function regression equation ( dotted line):λ=0.1056 T 0.629,r=0.9948;Figure 6(3) shows the relationship between the thermal conductivity of basalt fabric and the temperature. The regression equation and correlation coefficient r of two curves are given. (a)one-dimensional linear regression equation(linear): λ=0.1153+0.00007t,r=0.9723: (b) power function regression equation ( dotted line):λ=0.0919 T 0.064,r=0.9965;Figure 6(4) shows the relationship between the thermal conductivity of carbon fabric and the temperature. The regression equation and correlation coefficient r of two curves are given. (a)one-dimensional linear regression equation(linear):λ=0.1521+0.0001t,r=0.9511; (b) power function regression equation(dotted line): λ=0.1179 T 0.0714,r=0.9897; The thermal conductivities of four fabrics as a function of elevated temperatures are compared in Figure 7. The thermal conductivities of fabrics at low temperatures are set forth in Table I. Journal of Engineered Fibers and Fabrics 12 http://www.jeffjournal.org
(1) Thermal conductivity of aramid fabric vs. temperature. FIGURE 7. Comparison among four kinds of fabrics at high temperature. TABLE I. Thermal conductivity of fabrics at low temperature. Thermal conductivity (W/m K) Temperature( ) Aramid fabric Glass fabric Basalt fabric Carbon fabric 0 0.0995 0.1222 0.1288 0.1532-25 0.0946 0.1203 0.1229 0.1468-50 0.0969 0.1192 0.1124 0.1148 (2) Thermal conductivity of glass fabric vs. temperature. (3) Thermal conductivity of basalt fabric vs. temperature. (4) Thermal conductivity of carbon fabric vs. temperature. FIGURE 6. Thermal conductivity of four kinds of fabrics vs. temperature. RESULTS AND DISCUSSION The thermal conductivities of four fabrics as a function of elevated temperatures are compared in Figure 7. The thermal conductivities of fabrics at low temperatures are set forth in Table I. From the experimental data, the error rates of five tests for each fabric at each temperature are within ±2% at the same position. Influence of Temperature on Thermal Conductivity The thermal conductivity of fabric varies with the temperature change (Figure 6). The thermal conductivities all four types of fabric increase as a function of temperature. From a micro perspective, most of fibers consist of both crystalline and non-crystalline regions. The mean free path of a phonon depends on the scattering caused by collisions among phonons and interactions between phonon and the boundary of crystal, lattice defects and impurities. It is also the main factor that affects the thermal transfer of phonon. Due to the phonon scattering, the mean free path of a phonon is much smaller than its theoretical value. As crystal defects increase in the fiber, the non-harmonic vibration grows drastically and phonon scattering grows powerful. In different fibers, phonons with different frequency or wavelength will scatter to varying degrees since they will have different phonon mean free paths. Therefore fabrics consisting of different fiber materials will vary in thermal conductivity. Journal of Engineered Fibers and Fabrics 13 http://www.jeffjournal.org
Furthermore, temperature affects the integrity and non-harmonic vibration of crystals. Increasing temperature (T< Debye temperature) can accelerate the phonon vibration and enhance the interaction between phonons, leading to a decrease in the mean free path. Thus, the thermal conductivity of fiber increases [13]. According to the ideal gas molecule motion theory, when temperature rises, molecular energy grows and more heat is transferred between molecules. The change of the thermal conductivity in the gas phase is always less than the change in the solid phase. In summary, the thermal conductivity of most non-metallic fabric rises as the temperature increases. Influence of High Temperature (50 ~200 ) on Thermal Conductivity of Woven Fabrics As shown in Figure 6(1), one-dimensional linear regression equation can be used to describe the trend of the thermal conductivity of aramid fabric as a function of temperature as opposed to power function based equations. In other words, the thermal conductivity of aramid fabric rises linearly with increasing temperature. This is because the aramid fiber consists of high molecular polymer chains with high degree of orientation, crystallinity and molecular symmetry. With the higher crystallinity, less lattice defects and impurities are present in the crystal. So the scattering caused by collisions among phonons and interaction between phonon and the boundary of crystal, lattice defects and impurities can be ignored. Accordingly, scattering caused by collision between phonons is the major factor affecting thermal resistance. The literature [14] suggests that if the inelastic scattering of phonons is the only factor to generate thermal resistance, the thermal conductivity should be proportional to temperature. Separate from aramid fabric, the power function regression equation is more suitable for describing the thermal conductivity of the glass, basalt and carbon fabrics as a function of temperature. Thus, at temperatures between 50 and 200, the thermal conductivity of the three types of fabrics increase non-linearly as the temperature rises. This is because that basalt and glass are amorphous materials and carbon is polycrystalline graphite structure. The amorphous area inside these fibers is much larger than that in other polymeric fibers. In the thermal conduction process, scattering resulted from not only collision between phonons but also interaction between phonons and a large number of defects, impurities and crystal boundaries [15]. The mean free path in non-crystalline regions is much smaller than that in crystalline regions at most temperatures. As the temperature rises, molecular conduction plays an important role in thermal conduction. Meanwhile, with increasing temperature, the collision and vibration of phonons increased, leading to the lattice defects. Therefore, the scattering caused by interaction between phonons, crystal boundaries and lattice defects increases and the non-harmonic vibration of phonon increases. Tus, the thermal conductivity of the three fabrics from lower crystallinity fibers shows non-linear variation as a function of temperature. Influence of Low Temperature (0 ~-50 ) on Thermal Conductivity of Woven Fabrics From 0 to -50, the thermal conductivity of the glass, basalt and carbon fabrics decreases as temperature drops (Table I). Thermal conductivity of aramid fabric declines with decreasing temperature from 0 to -25, but increased by 2.4% between -25 and -50. The thermal conductivity of carbon fabric is still the highest of the four, and the thermal conductivity of aramid is smaller than basalt fabric, exhibiting excellent insulation properties at low temperature. In addition, the rate of change in thermal conductivity of the four fabrics is different (Table II). The thermal conductivity of aramid and glass fabrics changes slowly from 0 to -50 (2.61 and 2.45% respectively). The rate of change of the thermal conductivity of the basalt and carbon fabrics is much greater in this temperature range (12.73% and 25.97% respectively). TABLE II. Change rate of fabrics at different temperature ranges. Temperature( ) Change rate (%) Aramid fabric Glass fabric Basalt fabric Carbon fabric 200~150 1.6 1.29 1.09 0.59 150~100 6.31 2.48 3.14 3.47 100~50 6.16 4.67 4.22 5.18 0~-50 2.61 2.45 12.73 25.07 Journal of Engineered Fibers and Fabrics 14 http://www.jeffjournal.org
Thermal Conductivity of Four Kinds of Woven Fabrics As shown in Figure 7, carbon fabrics have the highest thermal conductivity among four types of fabrics while basalt fabric showed lowest thermal conductivity at temperatures ranging from 50 to 200. The thermal conductivity of aramid fabric is slightly below that of glass fabric in the range of 50 ~140. When the temperature is beyond 140, it becomes larger and the increase rate is also slightly larger. As the temperature increases, change rate of thermal conductivity of the 4 fabrics decreases in different temperature ranges and the thermal conductivity trends toward smooth. Carbon fabric is not suitable as an insulation material due to the high thermal conductivity. For aramid fabric, a lot of research on the factors affecting the thermal conductivity of polymer fiber has been reported. Because of viscoelasticity and differences in crystallinity, the mechanism of thermal conduction in polymeric materials is more complicated than that in metallic and ceramic material. Aramid is an excellent thermal insulator with low thermal conductivity at low temperature, especially below 0. It can be used for automobile brake pads and washers, friction sealing material and high performance thermal insulation paper. Glass fabric is also used as an insulation material at higher temperatures. It can take the place of aramid especially over 140. The structure and performance of basalt fiber are similar to those of similar to that of glass fiber. However, it is superior to glass fiber in heat resistance, insulation and other aspects. Because of its low thermal conductivity above 0, wide range of use temperatures, low moisture absorption and good anti-seismic performance, basalt fabric can be widely used as heat insulation material at high temperature. CONCLUSION As the hot wire method was selected to measure thermal conductivity of fabric, the heat inside the woven fabrics could be transferred mainly by phonon conduction and molecular conduction. In fiber, phonon conduction is the main factor influencing thermal conductivity. It is influenced by phonon mean free path, which is a function of temperature. As temperature increasing, the velocity of included air molecules may increase, thus improving the thermal conductivity of the air space in the fabric. From 50 to 200, the thermal conductivity of aramid fabric increases linearly as the temperature rises. In this temperature range, the thermal conductivities of glass, basalt and carbon fabrics increase in a non-linear fashion. The thermal conductivity of aramid decreases and then increases slightly with decreasing temperature, while that in other three kinds of fabrics declines as temperature decreases from 0 to -50 As the temperature increases, rate of change of the thermal conductivity decreases in different temperature ranges for the four fabric types. The thermal conductivity trends toward smooth as temperature increases from 50 to 200. At 50 ~100 the thermal conductivity of aramid fabric is significantly influenced by the temperature. The thermal conductivities of carbon and basalt fabrics are strongly affected by temperature. Thermal conductivities of aramid and glass fabrics is little changed affected in the temperature range between 0 and -50. Among the four types of woven fabrics considered in this study, carbon fabric always has the highest thermal conductivity. It would thus be the least suitable of the four for insulation purposes. Basalt fabric and glass fabric are better insulation materials with lower thermal conductivity. Organic aramid fabric is significantly affected by the temperature with the lowest thermal conductivity below 0, showing excellent insulation performance at low temperature. But its thermal conductivity rises rapidly with temperature increasing and is larger than that of basalt and glass fabric at about 140. According to the experimental results, basalt and glass fabric are considered to be the most suitable of the four for insulation at high temperatures, while aramid fabric is most suitable for insulation at low temperature. ACKNOWLEDGEMENT This study was supported by Shanghai Municipal Education Commission ( No.15cxy36 ) and Shanghai Science and Technology Committee (Grant No. 14YF1409600). Journal of Engineered Fibers and Fabrics 15 http://www.jeffjournal.org
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