Thermal resistance models of selected fabrics in wet state and their experimental verification

Abstract

This study investigated the structural model of textile fabrics affected by moisture. The model has been verified through five fleece fabrics made up of various textile materials and subjected to several mechanical surface treatment levels. Thermal resistance is one of the key parameters of thermal comfort along with water vapor permeability. In recent times, a keen interest has been focused on the mathematical modelling of this parameter and its experimental verification. However, most of these efforts are made to describe dryness in thermal resistance of fabrics, ignoring the wet condition found in protective and outdoor clothing. To determine the thermal resistance value of the studied fabrics, the ALAMBETA semiautomatic nondestructive thermal tester was used. The findings show that the proposed model displays substantial harmony with the experimental data.

Keywords

thermal resistance fleece fabric wet conditions

Thermal resistance, which is an important property of textile fabrics, continues to be the subject of many studies. It depends upon the thermal conductivity of fibers, thickness of material and arrangement of yarn and fibers. Thermal conductivity indicates the ability of a material to allow the passage of heat from one side to another. Thermal conductivity is anisotropic in nature and largely depends upon the structure of the material. The thickness of a material determines its resistance to the passage of heat through it. A fabric is composed of polymers (fibers), air trapped inside the fabric, and moisture present in voids. Thermal resistance of dry fabric is higher than thermal resistance of wet fabric. In wet fabric, water molecules replace air. There is a drastic reduction in thermal resistance of the wet fabric due to the higher thermal conductivity of water as compared to air. Thermal conductivity of water is 0.6 W m⁻¹ K⁻¹. It is around 25 times higher than the thermal conductivity of air, which is 0.024 W m⁻¹ K⁻¹.

A prediction of the reduction in thermal resistance due to moisture is needed when a fabric is designed for people working under moist conditions. Models capable of predicting the thermal resistance at a certain level of moisture in the fabric are highly useful, especially for people wishing to save themselves from hypothermia. Hypothermia is a condition in which the human body loses its heat. In such conditions, the core temperature of humans becomes low. Fabrics having high porosity trap more water compared to dense fabrics having a high ratio of fibers (polymers). Moreover, moisture pickup also depends on the absorbing nature of the fibers. Cotton is more absorbent (8.5%) as compared to polyester (0.4%). Fabrics made using 100% cotton absorb around 21 times more moisture as compared to those made from 100% polyester. It shows there are two key factors in moisture uptake by the fabric; porosity and type of fiber. Porosity is a property of the fabric, which represents the space filled by air in the fabric in a dry state.

Thermal resistance of the fabric depends on the chemical and physical elements of the material. No exact prediction of the thermal resistance of a fabric is possible, due to the anisotropic nature of thermal conductivity in the dry state. Even a minor change in the structure and composition of the fabric may affect its thermal conductivity. Further to this problem, prediction of thermal resistance of the wet fabric is more complicated due to the continuous evaporation process that changes the ratio of moisture, air, and polymer in the fabric. Any change in the amount of moisture present in the fabric causes substantial changes in the thermal resistance, which ultimately affects the thermo-physiological comfort of clothing. There are many models developed by various scholars to predict thermal resistance under dry conditions. However, the literature does not provide any model for the prediction of thermal resistance under wet conditions. This study is an effort to develop a model for the prediction of thermal resistance of fabric under dynamic wet conditions.^1–6

Heat flow through dry fabric

A number of scholars have conducted theoretical analyses of heat transfer through fabrics.^1–7 Their results show that the process of heat transfer through fabrics mainly takes place by conduction, which is governed by the following equation:
$q = \frac{λ Δ T}{h}$
(1)
where q indicates heat flux [W m⁻²], T is temperature [K], λ is the thermal conductivity [W m⁻¹ K⁻¹], and h is thickness [m]. This was also confirmed in an extensive experimental study of heat transfer through woven and nonwoven fabrics, conducted by Hes and Stanek,⁸ where the Grasshoff number (Gr) describing the effect of free convection was recorded as being lower than 1000. They further showed that the proportion of heat flow transferred by radiation does not exceed 20% of the total heat flow. Therefore, the linearity of the mathematical model is conserved. The classical dependence of radiation on the 4th power of temperature of the heat transmitting bodies can be approximated by a linear equation.
$λ = λ cond + λ rad$
(2)

In equation (2), λ indicates total thermal conductivity [W m⁻¹ K⁻¹] of any fabric. It is sum of heat transfer capability through conduction (λ_cond) and through radiation (λ_rad). Equation (2) shows that, in the case of a fabric, heat transfer capability depends upon conduction and radiation not on convection, as put forward by Hes and Stanek.⁸

Thermal conductivity of dry fabrics has to depend on the structure and properties of the yarns or fibers. Crow concludes that two factors that play a significant role here are the density of the fabric and the fiber arrangement.⁶ Parallel fibers result in three times higher thermal resistance in relation to fibers that are perpendicular to the fabric surface. When more than one type of fiber is used in fabric manufacturing, an estimation of thermal conductivity can be carried out with the help of the following equation proposed by Militky:⁵
$λ ab = r λ a + (1 - r) λ b$
(3)
where a and b are types of fibers, λ_a and λ_b are their thermal conductivities, r is the portion of fiber a, and λ_ab is the estimated thermal conductivity of the blend. Equation (3) has been used to estimate thermal conductivity of blended fabric for this study.

Heat flow through wet fabric

Heat flow through wet fabric by conduction depends on the thermal conductivity of materials according to their composition and the amount of moisture present in them. A more porous fabric can trap more air and provides space for water molecules, which increases its absorbency. The water absorbed in fibers and yarns considerably affects the thermal conductivity of fabrics.^2,7,9 There is a big difference between the thermal conductivity values of fibers, air, and water. Materials with higher thermal conductivity create less resistance. Thermal resistance R [m² K W⁻¹] is determined by using the following equation:
$R = \frac{h}{λ}$
(4)
where h is the fabric thickness [m] and λ is its thermal conductivity [W m⁻¹ K⁻¹]. Equation (4) shows that thickness has a direct impact on the thermal resistance. Any change in thickness can change the thermal resistance of a fabric. The measurement of fabric thickness is quite sensitive, particularly due to the compressibility of the fabric. A minor change in pressure will change the thickness of a fabric. Such a change is due to the high porosity and protruding fibers on the surface of the fabric. Likewise, dense fabrics having a smooth surface will not be affected significantly by compression.

Water and fabric interaction

The following are possible interactions between water molecules and the fabric, as described by Hes:³
a) Hydrophilic fibers create strong hydrogen bonds with water molecules.

b) Microporous organization of fibers with porosity allows water molecules to penetrate.

c) Water molecules reach macro pores due to the fabric's weave, the sett of yarns, and their fineness.

d) Superficial attachment on the surface of the fabric.

The list given above shows that the porosity of fibers and fabric structures play a critical role in the wicking process, in which water molecules become part of the fabric. The amount of water in the fabric is changing continuously due to the evaporation process. Water exists in an amorphous region of fibers, between the yarns, and on both (front and back) surfaces. There is a regular decline in moisture present in the fabric due to evaporation. Evaporation depends upon the difference in moisture present in the atmosphere and in the fabric. The space left by water molecules is filled by air, which ultimately reduces the weight per square meter of the fabric.

The thermal conductivities [W m⁻¹ K⁻¹] of water, air, PET, and compacted cotton in a dry state are 0.60, 0.024, 0.30, and 0.352, respectively.¹⁰ Equation (4) shows that thermal resistance has a direct relationship with material thickness and an indirect relationship with thermal conductivity. The proportions of fiber, air, and water in the fabric will influence the effective (total) thermal conductivity of a fabric. The ratio of moisture, air, and polymers in the fabric is in a dynamic condition.

The following assumptions were made regarding the model:
The sample thickness and geometric properties of fibers are considered constant with increasing moisture content.

Part of the air is substituted by moisture in the fiber.

Moisture distribution in fabrics and thermal resistance

The presence of water in the fabric decreases the thermal resistance. A fabric has a certain makeup and thickness (height), and when its gaps are entirely filled with water, the height of the water column becomes equal to the fabric thickness. In the case of a low moisture level, gaps are filled with water and partly by air, and there is no correct information about the length of the water and air columns.^11–13

Another problem associated with moisture is the amount of water inside and on the surface of fibers. When the fabric swells, its volume also changes. The changes in the volume of hydroscopic fibers increase the volume and control fibers' capacity as well as reducing the voids between the yarns.

Woven fabric surface area can be divided into five categories:
free length of warp;

free length of weft;

intersection of warp and weft;

pores filled by air;

pores filled by moisture.

The thermal resistances for the above mentioned five areas differ from one another because of their chemical and physical structure, the porosity of the fabric, and the layout of warp and weft. There is also a great difference between the yarn package densities of warp and weft. Li et al. have studied fiber hygroscopic behavior and perceptions regarding dampness.¹⁴ They found that near a 100% moisture level, also called the saturation level, the speed of drying for wool and polyester is similar, whereas variation occurs when the moisture is at around 50%. This study proves that at saturation level, the role of the type of fiber is not important, because maximum evaporation is from the surface. However, at below saturation levels, the absorbency behavior of fiber plays a significant role in drying. In this study, we have used fabric made by yarns. In this way, we are observing the behavior of fibers in a composed shape.

Porosity of fabric and its effect on thermal conductivity

Porosity characterizes the portion of air enclosed in the fabric. Porosity is of three main categories:^6,9,11,15,16
a) inter-yarn spaces (macro porosity);

b) inter-fiber spaces in the inner parts of the yarns (meso porosity);

c) spaces in the fiber substances.

Higher porosity means that the fabric has more space for air and water. The amount of air and water in the fabric has a significant impact on the thermal conductivity, because there is a great difference in the thermal conductivity of water and air. Higher thermal conductivity means lower thermal resistance, and a low thermal conductivity value means higher thermal resistance, because thermal conductivity has an inverse relationship with thermal resistance. There are many ways to determine the porosity of fabrics. We have used area weight [kg m⁻²], thickness [m] of the fabric, and fiber density [kg m⁻³] for the calculation of porosity. The following equation has been used for the calculation of porosity:¹²
$ɛ = \frac{ρ fab}{ρ fib}$
(5)
where ɛ is the ratio of fabric density to fiber, ρ_fib is the fiber density [kg m⁻³], and ρ_fab is the fabric density [kg m⁻³]. Porosity can be calculated by subtracting ɛ from 1 (1 − ɛ). Fabric is flexible in nature and there is a space between yarns. This pace is filled by air and reduces its density. Density of fleece fabric used for sweatshirts is around five times less than density of fibers used for making yarn.

Sugawara and Yoshizawa concluded that the thermal conductivity of a porous material depends upon the thermal conductivity of the fluid and the solid.⁷ Pabst and Gregorova have developed a second-order relation between porosity and thermal conductivity.¹⁷ Zhu and Li consider thermal conductivity as a function of porosity,¹ and they have also presented seven types for thermal resistance in fabrics, on the basis of combination of parallel and serial arrangements of individual resistance. The above discussion reveals that porosity has a significant impact on thermal conductivity.

Thermal resistance of fibers in wet fabric

Wet fabric is composed of organic or inorganic materials, air layers, and moisture (present in different parts of the fabric). In the following sections, the approach taken in order to calculate the thermal resistance of fibers in wet fabric will be discussed. There is no application of any geometry of the fabric to calculate the thermal resistance of fibers in wet fabric, because it is difficult to address all issues related to it. The most complex factor is the amount of moisture present inside or outside the fibers. Many situations have been assumed and finally agreed on the following proposition, because it gave us results that are closer to measured values:
$R f = \frac{h ɛ}{λ f}$
(6)

In equation (6), R_f is the thermal resistance of the fiber [m² K W⁻¹], h is the thickness of the fabric [m], λ_f is the thermal conductivity of fibers [W m⁻¹ K⁻¹], and ɛ is the ratio of fabric to fiber in the fabric.¹

For the above equation, we need the thickness of the fabric to calculate the thermal resistance of the fibers. The fabric is not only composed of fibers, but air and water molecules are also present inside the fabric. To solve this issue, we have reduced the thickness by multiplying it by ɛ, which is ratio of the fiber and the fabric. It indicates that the fabric is not fully composed of fibers (polymers) but rather that moisture and air are also present in it.

Thermal resistance of air gaps (voids)

The second substance in wet fabric is air, which exists in different parts of the fabric. It may be inside the amorphous region of fibers, among fibers, or between yarns in the fabric. We do not have any exact information about the amount and thickness of air layers. The thickness is required to calculate the thermal resistance, which is not possible in partially wet fabric. To solve this issue, many situations were assumed and we finally found the following equation, which gave very close results to measured values:
$R a = \frac{h (1 - ɛ)}{λ a (1 - μ)}$
(7)

In equation (7), R_a is the thermal resistance due to air in the fabric [m² K W⁻¹], h is the thickness of the fabric [m], λ_a is the thermal conductivity of air [W m⁻¹ K⁻¹], ɛ is the ratio of fibers present in the fabric and μ is the amount of moisture in the fabric. We have used the following equation for the calculation of moisture in fabric:
$μ = \frac{wetweightoffabric - dryweightoffabric}{wetweightoffabric}$
(8)
where μ shows the amount of moisture in a wet sample. Equation (8) is very useful because it represents the actual amount of moisture in a wet sample. In equation (7), we have reduced the thickness of the fabric by multiplying it by the porosity. Porosity indicates the area of the fabric filled by air and moisture. Air is present inside the fibers and between the loops and wales of knitted fabric. Moreover, it was assumed that the fabric was partially filled with air. Thermal conductivity of air was multiplied with the amount of air present in the fabric. For this purpose, the amount of moisture (μ) has been deducted from 1, which shows the amount of air present in the fabric.

Wet fabric is composed of air, moisture, and fibers (polymers) in a certain ratio. Measurement of the ratio of moisture, air, and fiber in a fabric is quite complex due to a continuous evaporation of water, which changes the ratio of air, water, and polymer in the fabric. However, at a certain point, the amount of water and polymer can be measured in the fabric using ultra dry weight and wet weight of the fabric (equation (8)). The amount of air present in the fabric is quite difficult to measure due to its negligible mass. To solve this problem, it was assumed that when moisture evaporates, it provides space for air. Voids of the fabric will be filled with air. Equation (7) has been developed to measure the thermal resistance of air present in the fabric. For this purpose, the amount of moisture was deducted from 1. This is based on the fact that moisture value will be 0.5, if amount (weight) of moisture in the fabric is equal to weight of ultra dry fabric. The second issue is the thickness of the air in the fabric. It is required to measure thermal resistance of air trapped in fabric. For this purpose, thickness of fabric was multiplied with porosity. This shows the area filled by air in fabric. This assumption, which is based on simulation, gives values closer to the actual thermal resistance of fabric.

Thermal resistance of moisture in wet fabric

The third substance in wet fabric is water, present in different parts of the fabric. Water may be inside the amorphous region of fibers, between the fibers, and/or attached to the fiber surface. There is no precise information available about the location and amount of water inside and on the surface of the fabric. Different situations were assumed and finally achieved the maximum agreement between simulated and measured values from the following equation:
$R w = \frac{h (1 - ɛ)}{λ w μ}$
(9)
where R_w is the thermal resistance of water [m² K W⁻¹] present in the fabric, h is the thickness of the fabric [m], λ_w is the thermal conductivity of water [W m⁻¹ K⁻¹], ɛ is the ratio of fabric density [kg m⁻³] to fiber density [kg m⁻³], and 1 − ɛ represents the space in a unit volume of fabric, denoted as porosity. Moreover, μ is the amount of moisture in the fabric, calculated by using the wet weight of the fabric minus the dry weight of the fabric and then dividing by the wet weight of fabric. In equation (9), 1 − ɛ is used, which shows the voids filled by air and moisture in the fabric.

There is a need to know the height of the water column present in the fabric for the calculation of thermal resistance. Water is present in various parts of the fabric, and there is no continuous line. Height was multiplied with porosity, which shows the space among the fibers for moisture and air. Moreover, thermal conductivity of the water was multiplied by the amount of moisture present in the fabric.

Thermal resistance model for fabrics in wet state

The total thermal resistance [m² K W⁻¹] depends upon the arrangement of thermal resistance of fibers (R_f), the thermal resistance of air cells (R_a), and the thermal resistance of water present in fabric (R_w). There are two limit arrangements of thermal resistances:
Model 1: Thermal resistance in serial arrangement. The total resistance R_t is given by the relation:
$R t = R f + R a + R w$
(10)

Model 2: Thermal resistance in parallel arrangement. The total resistance R_t is given by the relation:
$R t = (R_{f}^{- 1} + R_{a}^{- 1} + R_{w}^{- 1}) - 1$
(11)

The parallel arrangement gives the higher limit value, while the serial formula deals with the lower limit. Out of these two limit models, six possible combinations can be formed:
Model 3: R_f and R_a in parallel arrangement and R_w added in serial arrangement

Model 4: R_f and R_w in parallel arrangement and R_a added in serial arrangement

Model 5: R_a and R_w in parallel arrangement and R_f added in serial arrangement

Model 6: R_f and R_a in serial arrangement and R_w added in parallel arrangement

Model 7: R_f and R_w in serial arrangement and R_a added in parallel arrangement

Model 8: R_a and R_w in serial arrangement and R_f added in parallel arrangement

Mangat et al. introduced a thermal resistance model that involves the effects of moisture.¹² This model has been used for denim fabric. In this study, this model is applied to knitted fabric. There is an inherent difference between knitted and woven fabric; warp and weft yarns are used for woven fabric, whereas a single yarn is used to make weft-knitted fabric. In this model, thickness of the fabric, the planar weight, and the share of different fibers in the fabric have been used. Keeping these kinds of variables, the model proposed by Mangat et al. can be used for any type of fabric,¹² either knitted or woven. This is the reason that knitted fabric was selected for the application of Mangat et al.'s model. The model explains the relationship between the thermal resistance of fibers and the presence of air and moisture besides porosity. The contributions of fibers, air and moisture were used to predict the total thermal resistance.

Weft-knitted fleece fabric was selected for analysis due to its importance in a cold environment. These fabrics are used for clothing to provide enhanced thermal insulation during cold weather. Such fabric is commonly used in sweatshirts, which derive their name from being worn in cold-weather situations where sweat is likely. Moreover, fleece fabric is used to make clothes worn by people outdoors. It is understood that thermal resistance decreases due to moisture present in the fleece. This may be due to rain or due to a substantial increase of moisture in the air. People have always worried about the performance of fleece fabric under such conditions. The industry is using water repellant finishing processes to keep the thermal resistance of fleece intact. This model will serve to help them develop such fabric, which should be able to provide better thermo physiological comfort during the winter season and especially during rainy winters.

Experimental section

Sample description

This study used weft-knitted fleece fabrics in order to verify the abovementioned thermal resistance model in a wet state. A weft-knitted fleece fabric is highly porous by nature. After brushing, a considerable change in porosity is expected. Fleece consists of two types of yarn including knit yarn and loop yarn. Knit yarn is always finer than loop yarn and is used to make the outer side of the fabric. Loop yarn remains on the inner side of the fabric, which touches the human body or any undergarment. In order to increase the ratio of polyester (PET) in fleece, polyester (PET) filament is used. Brushing increases the thickness of a fabric, intensifying its thermal resistance and reducing its density, and enhances the capacity of the fabric to hold air.

Five types of weft-knitted fleece fabrics having a diverse composition of fiber ratio of cotton and polyester and different numbers of brushing cycles were used for testing purposes; see Table 1.
Table 1.
Basic characteristics of weft-knitted fleece fabrics

Sample No. Ratio of cotton/PET (%) Laying filament PET Level of brushing Planar mass (g m⁻²) Thickness (mm) Porosity

1 100/0 Un-brushed 208 1.00 0.86

2 100/0 Two-pass brushed 226 1.13 0.86

3 100/0 Four-pass brushed 240 1.26 0.87

4 80/20 Un-brushed 263 0.95 0.81

5 48/52 8.33 [tex] Un-brushed 215 1.15 0.87

Testing procedure

The determination of thermal resistance and conductivity of the fabric in a wet state requires the use of a special testing instrument that enables a researcher to record a measurement quickly while the level of moisture remains constant during the measurement. One of the unique instruments in which the full signal is achieved in less than three minutes is the Alambeta (Sensora Czech Republic). The Alambeta is a computer-controlled, semiautomatic, nondestructive thermal tester for testing textile fabrics. The biggest advantage of the Alambeta testing is that the instrument immediately displays the thermal conductivity levels of the tested fabrics. The Alambeta has been used in various other studies. Selection of Alambeta was based on its effective and efficient use along with its application in many studies.^3,18–20

Samples were dried at 105℃ for 30 min in an oven. The planar weight (W) in the dry state and the thickness (h) in the dry state were obtained for use in the calculation of porosity (equation (5)). Then the sample was submerged for 2 h in tap water containing 1% nonionic detergent. This water is used as drinking water, having a minimum of impurities. (One should be careful in using water, since highly impure water has higher thermal conductivity due to the presence of salt, etc.) After that, the sample was kept freely in a horizontal position on a net made up of nylon strings, to allow free evaporation of water molecules. After five minutes, the sample was weighed and put on the Alambeta plate, and the thermal resistance of the wet sample (R_t) was measured. After the values were noted, the samples were put back onto the net for 5 min. During this period, there was continuous water evaporation in the open air of the lab, where the temperature was kept between 20℃ and 22℃, and the relative humidity was between 24% and 25%. This practice was carried out 11 times and found a gradual decrease of moisture in the fabric.

Results and discussion

The theoretical thermal resistance, R_t, was calculated in accordance with models 3–8, repeated here for ready reference.
Model 3: R_f and R_a in parallel arrangement and R_w added in serial arrangement

Model 4: R_f and R_w in parallel arrangement and R_a added in serial arrangement

Model 5: R_a and R_w in parallel arrangement and R_f added in serial arrangement

Model 6: R_f and R_a in serial arrangement and R_w added in parallel arrangement

Model 7: R_f and R_w in serial arrangement and R_a added in parallel arrangement

Model 8: R_a and R_w in serial arrangement and R_f added in parallel arrangement

The thermal conductivities (in W m⁻¹ K⁻¹) of dry air, λ_a = 0.024, water, λ_w = 0.6, PET fibers, λ_PET = 0.30, and compacted cotton in a dry state, λ_cot = 0.352, were used. According to the criteria, the sum of squares of deviations (SSD), the sum of absolute deviations (SAD) from the theoretical models, and the measured results were applied:
$MSSD = \frac{1}{n} \sum_{i = 1}^{n} (R tm, i - R t) 2$
(12)

$MSAD = \frac{1}{n} \sum_{i = 1}^{n} | R tm, i - R t |$
(13)
where i is the i-th measurement of thermal resistance R_t. Due to the square of deviation, criterion SSD gives the higher weight to larger deviations in comparison with criterion SAD. Results are presented in Tables 2 and 3. Both types of criteria provide the same results, and the two best results are highlighted in bold.
Table 2.
Comparison of models using criterion SSD

Sample No Model 3 Model 4 Model 5 Model 6 Model 7 Model 8

1 0.00011 0.04095 0.00012 0.00015 0.00013 0.00092

2 0.00031 0.06511 0.00013 0.00016 0.00013 0.00113

3 0.00015 0.07782 0.00013 0.00016 0.00013 0.00112

4 0.00158 0.02321 0.00008 0.00010 0.00008 0.00112

5 0.00109 0.04352 0.00010 0.00012 0.00011 0.00173

Table 3.
Comparison of models using criterion SAD

Sample No Model 3 Model 4 Model 5 Model 6 Model 7 Model 8

1 0.03306 0.61890 0.03485 0.03904 0.03566 0.08974

2 0.04320 0.77553 0.03466 0.03920 0.03551 0.09706

3 0.03706 0.86521 0.03566 0.04049 0.03644 0.09760

4 0.07216 0.45710 0.02731 0.03113 0.02741 0.09689

5 0.05235 0.62838 0.02752 0.03163 0.02814 0.11291

Table 4 shows that the best simulations are given by model 5 (R_a and R_w are in parallel arrangement, and R_f is added in serial arrangement) and by model 7 (R_f and R_w are in serial arrangement, and R_a is added in parallel arrangement). Considering the statistical values, it can be concluded that models 5 and 7 are the best among the six possible simulations for delivering the best simulation model of thermal resistance R_t. The final equations of models 5 and 7, respectively, are as follows:
$R t = \frac{R a \cdot R w}{R a + R w} + R f$
(14)

$R t = \frac{R a (R f + R w)}{R a + R w + R f}$
(15)

Table 4.
Correlation between the measured and predicted values

Sample No Model 3 Model 4 Model 5 Model 6 Model 7 Model 8

1 0.936 −0.843 0.968 0.968 0.968 −0.704

2 0.924 −0.846 0.969 0.968 0.968 −0.615

3 0.948 −0.845 0.976 0.976 0.976 −0.707

4 0.871 −0.908 0.955 0.954 0.954 −0.076

5 0.887 −0.803 0.956 0.956 0.956 −0.151

According to Tables 3 and 4, the best agreement between the experimental data and the model was achieved for thermal resistance combination number 5 and 7. It was found that model 5, which is applicable for weft-knitted fleece fabrics, is the same as the model that was originally developed for the prediction of thermal resistance of denim fabrics in a wet state.¹² It was found that model 7 also provides values closest to measured values. Models 5 and 7 have both been used to simulate the results shown in Figures 1–5. The figures enable comparison of theoretical and experimental results.
Figure 1.
Simulated course of the thermal resistance and calculated data: 100% cotton, un-brushed.

Figure 2.
Simulated course of the thermal resistance and calculated data: 100% cotton, 2 × brushed.

Figure 3.
Simulated course of the thermal resistance and measured data: 100% cotton, 4 × brushed.

Figure 4.
Simulated course of the thermal resistance and measured data: 80/20% cotton/PET, un-brushed.

Figure 5.
Simulated course of the thermal resistance and measured data: 48/52% cotton/PET, un-brushed.

Results show that in the case of 100% cotton, a first-class agreement between measured and simulated values was discovered for un-brushed, two times brushed, and four times brushed samples. For the fleece produced from combinations of cotton and PET yarns, good agreement was found with the un-brushed sample containing 48% cotton and 52% PET. It was confirmed that more than a 70% reduction in thermal resistance is caused by the presence of moisture (μ) ranging from approximately 0.03 to 0.30 in wet fabric. Despite a relatively small amount of water in the structure, the effect of moisture in macro pores is significant. It is assumed that in the beginning, moisture creates a continuous film on the surface of the fabric, showing adsorption. Adsorption is the adhesion of water molecules on the surface of the fabric. It is quite different from absorption. This film provides a passage for the heat flow, and consequently, thermal resistance decreases with higher magnitude. Obviously, the second step is the penetration of moisture inside the fabric due to the fibers' natural tendency to absorb moisture. Moreover, water molecules also fill the voids between the yarns. This shows that for very small amounts of moisture in the fabric, moisture is retained on the surface of yarns and creates conductive bridges among the yarns. In such cases, the real geometry of the fabrics exhibits a great effect, and the simple thermal resistance model does not exhibit good agreement with the experimental data. Amounts of moisture and the thermal conductivity of water, air and fibers have been considered along with their arrangements, both in series and in parallel, for the models discussed above. The suitability of these models is supported by the results, which show that there is a substantial agreement between measured and predicted values.

The main goal of modeling was to achieve simplicity. That is why these models were not based on the real geometry of the fabrics but were artificial ‘composition and porosity’ models, based on the assumption that in a wet state, many pores are filled with water with a relatively high thermal conductivity. Thus, the presence of water caused a ‘thermal shortcut’ that might eliminate the effect of fabric geometry, especially when the thermal measurements were conducted at a higher contact pressure in the Alambeta instrument. The best combination of thermal resistances of individual components of the tested fabrics, offering the best fit among the theoretical and experimental data, was then chosen by means of statistical methods (SSD and SAD criteria).

Conclusion

The proposed model has been used to predict the thermal resistance of weft-knitted fleece fabrics consisting of cotton and polyester yarns, brushed at two different levels. Weft-knitted fleece fabric samples were moistened, and after stepwise drying, their thermal resistances were measured, and finally, the measured values were compared with model values. The results show that there is a substantial agreement between experimental and calculated values. The study shows that this model can be used for the prediction of thermal resistance of the studied fabrics under varying levels of moisture content for most of the moisture content range.

It was found that this model has better predictability for fleece made using 100% cotton as compared to blends of polyester and cotton. One of the outcomes of the study is the confirmation that more than a 70% reduction in thermal resistance occurs between a 0.03 to 0.30 water ratio (μ) in wet fabric. This shows that a small amount of moisture present in a fabric has a significant impact on its thermal resistance. This is primarily due to the presence of moisture in macro pores. Increasing moisture provides a continuous film for the transfer of heat along with a reduction in overall thermal resistance, due to moisture being present in the fabric. Considering this study, and keeping in view the application of this model for fleece fabric, it can be concluded that this model can be used for other types of fabrics as well.

Sample No.	Ratio of cotton/PET (%)	Laying filament PET	Level of brushing	Planar mass (g m⁻²)	Thickness (mm)	Porosity
1	100/0		Un-brushed	208	1.00	0.86
2	100/0		Two-pass brushed	226	1.13	0.86
3	100/0		Four-pass brushed	240	1.26	0.87
4	80/20		Un-brushed	263	0.95	0.81
5	48/52	8.33 [tex]	Un-brushed	215	1.15	0.87

Sample No	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
1	0.00011	0.04095	0.00012	0.00015	0.00013	0.00092
2	0.00031	0.06511	0.00013	0.00016	0.00013	0.00113
3	0.00015	0.07782	0.00013	0.00016	0.00013	0.00112
4	0.00158	0.02321	0.00008	0.00010	0.00008	0.00112
5	0.00109	0.04352	0.00010	0.00012	0.00011	0.00173

Sample No	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
1	0.03306	0.61890	0.03485	0.03904	0.03566	0.08974
2	0.04320	0.77553	0.03466	0.03920	0.03551	0.09706
3	0.03706	0.86521	0.03566	0.04049	0.03644	0.09760
4	0.07216	0.45710	0.02731	0.03113	0.02741	0.09689
5	0.05235	0.62838	0.02752	0.03163	0.02814	0.11291

Sample No	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
1	0.936	−0.843	0.968	0.968	0.968	−0.704
2	0.924	−0.846	0.969	0.968	0.968	−0.615
3	0.948	−0.845	0.976	0.976	0.976	−0.707
4	0.871	−0.908	0.955	0.954	0.954	−0.076
5	0.887	−0.803	0.956	0.956	0.956	−0.151

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflict of interest

None declared.

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