1. bookVolume 21 (2021): Issue 2 (June 2021)
Journal Details
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Format
Journal
eISSN
2300-0929
First Published
19 Oct 2012
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4 times per year
Languages
English
Open Access

A New Approach for Thermal Resistance Prediction of Different Composition Plain Socks in Wet State (Part 2)

Published Online: 18 May 2021
Volume & Issue: Volume 21 (2021) - Issue 2 (June 2021)
Page range: 238 - 247
Journal Details
License
Format
Journal
eISSN
2300-0929
First Published
19 Oct 2012
Publication timeframe
4 times per year
Languages
English
Introduction

Consumers consider comfort as one of the most important attributes in their purchase of apparel products; therefore, companies tend to focus on the comfort of apparel products. Comfort is a pleasant state of physiological, psychological, and physical harmony between a human being and the environment [1]. Clothing comfort has two main aspects that combine to create a subjective perception of satisfactory performance: thermo-physiological and sensorial. The thermo-physiological relates to the way clothing safeguards and dissipates metabolic heat and moisture [2,3], whereas the sensorial relates to the interaction of clothing with the senses of the wearer [4,5]. Thermal-wet comfort being the strongest among tactile and pressure comfort perceived by subjects during exercise [6].

Dry heat transfer occurs through conduction, radiation, convection, and ventilation, whereas wet heat transfer when sweating includes several additional complex processes including evaporation, wicking, sorption and desorption, wet conduction (additional conductive heat transfer due to the clothing being wet), and condensation of moisture [7,8].

Thermal-wet comfort is mainly determined by the heat and moisture transport of fabric, which is related to fiber characteristics as well as yarn, fabric construction, and fabric finish, recognizing that the extent of their relationship to comfort perception in clothing is also influenced by garment design, cut, and fit. The basic thermal comfort properties are just two: thermal resistance (or insulation) and water vapor resistance (or permeability) [8]. Increasing moisture content in fabrics significantly worsens their ability to transport water vapor. For wool fabrics and wool/viscose blended fabric, the value decreases by over 70–80%. However, in the case of the addition of polyester fibers, the effective permeability of water vapor almost disappears, which is caused by substituting the air in pores by water with higher thermal conductivity. This means also that the physiological properties of the fabric, which is becoming increasingly wet as a result of use, are subject to sudden changes, which significantly affects the quality of the apparel [9]. Oğlakcioğlu and Marmarali measured the thermal resistance of cotton knitted fabric in a wet state. Coolmax wetted fabric was used to simulate wetted skin. About 0.5 ml of water (containing detergent) was injected onto its surface and waited for 1 min for the liquid had been uniformly distributed within a circle of 45–50 mm. It was found that the wetted fabrics indicate lower thermal insulation and cooler feeling [10]. Clothing thermal insulation decreases during perspiration, and the amount of reduction varies from 2 to 8%, as related to water accumulation within clothing ensembles [11]. Another study on footwear reported about 19–25% (30–37% in toes) reduction of thermal insulation during sweating [12]. Kuklane et al. measured the effect of different sweat rates on thermal insulation and found a strong negative correlation. Furthermore, they found that 30% of the total moisture can stay in socks [13]. Thermal manikin results of dry and wet heat loss are presented from different laboratories for a range of two-layer clothing with similar dry insulations but different water vapor permeabilities and absorptive properties. For each climate, total wet heat loss is predominately dependent on the permeability of the outer layer. At 10°C, the apparent evaporative heat loss is remarkably higher than expected from evaporation alone (measured at 34°C), which is attributed to condensation within the clothing and increased conductivity of the wet clothing layers [14]. The characterization of insulation in wet states is very critical. There are many experimental and prediction models available to fulfill this need. Some researchers employed artificial neural networks (ANNs) models for thermal resistance predictions [15,16]. Hes and Loghin assumed thermal resistance of textile linked parallel to the thermal resistance of water in their suggested mathematical model [17]. Dias and Delkumburewatte’s mathematical model predicted higher thermal conductivity than experimental [18]. In the thermal resistance model of Matusiak, all the multilayered fabric assemblies can be defined as cuboids filled with randomly oriented infinite cylinders (fibers). Conductive heat transfer can be calculated by analogy to electrical resistance and Fricke’s law [19]. In most of the studies, thermal resistance is predicted by statistical models [16,17]. Mangat et al. presented a mathematical model for thermal resistance in the wet state with the series and parallel combinations of air, fiber, and water resistance. Their predictions are in good correlation with experiments by model-3 (air and fiber resistance in series, water in parallel) for denim fabrics while model-5 (Ra and Rw in parallel arrangement and Rf in series) and model-7 (Rf and Rw in serial arrangement and Ra in parallel arrangement) for weft knitted fleece fabric of differential fiber composition [18,19]. Hollies and Bogaty have suggested a parallel combination for measuring the effective thermal conductivity of moisten fabric by combining the volume fraction and thermal conductivity of water and polymer [20]. Naka and Kamata suggested three parameters (air, water, and polymer) model with the combination of parallel and series arrangements [21]. The problem with Mangat’s models that they assumed the filling coefficient or conversely porosity as constant components. But they are changed with the changing of moisture levels because water has a different density. Their second assumption that the air is replaced by water is also not correct because of even >200% moisture content air still present in the fabric. A mathematical model for thermal resistance prediction, suggested by Wei et al. [22], is also very simple like Mangat’s model. But they considered only fiber and air resistances. They ignored the water content. Their recommended model has fiber and air in series plus air in parallel. Hollies and Bogaty have ignored the series arrangement and their calculation for water volume presented in the fabric is also not clear. Naka and Kamata suggested three parameters (air, water, and polymer) model that was a good attempt but not conclusive, that is, use series, parallel, or combination of both.

Although there are enough prediction models available for different fabrics, these models are very complicated and limited to dry states. So the present research aims to measure the thermal resistance by different skin models and find or develop a simple mathematical model for thermal resistance prediction based on available physical parameters especially in wet states for socks with differential fiber composition.

Material and methods
Materials

All the socks samples have been knitted on the same machine (Lonati 144N 4″) settings by varying the main yarns to get the homogeneous samples with respect to specs and stretches for contrast comparison. After knitting, all the samples were processed for washing in the same machine bath followed by tumble drying and boarding.

Figure 1

Plain sock construction.

Sock samples specifications

Fiber composition (%) GSM (g/m−2) Thickness (mm) Fabric volumetric density (kg/m−3) Sock codes
Cotton 80%, polyester 18.20%, and elastene 1.8% 276.45 1.080 255.95 P1
Viscose 81.08%, polyester 17.22%, and elastene 1.70% 373.98 1.06 352.82 P2
Polyester 98.38% and elastene 1.62% 252.03 0.96 262.53 P3
Nylon 70.83%, polyester 26.54%, and elastene 2.63% 227.64 1.09 208.85 P4
Polypropylene 65.22%, polyester 31.65%, and elastene 3.13% 211.38 1.04 204.23 P5
Wool 76.19%, polyester 21.67%, and elastene 2.14% 268.29 1.32 203.25 P6
Acrylic 81.25%, polyester 17.06%, and elastene 1.69% 390.24 1.55 251.77 P7
Methods
Alambeta

Thermal resistance (Rct) assessed using the Alambeta tester [23], which enables fast measurement of both steady-state and transient-state thermal properties. This instrument simulates, to some extent, the heat flow q (Wm−2) from the human skin to the fabric during a short initial contact in the absence of body movement and external wind flow. Thermal resistance (Rct) (m2KW−1) is used to express the heat insulation properties of a fabric. Rct of textiles is affected by fiber conductivity, fabric porosity, and fabric structure. It is also a function of fabric thickness, as shown by the following expression: Rct=hλ {R_{ct}} = {h \over \lambda }

Theoretical models

All the theoretical models for thermal resistance prediction are used by feeding the wet fibre thermal conductivity (λwet polymer) and filling coefficient (Fwet polymer) of wet polymer instead dry and amended accordingly except Mangat’s model. Fwet polymer and λwet polymer are calculated as per Eqs (11)–(13). After this amendment, these models can also predict thermal resistance for wet fabrics.

Fricke’s modified model [24]

Thermal conductivity of fibrous material whose fibers are perpendicular to the heat flow can be determined by the following equation: λfab=[1{1λaλwetpolymer1+2(λaλwetpolymer)(FwetpolymerFa)1+λaλwetpolymer}]λwetpolymer {\lambda _{fab}} = \left[ {1 - \left\{ {{{1 - {{{\lambda _a}} \over {{\lambda _{wet\;polymer}}}}} \over {1 + {{2\left( {{{{\lambda _a}} \over {{\lambda _{wet\;polymer}}}}} \right)\left( {{{{F_{wet\;polymer}}} \over {{F_a}}}} \right)} \over {1 + {{{\lambda _a}} \over {{\lambda _{wet\;polymer}}}}}}}}} \right\}} \right]{\lambda _{wet\;polymer}}

λfab = Fabric thermal conductivity, λwet polymer = Wet fibre thermal conductivity, λa = Air thermal conductivity, Fwet polymer = Fiber filling coefficient + Water filling coefficient, and Fa = Air filling coefficient.

Ju Wie modified model

Wie et al. [22] have divided the fabric basic unit into three parts in heat transfer field: part I is composed of solid fibers, part II is the porosity vertical to the heat flow direction, and part III is the porosity parallel to the heat flow direction, as shown as Figure 2. Fabric thermal resistance depends largely on the heat transfer process in the basic unit. In this model, heat flow considered through the fabric in a combination of fiber and air in series plus air in parallel. Rfabric=Dλair[λwetpolymera(λwetpolymerλair)λwetpolymer(λwetpolymerλair)(aFwetpolymer)] {R_{fabric}} = {D \over {{\lambda _{air}}}}\left[ {{{{\lambda _{wet\;polymer}} - a\left( {{\lambda _{wet\;polymer}} - {\lambda _{air}}} \right)} \over {{\lambda _{wet\;polymer}} - \left( {{\lambda _{wet\;polymer}} - {\lambda _{air}}} \right)\left( {a - {F_{wet\;polymer}}} \right)}}} \right]

Figure 2

Ju Wie model diagram.

Rfabric = Fabric thermal resistance (m2KW−1), D = Fabric thickness (m), λair = Air thermal conductivity (Wm−1K−1), λwet polymer = wet fibre thermal conductivity (Wm−1K−1), a=Fabricstructuralparameter=DcompressedD a = {\rm{Fabric}}\;{\rm{structural}}\;{\rm{parameter}} = {{{D_{{\rm{compressed}}}}} \over D} , D = Thickness (m) measured at 2 kPa pressure, while Dcompressed = Thickness (m) measured at 15 kPa.

Maxwell–Eucken2 (ME2)’s modified model

Maxwell–Eucken (ME) model [25,26] (Eq. 4) can be used to describe the effective thermal conductivity of a two-component material with simple physical structures. In Eq. (4), λa, λwet polymer, Fa, and Fwet polymer are the thermal conductivities and volume fractions, respectively, and subscripts representing the two components of the system. λfab is the effective thermal conductivity of the two-component material. An emulsion is a dispersion of one liquid in another immiscible liquid. The phase that is present in the form of droplets is the dispersed phase and the phase in which droplets are suspended is called the continuous phase. Several effective thermal conductivity models require the naming of a continuous and dispersed phase. The materials with exterior porosity, individual solid particles are surrounded by a gaseous matrix, and hence the gaseous component forms the continuous phase and the solid component forms the dispersed phase [27]. For external porosity, λa and λwet polymer are considered as continuous and dispersed phases, respectively. λfab=λaFa+λwetpolymerFwetpolymer3λa2λa+λwetpolymerFa+Fwetpolymer3λa2λa+λwetpolymer {\lambda _{fab}} = {{{\lambda _a}{F_a} + {\lambda _{wet\;polymer}}{F_{wet\;polymer}}{{3{\lambda _a}} \over {2{\lambda _a} + {\lambda _{wet\;polymer}}}}} \over {{F_a} + {F_{wet\;polymer}}{{3{\lambda _a}} \over {2{\lambda _a} + {\lambda _{wet\;polymer}}}}}}

Fwet polymer and λwet polymer are calculated as per Eqs (11)–(13).

Schuhmeister’s modified model

Schuhmeister [28] summarized the relationship between the thermal conductivity of fabric and the fabric structural parameters by the following equations: λfab=0.67×λs+0.33×λp {\lambda _{fab}} = 0.67 \times {\lambda _s} + 0.33 \times {\lambda _p} λs=λwetpolymer×λaλwetpolymerFa+λaFwetpolymer {\lambda _s} = {{{\lambda _{wet\;polymer}} \times {\lambda _a}} \over {{\lambda _{wet\;polymer}}{F_a} + {\lambda _a}{F_{wet\;polymer}}}} λp=Fwetpolymerλwetpolymer+Faλa {\lambda _p} = {F_{wet\;polymer}}{\lambda _{wet\;polymer}} + {F_a}{\lambda _a} where λfab is the thermal conductivity of fabric, λwet polymer is the conductivity of wet fibers, λa is the conductivity of air, Fwet polymer is the filling coefficient of the solid fiber, and Fa is the filling coefficient of air in the insulation.

Militky’s modified model

Militký and Becker [29] summarized the relationship between the thermal conductivity of fabric and the fabric structural parameters by an empirical equation: λfab=(λs+λp2) {\lambda _{fab}} = \left( {{{{\lambda _s} + {\lambda _p}} \over 2}} \right) λs=λwetpolymer×λaλwetpolymerFa+λaFwetpolymer {\lambda _s} = {{{\lambda _{wet\;polymer}} \times {\lambda _a}} \over {{\lambda _{wet\;polymer}}{F_a} + {\lambda _a}{F_{wet\;polymer}}}} λp=Fwetpolymerλwetpolymer+Faλa {\lambda _p} = {F_{wet\;polymer}}{\lambda _{wet\;polymer}} + {F_a}{\lambda _a} where λfab is the thermal conductivity of a fabric, λwet polymer is the conductivity of wet fibers, λa is the conductivity of air, Fwet polymer is the filling coefficient of the solid fiber, and Fa is the filling coefficient of air in the insulation.

Suggested amendments and calculations

By assuming that fabric density is changing with wetting, which causes to change the filling coefficient, porosity, and thermal conductivity of the fabrics. Based on these assumptions, the following three equations are developed that will be used to find the fabric density, filling coefficient, and thermal conductivity for different moisture levels. Average thermal conductivity for different fibers (within socks) at different moisture levels will be calculated as per Eq. (11): AverageThermalConductivity(λwetpolymer)=(Fwλw+Ffib1λfib1+Ffib2λfib2+Ffib3λfib3Fw+Ffib1+Ffib2+Ffib3) Average\;Thermal\;Conductivity\left( {{\lambda _{wet\;polymer}}} \right) = \left( {{{{F_w} \cdot {\lambda _w} + {F_{fib1}} \cdot {\lambda _{fib1}} + {F_{fib2}} \cdot {\lambda _{fib2}} + {F_{fib3}} \cdot {\lambda _{fib3}}} \over {{F_w} + {F_{fib1}} + {F_{fib2}} + {F_{fib3}}}}} \right)

Fw = Water filling coefficient, Ffib1 = First fiber filling coefficient, Ffib2 = Second fiber filling coefficient, Ffib3 = Third fiber filling coefficient, λw = Water thermal conductivity, λfib1 = First fiber thermal conductivity, λfib2 = Second fiber thermal conductivity, and λfib2 = Third fiber thermal conductivity.

The filling coefficients for water, fiber, wet polymer, and air are calculated as per below steps:

Air filling coefficient (Fa) is calculated as per the following Eq. (12): Airfillingcoefficient(Fa)=1(Fw+Ffib) {\rm{Air}}\;{\rm{filling}}\;{\rm{coefficient}}\left( {{F_a}} \right) = 1 - \left( {{F_w} - {F_{fib}}} \right)

Filling coefficient for wet polymer will be calculated as per Eq. (13). This value will be used as input in all the above models for the measurement of thermal resistance in wet states. Wetpolymerfillingcoefficient(Fwetpolymer)=Fw+Ffib {\rm{Wet}}\;{\rm{polymer}}\;{\rm{filling}}\;{\rm{coefficient}}\left( {{F_{wet\;polymer}}} \right) = {F_w} + {F_{fib}}

Filling coefficients calculation

Measurement Fw = Water filling coefficient Ffib = Fiber filling coefficient
Content % %
Weight g g
Area m2 (Fabric) m2 (Fabric)
Areal density gm−2 gm−2
Volumetric density ArealDensity(water)FabricThickness(kgm3) {{{\rm{Areal}}\;{\rm{Density}}\;\left( {{\rm{water}}} \right)} \over {{\rm{Fabric}}\;{\rm{Thickness}}}}\left( {{\rm{kg}}{{\rm{m}}^{ - 3}}} \right) ArealDensity(Fabric)FabricThickness(kgm3) {{{\rm{Areal}}\;{\rm{Density}}\;\left( {{\rm{Fabric}}} \right)} \over {{\rm{Fabric}}\;{\rm{Thickness}}}}\left( {{\rm{kg}}{{\rm{m}}^{ - 3}}} \right)
Filling coefficient VolumetricDensityWaterDensity {{{\rm{Volumetric Density}}} \over {{\rm{Water Density}}}} VolumetricDensityFibreDensity {{{\rm{Volumetric Density}}} \over {{\rm{Fibre Density}}}}

The output of Eqs (11)–(13) is used as input in all the above models. So with the combinations of suggested and abovementioned models, thermal resistance at different moisture levels will be predicted. The thermal conductivity of water and air is taken as 0.6 and 0.026 Wm−1K−1, respectively, while the density of water is 1000 kgm−3. The values of the different input parameters used in this study are given in Table 3 [30].

Different fibers’ properties

Fiber name Density (kgm−3) Thermal conductivity (Wm−1K−1)
Cotton 1540 0.5
Viscose 1530 0.5
Polyester 1360 0.4
Nylon 66 1140 0.3
Polypropylene 900 0.2
Wool 1310 0.5
Acrylic 1150 0.3
Statistical analysis

Theoretical and experimental results are statistically analyzed by the coefficient of determination (R2) and the sum of squares of deviation (SSD). Correlation graphs are drawn through scatter diagrams in Microsoft excel. The following are the equations behind the calculation of (R2) and SSD [31]. R2=Sxy2Sx2Sy2 {R^2} = {{S_{xy}^2} \over {S_x^2S_y^2}} SSD=i=1n(experimentalpredicted)2 {\rm{SSD}} = \sum\nolimits_{i = 1}^n {{{\left( {{\rm{experimental}} - {\rm{predicted}}} \right)}^2}}

Results and discussion

Sock samples were tested for a relative cooling effect, thermal resistance, and thermal absorptivity in the dry state (laboratory conditions moisture content). Then, wet to saturated level (70% moisture content) by BS EN ISO 105-X12 standard test method. Establish technique for preparing wet fabric of a known oven-dry weight of the fabric, then thoroughly wet out it in distilled water. Bring the wet pick-up to 70 ± 5% by putting wet testing fabric on a blotting paper. Avoid evaporative reduction of the moisture content below the specified level before the tests are run. Furthermore, tested again after 2, 4, 6, and 8 h of conditioning successively in laboratory standard environmental conditions at known moisture level.

Effect of moisture on thermal resistance (m2KW−1)

As mentioned earlier, dry and wet socks with differential moisture content were checked on Alambeta. The Alambeta is selected to avoid the effect of convection. Figures 3–11 demonstrated that as the moisture (%) increased thermal resistance decreased and vice versa irrespective of sock fiber composition or structure. Only P3, P4, and P5 socks have resumed their dry (lab conditions) Rct after 6 h of conditioning. P2, P6, and P7 could not resume their thermal resistance even after 8 h. P5 (polypropylene) has the highest moisture loss or evaporation rate followed by P6 (wool) and P3 (polyester). P1 (cotton) and P2 (viscose) are the worst ones. P4 (nylon) and P7 (acrylic) fallen in the middle. Predicted (by different models) and experimental thermal resistance is given in Table 4. For all the models, the input thermal conductivity and filling coefficients were measured for wet polymer at different moisture levels. The correlation between experimental and predicted models is checked by r2 value. The values of coefficient of determination for all the models showed that these models can make reasonable predictions of thermal resistance in dry as well as the wet state also at different moisture levels for all the major fiber blends being used for socks.

Thermal resistance at various moisture levels (predicted vs experimental)

Sock code Moisture content (%) Thermal resistance (m2KW−1)
Fricke modified Ju Wie modified Maxwell modified Schuhmeister modified Militky modified Experimental
P1 10.10 0.029075 0.026768 0.0259 0.017867 0.014374 0.0256
20.61 0.027054 0.025002 0.0236 0.015748 0.012458 0.0204
44.03 0.02069 0.020234 0.0172 0.010955 0.008389 0.0105
61.17 0.01311 0.015747 0.0104 0.007288 0.005534 0.0082
67.02 0.009509 0.013955 0.0075 0.005909 0.004538 0.0071
P2 6.62 0.025473 0.023683 0.0221 0.01491 0.011775 0.0275
20.22 0.022432 0.021359 0.0190 0.012422 0.009634 0.0208
43.83 0.015047 0.016653 0.0121 0.008206 0.006242 0.0101
57.88 0.008557 0.013343 0.0068 0.005574 0.004311 0.008
64.46 0.004649 0.011632 0.0038 0.003955 0.003246 0.0076
P3 0.58 0.026292 0.024315 0.0236 0.017934 0.014817 0.0304
0.70 0.026276 0.0243 0.0236 0.017911 0.014795 0.0277
1.39 0.026183 0.024212 0.0235 0.01778 0.014667 0.0271
34.26 0.020171 0.019273 0.0171 0.011545 0.009006 0.016
49.55 0.015646 0.01628 0.0128 0.008636 0.006615 0.0154
P4 2.57 0.030954 0.028764 0.0281 0.023101 0.019639 0.0346
6.03 0.030477 0.028291 0.0276 0.022303 0.018822 0.0339
19.67 0.028311 0.026266 0.0251 0.019125 0.015691 0.0232
36.99 0.024601 0.02319 0.0212 0.015009 0.011907 0.0223
52.27 0.019801 0.019791 0.0164 0.011276 0.008725 0.0183
P5 0.00 0.028914 0.027095 0.0264 0.023489 0.020484 0.0231
0.72 0.028821 0.027001 0.0263 0.023319 0.020302 0.0225
21.45 0.025759 0.024122 0.0228 0.018425 0.015291 0.0221
53.34 0.017837 0.01824 0.0148 0.010739 0.008376 0.0127
66.20 0.012062 0.014911 0.0097 0.007466 0.005771 0.0107
P6 4.24 0.038036 0.035071 0.0344 0.024769 0.020317 0.0488
11.46 0.036815 0.033891 0.0330 0.023166 0.018792 0.0408
17.99 0.035563 0.032729 0.0316 0.021677 0.017409 0.0353
43.62 0.028582 0.027029 0.0242 0.015439 0.011936 0.0202
54.13 0.024144 0.023973 0.0199 0.012662 0.009662 0.019
P7 3.53 0.040875 0.038067 0.0366 0.029739 0.02492 0.0428
7.01 0.040085 0.037346 0.0357 0.028579 0.023773 0.0339
22.11 0.036104 0.03396 0.0313 0.023589 0.01904 0.0329
40.37 0.029509 0.029102 0.0247 0.01762 0.013786 0.0223
51.56 0.023884 0.025541 0.0195 0.013954 0.010773 0.0183

The predicted and experimental thermal resistance of P1 (cotton 80%, polyester 18.20%, and elastene 1.8%) at various moisture levels is given in Figure 3. Maxwell model has the best prediction at 10.1%, 20.61%, 61.17%, and 67.02% moisture levels followed by Frick, Schuhmeister Militký, and Ju Wie. P1 sample has still about 21% moisture content after 8 h of conditioning due to the higher composition of cotton fiber content (80%).

Figure 3

Theoretical thermal resistance vs experimental at different moisture levels (P1).

In the case of P2 sock (viscose 81.08%, polyester 17.22%, and elastene 1.77%), the almost same trend is observed as well as moisture loss is concerned after consecutive periods of conditioning as shown in Figure 4. Maxwell and Fricke have the best thermal resistance prediction at all moisture contents. Schuhmeister and Militký have a good prediction at 43.83%, 57.88%, and 64.46% moisture contents. Militký has the best prediction at 44%, 58%, and 64% moisture content. Ju Wie has a better prediction where the moisture level is less than 20%.

Figure 4

Theoretical thermal resistance vs experimental at different moisture levels (P2).

P3 sock (polyester 98.38% and elastene 1.62%) has the highest moisture loss (evaporation rate) due to polyester hydrophobic nature after successive periods of conditioning as shown in Figure 5. Militký’s model’s prediction is a bad one among all the models. Overall, Fricke has the best prediction in dry and wet states at all the moisture levels followed by Ju Wie and Maxwell.

Figure 5

Theoretical thermal resistance vs experimental at different moisture levels (P3).

Fricke has overall top thermal resistance prediction generally at 3%, 6%, 36%, and 52% moisture level specifically for P4 (nylon 70%, polyester 26.54%, and elastene 2.63%) as shown in Figure 6 followed by Ju Wie and Maxwell. Militký again got the lowest position. Schuhmeister on the second number from the lower side. This is also verified from SSD values, that is, 0.0000382, 0.0000797, 0.0000901, and 0.000404 for Fricke, Ju Wie, Maxwell, Schuhmeister, and Militký, respectively.

Figure 6

Theoretical thermal resistance vs experimental at different moisture levels (P4).

In Figure 7 for P5 (polypropylene 65.22%, polyester 31.65%, and elastene 3.13%) sock, Schuhmeister and Maxwell’s prediction is the best among all other models with less SSD, that is, 0.0000286325 and 0.000031 with respect to experimental thermal resistance. Then, Ju Wie (SSD = 0.0000887) followed by Militký (SSD = 0.000101) and Fricke (SSD = 0.000115).

Figure 7

Theoretical thermal resistance vs experimental at different moisture levels (P5).

Figure 8 shows the effect of moisture content (%) on the thermal resistance of P6 sock (wool 76.19%, polyester 21.67%, and elastene 2.14%). P6 sock could not resume its dry state moisture content and ultimately thermal resistance after 8 h of conditioning due to its hydrophilic nature. 7.43% moisture content is due to the presence of polyester fiber in the composition in the dry state. All the models have a reasonable prediction of thermal resistance as evident in Figure 8.

Figure 8

Theoretical thermal resistance vs experimental at different moisture levels (P6).

Fricke has the lowest SSD (0.000229) followed by Maxwell (0.000297), Ju Wie (0.000314), Schuhmeister (0.001136876), and Militký (0.00171).

Figure 9 shows the effect of moisture content (%) on the thermal resistance of P7 sock (acrylic 81.25%, polyester 17.06%, and elastene 1.69%). All the models have a reasonable prediction of thermal resistance as evident in Figure 11. Lesser the SSD, better the prediction. Maxwell has the lowest SSD (0.0000517) followed by Ju Wie (0.00134), Fricke (0.000135), Schuhmeister (0.00032638), and Militký (0.000744).

Figure 9

Theoretical thermal resistance vs experimental at different moisture levels (P7).

Figure 10 shows the model wise coefficient of correlation between theoretical and experimental thermal resistance in dry/wet states by all the models for all the sock samples irrespective of sock composition. Maxwell has the highest correlation (R2 = 0.8559) followed by Fricke (R2 = 0.8312), Ju Wie (R2 = 0.8224, Schuhmeister (R2 = 0.8079), and Militký (R2 = 0.873).

Figure 10

Coefficient of determination predicted vs experimental thermal resistance (m2KW−1).

Conclusion

By adopting the new approach of feeding wet polymer filling coefficient and thermal conductivity instead of dry polymers, different models can make a reasonable prediction of thermal resistance in wet states as well. All the models have a coefficient of determination (R2) >0.78.

Polymer filling coefficient remains constant while water and air filling coefficients are changing with the variation of moisture which leads to change the thermal conductivity.

P3, P4, and P5 socks samples have resumed their dry (laboratory conditions) Rct after 6 h of conditioning. P1, P6, and P7 could not resume their insulation even after 8 h of conditioning.

This study was conducted after successive periods of intervals to monitor the evaporation rate as well. So that many moisture contents (%) point missed in the graphs for some samples. The next study could be planned to test controlled moisture [32].

Figure 1

Plain sock construction.
Plain sock construction.

Figure 2

Ju Wie model diagram.
Ju Wie model diagram.

Figure 3

Theoretical thermal resistance vs experimental at different moisture levels (P1).
Theoretical thermal resistance vs experimental at different moisture levels (P1).

Figure 4

Theoretical thermal resistance vs experimental at different moisture levels (P2).
Theoretical thermal resistance vs experimental at different moisture levels (P2).

Figure 5

Theoretical thermal resistance vs experimental at different moisture levels (P3).
Theoretical thermal resistance vs experimental at different moisture levels (P3).

Figure 6

Theoretical thermal resistance vs experimental at different moisture levels (P4).
Theoretical thermal resistance vs experimental at different moisture levels (P4).

Figure 7

Theoretical thermal resistance vs experimental at different moisture levels (P5).
Theoretical thermal resistance vs experimental at different moisture levels (P5).

Figure 8

Theoretical thermal resistance vs experimental at different moisture levels (P6).
Theoretical thermal resistance vs experimental at different moisture levels (P6).

Figure 9

Theoretical thermal resistance vs experimental at different moisture levels (P7).
Theoretical thermal resistance vs experimental at different moisture levels (P7).

Figure 10

Coefficient of determination predicted vs experimental thermal resistance (m2KW−1).
Coefficient of determination predicted vs experimental thermal resistance (m2KW−1).

Different fibers’ properties

Fiber name Density (kgm−3) Thermal conductivity (Wm−1K−1)
Cotton 1540 0.5
Viscose 1530 0.5
Polyester 1360 0.4
Nylon 66 1140 0.3
Polypropylene 900 0.2
Wool 1310 0.5
Acrylic 1150 0.3

Sock samples specifications

Fiber composition (%) GSM (g/m−2) Thickness (mm) Fabric volumetric density (kg/m−3) Sock codes
Cotton 80%, polyester 18.20%, and elastene 1.8% 276.45 1.080 255.95 P1
Viscose 81.08%, polyester 17.22%, and elastene 1.70% 373.98 1.06 352.82 P2
Polyester 98.38% and elastene 1.62% 252.03 0.96 262.53 P3
Nylon 70.83%, polyester 26.54%, and elastene 2.63% 227.64 1.09 208.85 P4
Polypropylene 65.22%, polyester 31.65%, and elastene 3.13% 211.38 1.04 204.23 P5
Wool 76.19%, polyester 21.67%, and elastene 2.14% 268.29 1.32 203.25 P6
Acrylic 81.25%, polyester 17.06%, and elastene 1.69% 390.24 1.55 251.77 P7

Thermal resistance at various moisture levels (predicted vs experimental)

Sock code Moisture content (%) Thermal resistance (m2KW−1)
Fricke modified Ju Wie modified Maxwell modified Schuhmeister modified Militky modified Experimental
P1 10.10 0.029075 0.026768 0.0259 0.017867 0.014374 0.0256
20.61 0.027054 0.025002 0.0236 0.015748 0.012458 0.0204
44.03 0.02069 0.020234 0.0172 0.010955 0.008389 0.0105
61.17 0.01311 0.015747 0.0104 0.007288 0.005534 0.0082
67.02 0.009509 0.013955 0.0075 0.005909 0.004538 0.0071
P2 6.62 0.025473 0.023683 0.0221 0.01491 0.011775 0.0275
20.22 0.022432 0.021359 0.0190 0.012422 0.009634 0.0208
43.83 0.015047 0.016653 0.0121 0.008206 0.006242 0.0101
57.88 0.008557 0.013343 0.0068 0.005574 0.004311 0.008
64.46 0.004649 0.011632 0.0038 0.003955 0.003246 0.0076
P3 0.58 0.026292 0.024315 0.0236 0.017934 0.014817 0.0304
0.70 0.026276 0.0243 0.0236 0.017911 0.014795 0.0277
1.39 0.026183 0.024212 0.0235 0.01778 0.014667 0.0271
34.26 0.020171 0.019273 0.0171 0.011545 0.009006 0.016
49.55 0.015646 0.01628 0.0128 0.008636 0.006615 0.0154
P4 2.57 0.030954 0.028764 0.0281 0.023101 0.019639 0.0346
6.03 0.030477 0.028291 0.0276 0.022303 0.018822 0.0339
19.67 0.028311 0.026266 0.0251 0.019125 0.015691 0.0232
36.99 0.024601 0.02319 0.0212 0.015009 0.011907 0.0223
52.27 0.019801 0.019791 0.0164 0.011276 0.008725 0.0183
P5 0.00 0.028914 0.027095 0.0264 0.023489 0.020484 0.0231
0.72 0.028821 0.027001 0.0263 0.023319 0.020302 0.0225
21.45 0.025759 0.024122 0.0228 0.018425 0.015291 0.0221
53.34 0.017837 0.01824 0.0148 0.010739 0.008376 0.0127
66.20 0.012062 0.014911 0.0097 0.007466 0.005771 0.0107
P6 4.24 0.038036 0.035071 0.0344 0.024769 0.020317 0.0488
11.46 0.036815 0.033891 0.0330 0.023166 0.018792 0.0408
17.99 0.035563 0.032729 0.0316 0.021677 0.017409 0.0353
43.62 0.028582 0.027029 0.0242 0.015439 0.011936 0.0202
54.13 0.024144 0.023973 0.0199 0.012662 0.009662 0.019
P7 3.53 0.040875 0.038067 0.0366 0.029739 0.02492 0.0428
7.01 0.040085 0.037346 0.0357 0.028579 0.023773 0.0339
22.11 0.036104 0.03396 0.0313 0.023589 0.01904 0.0329
40.37 0.029509 0.029102 0.0247 0.01762 0.013786 0.0223
51.56 0.023884 0.025541 0.0195 0.013954 0.010773 0.0183

Filling coefficients calculation

Measurement Fw = Water filling coefficient Ffib = Fiber filling coefficient
Content % %
Weight g g
Area m2 (Fabric) m2 (Fabric)
Areal density gm−2 gm−2
Volumetric density ArealDensity(water)FabricThickness(kgm3) {{{\rm{Areal}}\;{\rm{Density}}\;\left( {{\rm{water}}} \right)} \over {{\rm{Fabric}}\;{\rm{Thickness}}}}\left( {{\rm{kg}}{{\rm{m}}^{ - 3}}} \right) ArealDensity(Fabric)FabricThickness(kgm3) {{{\rm{Areal}}\;{\rm{Density}}\;\left( {{\rm{Fabric}}} \right)} \over {{\rm{Fabric}}\;{\rm{Thickness}}}}\left( {{\rm{kg}}{{\rm{m}}^{ - 3}}} \right)
Filling coefficient VolumetricDensityWaterDensity {{{\rm{Volumetric Density}}} \over {{\rm{Water Density}}}} VolumetricDensityFibreDensity {{{\rm{Volumetric Density}}} \over {{\rm{Fibre Density}}}}

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