A Review on Sustainable Method to Evaluate Heat and Moisture Transfer in Clothing Material

Abstract

Clothing as a tool connecting the human body and environment provides thermal and moisture comfort, and protective performance in cold, moderate, and extremely hot environments. Some methods have been proposed to analyze the heat and moisture transfer of clothing materials in various industrial fields. The numerical model as a sustainable method has made considerable progress in recent decades since it provides an efficient and cost-effective way of characterizing new designs or testing new materials. However, no comprehensive review paper focuses on the numerical model of moisture transfer in clothing materials, let alone the numerical model of heat and moisture transfer. This study aims to investigate the development of the numerical model of heat and moisture transfer. The models of heat transfer in clothing materials are briefly reviewed in this study, and then a comprehensive report on the moisture transfer and the coupled mechanism with the heat transfer in clothing materials is summarized. In addition, the keywords in the sustainable method on the heat and moisture transfer were displayed at various phases for analyzing the status of development and application of the sustainable method. This work suggests future development of the sustainable method to address research gaps and serves as a sharing and easy-to-operate platform for researchers, clothing designers, and manufacturers to enhance their knowledge for achieving thermal and moisture comfort, and developing new clothing products.

1. Introduction

In most environmental conditions, the human body is capable of maintaining a constant core temperature. However, extreme environmental exposure makes it difficult for the human body to regulate its core temperature. This might induce hyperthermia or hypothermia in the human body [1]. Clothing that serves as a functional second skin can regulate the interaction effect between the human body and the external environment. The clothing can provide comfort, warmth retention, water resistance, thermal insulation, protection, etc., thus helping with personal thermal and moisture management [2].

A material with many interconnected pores can be treated as a porous medium [3]. Thus, clothing material is usually assumed as a porous media. However, the structure of the fabric becomes more complex due to the interweaving of the fibers and threads. Additionally, unlike conventional industrial materials, the majority of garment materials absorb moisture. Thus, understanding the mechanisms and behaviors associated with the coupled heat and moisture transfer in clothing materials is essential for personal thermal and moisture management. This helps to develop emerging clothing materials for improving human thermal and moisture comfort [4].

The heat and moisture transfer properties of clothing materials are commonly evaluated using experimental study, mathematical modeling, and computer simulation. Although the experimental study can objectively characterize the performance of clothing, there are limitations compared with the numerical simulation, such as the complexity of the experimental operation, the time consumption, and the costly test apparatus [5]. Besides, it is hard to simulate the actual operational environments using the experimental facility, such as flash fire and extremely cold environments. In addition, the clothing materials can be damaged in the experimental measurement, such as deformation and thermal degradation, so most experimental specimens are rarely reused [6]. This results in a waste of the clothing materials.

With the rapid development of computer technology, numerical simulation as a sustainable method has been widely used to study heat and moisture transfer in clothing materials. In previous applications, numerical simulation becomes increasingly important since it provides an efficient and cost-effective way of evaluating heat and moisture transfer [7]. For one thing, the study of heat and moisture transfer behavior in the environment, clothing, and human body as well as predicting the physiological reaction of the human body under various experimental conditions are made easier by numerical models. For another, parameter studies, such as material properties, environmental parameters, and clothing design parameters are carried out to better establish a solid foundation for the improvement of thermal and moisture comfort.

Therefore, an overview of the literature on the heat and moisture transfer models in clothing materials is presented in this study. For a more efficient comparison, the modeling of heat and moisture transfer through clothing materials can be divided into three sections, including heat transfer, moisture transfer, and their coupled relation. The development history for modeling the heat and moisture transfer is summarized in detail. In addition, the research threads for different types were investigated. The application of the heat and moisture transfer model is also mentioned. Under the circumstance that few comprehensive review papers focus on the numerical model of heat and moisture transfer, the moisture transfer and the coupled mechanism with the heat transfer in clothing materials are summarized in this literature. The objective of this literature review was to provide a knowledge understanding of heat and moisture transfer for clothing designers, researchers, and manufacturers. This information may then be applied to thermal and moisture management for better human health and to future research, helping address research gaps. The three main objectives of this review are:

(1)

To understand the mechanism of heat and moisture transfer in clothing materials, and summarize the methods of model establishment.

(2)

To evaluate the recent development of the heat and moisture transfer model and discuss the directions of future development.

(3)

To discuss the importance of developing heat and moisture transfer models for wide application.

2. Status Analysis of Sustainable Method

A novel means was proposed to analyze the research progress in the sustainable evaluation of the heat and moisture transfer of clothing materials. A logic grid of keywords and the respective alternative terms were created as a precondition for the search. Then, different model categories were added as search terms to build three separate databases, as shown in

Table 1. Logic grid of keywords.

Precondition 1	Precondition 2	Precondition 3	Model Category
“Model” OR “Numerical” OR “Simulation”	“Fibrous” OR “materials” OR “Textile” OR “material” OR “Smart” OR “textile” OR “Fabric” Clothing	“Cold protective clothing” OR “Cold environment” OR “Low temperature” OR “Thermal protective clothing” OR “Hot environment” OR “Fire exposure” OR “High temperature” OR “Smart clothing” OR “phase change” OR “thermal management” OR “Common clothing” OR “Sports clothing” OR “Moderate environment”	·“Heat transfer” ·“Moisture transfer” OR “Mass transfer” ·“Heat and moisture transfer”

. The elements of the document type, title, keywords, abstract, author name, institution, cited references, total citations, etc., should be presented in every document downloaded from the Web of Science Core Collection to perform the co-occurrence (keywords) analysis. The searched works of the literature were further filtered according to the title, abstract, and keywords, and the duplicate files were removed. Finally, 542 articles were screened for systematic analysis. The development procedure of the database is presented in Figure 1. The software CiteSpace was used to explore the research status of the sustainable method. The sustainable methods were categorized into three types, including heat transfer, moisture transfer, and coupled transfer.

Figure 2 presents the changes in total publications about the three types. It was found that publications on the sustainable method increased sharply from 2003 to 2022. The sum of publications for heat transfer (360) was more than the other two types. There were few studies to individually develop the moisture transfer models (17) for clothing materials. In most cases, the moisture transfer models were incorporated into the heat transfer models for developing the coupled models (165). This might be attributed to the fact that the thermal regulative performance of clothing materials was more important for the thermal comfort of the human body in extreme environments.

Figure 3 shows the relationship between research keywords in the sustainable method. The degree centrality of the keywords of the sustainable method at various phases is displayed. The nodes and labels were represented by the degree of centrality. The larger node and label indicated higher importance in the network. It turned out that phase change was the keyword with the highest degree of centrality from 2003 to 2007, followed by diffusion. The water condensation acts as a source of local heat generation while the water evaporation acts as a heat sink. The water phase change significantly affects the temperature, the vapor density, the moisture content, and the vapor pressure distributions [8]. Models along with condensation, phase change, and fiber insulation were hot topics from 2004 to 2008, and sorption was widely investigated in this stage. The moisture sorption of fiber strongly affected the kinetic energy of the water molecule and the heat transfer [9] (pp. 359–378), [10,11]. The term performance became a prominent subject in the third stage, which lasted from 2013 to 2017. In terms of protective clothing, air gap, and phase change material, the keyword temperature, and numerical simulation ranked high for the heat and moisture transfer model in the last few years.

In addition,

Table 2. Top 10 keywords in sustainable method by frequency, bursts, and centrality.

Freq	Keywords	Bursts	Keywords	Centrality	Keywords
153	Heat Transfer	6.57	Condensation	0.38	Heat Transfer
51	Moisture Transfer	6.22	Phase Change	0.12	Simulation
48	Phase Change	5.30	Fibrous Insulation	0.10	Heat
46	Simulation	3.62	Clothing Assembly	0.10	Fibrous Insulation
44	Heat	3.57	Mass Transfer	0.09	Mass Transfer
34	Mass Transfer	3.14	Protective Clothing	0.08	Phase Change
32	Fibrous Insulation	2.60	Unsteady Heat	0.07	Condensation
28	System	2.54	Heat and mass transfer	0.05	System
26	Condensation	2.36	Heat	0.04	Moisture Transfer
16	Clothing Assembly	2.22	Assembly	0.04	Energy Storage

lists the top 10 keywords in the heat and moisture model on the basis of frequency, bursts, and centrality. Condensation, which had a value of 6.57, ranked first in terms of bursts, and the burst period was from 2004 to 2013. Phase change ranked second with bursts of 6.22 from 2003 to 2013. Protective clothing (2016–2022) had high bursts in recent years. The top centrality was divided into three categories, including heat transfer, mass/moisture transfer and coupled transfer/phase change. The development status for the three types of research in clothing materials is discussed in further detail below.

3. Heat Transfer in Clothing Materials

Heat transfer in the clothing materials was affected by multiple factors. Both conduction and convection require the presence of a medium for the transfer of thermal energy, but the radiative heat transfer is independent of any medium. Since the porosity of the commonly used fabrics is small enough, the convective heat transfer in the clothing is usually ignored [12]. The conductive heat transfer occurs in the fiber and the embedded air and moisture, while the radiative heat is just transported in the pore of the fabric. The conductive heat transfer is relatively simple and conformed to Fourier’s law while the radiant heat transfer in a porous medium is a complex process [13]. In the early stage, some conductive models were proposed to simulate the radiative heat transfer in clothing materials [14,15]. The conductive heat transfer in these models was treated as the main mode of heat transfer. An improved model that considered the radiative absorption and back-scattering property was developed by Schuster [16] for simulating the radiative heat transfer in fibrous materials [17]. At the end of the 20th century, Tong et al. [18] proposed a spectral two-flux model of the porous medium that simulated the thermal radiation with absorbing, emitting, and scattering, which can be expressed as,

$$\frac{{\mathrm{dq}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right)}{\mathrm{dx}}{=-2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right)-{2\mathsf{\sigma }}_{\mathrm{s}\mathsf{\lambda }}{\mathrm{b}}_{\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right){+2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{e}}_{\mathrm{b}\mathsf{\lambda }}\left(\mathrm{T}\right){+2\mathsf{\sigma }}_{\mathrm{s}\mathsf{\lambda }}{\mathrm{b}}_{\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right)$$

(1)

$$\frac{{\mathrm{dq}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right)}{\mathrm{dx}}{=2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right){+2\mathsf{\sigma }}_{\mathrm{s}\mathsf{\lambda }}{\mathrm{b}}_{\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right)-{2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{e}}_{\mathrm{b}\mathsf{\lambda }}\left(\mathrm{T}\right)-{2\mathsf{\sigma }}_{\mathrm{s}\mathsf{\lambda }}{\mathrm{b}}_{\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right)$$

(2)

where q_λ⁺ and q_λ⁻ are the forward and backward radiant heat flux of micro-unit, respectively, σ_aλ and σ_sλ are the average absorptivity and scattering coefficient, e_bλ is the emission of thermal radiation from blackbody, and b_λ is the back-scattering factor.

There are two terms relating to the scattering of radiation in Equations (1) and (2). The first is the attenuation of energy by scattering for the second term on the right-hand side of Equations (1) and (2), while the final term on the right-hand side represents the augmentation of thermal radiation owing to the scattering. To simplify the solution method on the two-flux model, the effect of the radiative scattering portion in the fibrous materials was ignored. This was because the back- and forward-scattering of radiation could balance out in the one-dimensional heat transfer [19]. Therefore, the simple equations for the radiant heat transfer are given by,

$$\frac{{\mathrm{dq}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right)}{\mathrm{dx}}=-{2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{+}\left(\mathrm{x}\right){+2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{e}}_{\mathrm{b}\mathsf{\lambda }}\left(\mathrm{T}\right)$$

(3)

$$\frac{{\mathrm{dq}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right)}{\mathrm{dx}}{=2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{q}}_{\mathsf{\lambda }}{}^{-}\left(\mathrm{x}\right)-{2\mathsf{\sigma }}_{\mathrm{a}\mathsf{\lambda }}{\mathrm{e}}_{\mathrm{b}\mathsf{\lambda }}\left(\mathrm{T}\right)$$

(4)

Since then, the simple two-flux model was commonly utilized in modeling the radiative heat transfer in clothing materials under diverse environmental conditions [19,20,21]. Wan and Fan [22] employed the two-flux model to analyze the radiant heat transfer in fibrous assemblies incorporating reflective interlayers. Fu et al. [23] investigated the moisture influence on the absorption of thermal radiation under a low-level radiation exposure based on the two-flux model. Furthermore, the effects of self-emission and absorption of radiative heat transfer were investigated using the two-flux model to simulate thermal transfer in air gaps [24,25].

Another meaningful radiative transfer model was developed and validated experimentally by Torvi [26]. According to the structural model of fabric and the radiative transfer properties, it was found that the radiative heat transfer in the tested fabrics conformed to Beer’s law, as shown in Equation (5).

$$\frac{{\mathrm{dq}}_{\mathsf{\lambda }}\left(\mathrm{x}\right)}{\mathrm{dx}}=-{\mathsf{\gamma }\mathrm{q}}_{\mathsf{\lambda }}\left(0\right)\exp \left(-\mathsf{\gamma }\mathrm{x}\right)$$

(5)

The thermal radiation through the fabrics exponentially decayed due to the fabric’s absorption and scattering [27]. The scattering and emission sources of radiative heat transfer were ignored in the model. It was suitable to the phenomenon that the decay of thermal radiation through the medium was far more than the emission of that, or the incident radiant heat unless the forward direction was rather less [13]. The model was popularly used to analyze the radiant heat transfer in thermal protective clothing [26,28,29,30]. In addition, an improved radiant heat transfer model (New model) was derived by considering the effect of the emission and compared with Torvi’s model [26], and the thermal protective performance test in low-level radiation (Experiment), as can be seen from Figure 4 [31]. The contrastive results demonstrated that the self-emission in the clothing material accelerated the rate of thermal energy transferred to the human skin during the thermal exposure and the cooling stage.

However, the aforementioned heat transfer models mostly considered one-dimensional heat transfer along the thickness direction of the clothing. The multi-dimensional heat transfer would occur if temperature differences existed on the surface of the clothing. In recent years, some CFD software was used to simulate the multi-dimensional heat transfer in clothing materials [32,33,34,35,36]. The irregular shape of a clothed body was accurately simulated to investigate the effects of clothing ventilation opening on heat transfer [37,38]. However, only conductive heat transfer was taken into account in the CFD models rather than the radiative heat transfer, and the porous property of the clothing materials was ignored, which created an obvious difference from the actual heat transfer [35,39].

4. Moisture Transfer in Clothing Materials

The moisture within the porous materials exists in three states: solid, liquid, or gas. The fiber and the absorbed water (bound water) become the solid phase of the fabric, while the gas phase is made up of a combination of entrapped air and water vapor [40]. Most moisture transfer models overlook the swelling or shrinkage of the fiber caused by moisture desorption or sorption since it is usually believed that the solid phase remains stationary. Therefore, the moisture transfer consists of the movement of water vapor due to the Fickian diffusion and Darcy’s flow, as well as the transport of liquid water depending on the external driving forces (such as pressure difference and gravity) and the internal driving forces (including capillary, intermolecular force, and permeation) [41], as given in Figure 5. Three states of water transform reciprocally owing to phase change and the fiber’s absorption/desorption.

4.1. Water Vapor Transfer

Table 3. Typical water vapor transfer models used in the clothing.

Representative Researchers	Factors Influencing the Water Vapor Transfer
	Molecular Diffusion	Darcy’s Flow	Sorption/Desorption	Phase Change	Air Resistance	Others
Henry [44], Nordon and David [45], Li and Holcombe [46]	YES	NO	YES	NO	NO	NO
Morton and Hearle [47], Gibson and Charmchi [48]	YES	NO	YES	NO	NO	Swelling
Ogniewicz and Tien [49]	YES	NO	NO	YES	NO	NO
Li and Zhu [50]	YES	NO	YES	YES	NO	NO
Fan et al. [51]	YES	YES	NO	YES	NO	NO
Huang et al. [52]	YES	YES	YES	YES	YES	NO
Li et al. [53]	YES	YES	YES	YES	YES	NO
Luo et al. [54]	YES	YES	YES	YES	YES	Wind and velocity, body motion

shows the typical models for water vapor transfer used in clothing materials. A mechanism for the transient diffusion of moisture in an assembly of textile fibers was first proposed and analyzed by Henry in 1939 [42]. The diffusion of water vapor in the fabric’s void space is driven by the component concentration gradient, required by the Fickian law [43]. Meantime, the water vapor diffuses through the fiber due to the molecular attraction on the fibrous surface. However, it is expected that the water vapor diffusion through the pores is more rapid than that through the fiber. Many researchers, such as Henry [44], Nordon and David [45], and Li and Holcombe [46], presented the continuous equations of water vapor in the inter-fiber void space and the fiber. However, the fiber can undergo swelling or shrinkage when the fiber absorbs or loses water, thus resulting in the variation of void space in the fiber and its geometry [9] (pp. 341–358). A thermal dynamic model was developed by Morton and Hearle [47] to evaluate the impacts of a fiber’s hygroscopicity, and physical and mechanical properties on the swelling effect, and. Gibson and Charmchi [48] proposed a mathematical model for the diffusion and convection of water vapor considering the influence of fiber’s swelling.

The phase change of moisture also influences water vapor transportation. The condensation process in the fabric would activate once the concentration of water vapor comes up to the saturated water vapor. Instead, the liquid water evaporates into water vapor. In previous studies, Ogniewicz and Tien [49] used an improved model to investigate the effect of evaporation/condensation on water vapor transfer. A more precise model of water vapor transfer considering the effects of absorption/desorption and evaporation/condensation was given by Li and Zhu [50]. In addition, the air in the fabric hinders the transfer of water vapor, since the gas phase is a mixture of air and water vapor [55]. The numerical models of the transfer of water vapor and air in the fabric were described by Huang et al. [52]. The effect of pressure gradient on the transfer of water vapor and air was also considered in the models. The pressure gradient can result in water vapor movement within the fibrous material, which was simulated according to Darcy’s law [51]. Li [53] and Luo et al. [54] derived a comprehensive moisture transfer model, which explained the effects of the concentration gradient, pressure gradient, air resistance, absorption/desorption, and evaporation/condensation on the transfer of water vapor.

4.2. Liquid Water Transport

Table 4 shows most factors influencing the liquid water transport in clothing materials. The early works of chemical engineers in drying processes were characterized by representing the fluid motion by diffusion equations, while some studies reported that the surface tension forces (capillary action) predominated the movement of liquid water in porous media [56,57]. To numerically simulate the liquid water transfer through the porous media, a threshold value of liquid water amount was given in some mathematical models for judging the beginning of liquid water flow [58,59]. Fan and Wen [60] derived a continuous equation on the liquid water diffusion in porous fibrous batting. The related dispersion coefficient was a function of the pore size and fiber surface treatment [60]. In accordance with Henry’s models, Li et al. [8,61] derived a special formula to describe the liquid water diffusivity in porous textiles. The condensation/evaporation, sorption/desorption, and liquid water transport by the capillary action were both considered in this equation.

However, the transportation of the liquid water was also dependent on gravity and convection, driven by the pressure gradient. It was supposed that the liquid water in a porous medium was a discontinuous phase. The impacts of the gravity and capillary action on the liquid water transport were analyzed in a moisture transfer model developed by Li and Zhu [62]. It was found that the gravity effects on the water transfer were dependent on the ratio of gravity to surface tension force in the porous textiles. Besides, Zhu et al. [63] presented a fractal model to investigate the physical model of liquid diffusion. It was assumed that the porous fibrous medium was a kind of fractal porous medium. Most factors affecting the liquid water flow were considered in this model (see Table 3). It was clear that porosity had a significant effect on the water vapor concentration in the void spaces and the liquid water flow.

However, there were few studies on multidimensional moisture transfer in past years. Until the early 21st century, Nashimura and Matsuo [64] presented a simple two-dimensional moisture transfer model of clothing materials that considered the water vapor transfer along the thickness and width direction based on Fickian second law and mass conservation law. However, the flow of liquid water and fiber sorption were ignored in the model. In addition, Luo and Xu [65] established a 3D geometric fiber model first and derived a new algorithm to simulate 2D transient moisture transport behavior. However, Darcy’s flow was not considered in this model. The liquid water transfer model was developed by Mao and Li [66] after an experimental method was used to investigate the multi-dimensional liquid moisture diffusion in clothing materials. However, the model precision and application should be further validated.

Table 4. Models on liquid water transfer in clothing materials.

Representative Researchers	Factors Influencing the Liquid Water Transfer
	Molecular Diffusion	Capillary Action	Darcy Flow	Sorption/Desorption	Phase Change	Gravity
Fan and Wen [60]	YES	YES	NO	YES	YES	NO
Li and Zhu [61]	YES	YES	NO	YES	YES	NO
Wang et al. [67]	YES	YES	NO	YES	YES	NO
Li and Zhu [50]	YES	YES	NO	YES	YES	NO
Li et al. [53]	YES	YES	YES	YES	YES	NO
Huang et al. [52]	YES	YES	YES	YES	YES	NO
Wu and Fan [68]	YES	YES	NO	YES	YES	NO
Li and Zhu [62]	YES	YES	NO	YES	YES	YES
Zhu et al. [63]	YES	YES	YES	YES	YES	YES

Table 4. Models on liquid water transfer in clothing materials.

Representative Researchers	Factors Influencing the Liquid Water Transfer
	Molecular Diffusion	Capillary Action	Darcy Flow	Sorption/Desorption	Phase Change	Gravity
Fan and Wen [60]	YES	YES	NO	YES	YES	NO
Li and Zhu [61]	YES	YES	NO	YES	YES	NO
Wang et al. [67]	YES	YES	NO	YES	YES	NO
Li and Zhu [50]	YES	YES	NO	YES	YES	NO
Li et al. [53]	YES	YES	YES	YES	YES	NO
Huang et al. [52]	YES	YES	YES	YES	YES	NO
Wu and Fan [68]	YES	YES	NO	YES	YES	NO
Li and Zhu [62]	YES	YES	NO	YES	YES	YES
Zhu et al. [63]	YES	YES	YES	YES	YES	YES

5. Coupled Heat and Moisture Transfer

5.1. Phase Change

Heat and moisture transfer in clothing materials is not a completely independent process. The evaporation and condensation of water in the clothing materials can take away or discharge the thermal energy [9] (pp. 359–378), [10,11]. The liquid water and the water vapor can both be absorbed or desorbed by the hydrophilic materials, thus changing the kinetic energy of the water molecule [9] (pp. 359–378), [10,11]. Meantime, the entrapped water in the clothing materials has a significant effect on fiber configuration, thermal properties, optical properties, etc. [69,70].

The condensation creates a liquid phase which may be a pendular or mobile state due to the capillary action and gravity [8]. The process of water condensation depends on the liquid water transfer that can represent three stages. In the first stage, the water condensation is mainly a bound state for a shorter time compared with other stages. There is less amount of water for the stage. In the next stage, the water condensation is usually presented in a discontinuous and pendular state as there has less liquid water accumulation by the phase change. This stage is assumed to be a steady-state that can be maintained over a long time due to the low rate of condensation occurring [49]. When the amount of the liquid water exceeds a specific critical value, the liquid water in the porous media starts to move under the action of the fiber’s surface tension and gravitation, eventually stabilizing [71].

Farnworth [72] presented the first dynamic model of heat and moisture transfer with sorption and condensation based on thermal and evaporation resistances. A simple proportional relation between the moisture regain and the relative humidity was developed to simulate the sorption and the condensation of moisture. This model was only appropriate for the steady-state, as the temperature and the moisture content in each clothing layer were assumed to be steady. Le et al. [73], and Su et al. [74] proposed the heat and mass transfer model in the condensing flow of steam through an absorbing fibrous medium. Considering the physical conditions during the steaming of a textile assembly, the volume fraction of condensed water at any stage was well below the critical value for liquid water mobility. Therefore, the condensation and evaporation equations for the immobile liquid water are derived as follows,

$${\mathsf{\Gamma }}_{\mathrm{e}}={\mathrm{h}}_{\mathrm{m}}{\mathsf{\alpha }}_{\mathrm{s}}\left({\mathsf{\rho }}_{\mathrm{v}}-{\mathsf{\rho }}_{\mathrm{v},\mathrm{sat}}\right)$$

(6)

$${\mathsf{\Gamma }}_{\mathrm{c}}={\mathrm{h}}_{\mathrm{m}}{\mathsf{\alpha }}_{\mathrm{s}}\frac{{\mathsf{\epsilon }}_{\mathrm{l}}}{{\mathsf{\epsilon }}_{\mathrm{l}}{}^{\mathrm{cr}}}\left({\mathsf{\rho }}_{\mathrm{v}}-{\mathsf{\rho }}_{\mathrm{v},\mathrm{sat}}\right)$$

(7)

where ρ_v is the water vapor density in the void pace of fabric, ρ_v,sat is the water vapor density at the condensing surface. The condensation rate is proportional to the difference in vapor density between the gas phase and the condensing surface. The difference between the density of the water vapor and the proportion of the surface that is covered by the liquid water, which is proportional to the normalized volume fraction of the liquid water, determines the rate of evaporation of the liquid water. Similar models were derived by Gibson [48] and Li et al. [50,61] to simulate the water condensation with the flow of liquid water driven by the pressure gradient and the capillary action. Based on the developed model, the effects of the fabric’s porosity, thickness, and phase change on the heat and moisture transfer were studied.

It was presumed that the condensation originated when the relative humidity in the porous fabric was more than 100% [60]. The concentration of water vapor and liquid water remained in thermodynamic equilibrium. The condensation rate of moisture is obtained by the continuity equation, written as:

$${\mathsf{\Gamma }}_{\mathrm{c}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=(\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathsf{\tau }}\frac{{\partial }^2{\mathrm{C}}_{\mathrm{a}}{}^{*}(\mathrm{x},\mathrm{t})}{\partial {\mathrm{x}}^2}-\frac{\partial {\mathrm{C}}_{\mathrm{a}}{}^{*}(\mathrm{x},\mathrm{t})}{\partial \mathrm{t}})$$

(8)

where C_a* is the saturated concentration of water vapor. The transient model was to study the effect of condensation on the effective thermal conductivity and the radiative heat transfer in clothing materials for the first time [75]. However, the condensation equation was primarily applied to a small amount of liquid water or immobile liquid water. Therefore, Fan et al. [60] developed an improved model to analyze the dynamical condensate behavior during the flow of liquid water. The rates of water condensation and evaporation are given by, respectively,

$${\mathsf{\Gamma }}_{\mathrm{e}}=\mathrm{E}\sqrt{\mathrm{M}/2\mathsf{\pi }\mathrm{R}}\left(1-\mathrm{RH}\right){\mathrm{P}}_{\mathrm{sat}}/\sqrt{{\mathrm{T}}_{\mathrm{s}}}$$

(9)

$${\mathsf{\Gamma }}_{\mathrm{c}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=(\frac{{\mathrm{D}}_{\mathrm{a}}}{\mathsf{\tau }}\frac{{\partial }^2{\mathrm{C}}_{\mathrm{a}}{}^{*}(\mathrm{x},\mathrm{t})}{\partial {\mathrm{x}}^2}-\frac{{\partial }^2{\mathrm{C}}_{\mathrm{a}}{}^{*}(\mathrm{x},\mathrm{t})}{\partial \mathrm{t}})\mathsf{\epsilon }$$

(10)

where E is the water evaporation coefficient, M is the relative molecular mass of water, R is the universal gas constant, and P_sat is the saturated pressure of water vapor at the absolute temperature (T_s). In addition, Huang et al. [52] presented a model of condensation and evaporation rates considering the effects of capillary and pressure gradient on the liquid water motion based on the Hertz–Knudsen relation [76].

$${\mathsf{\Gamma }}_{\mathrm{c}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=-\frac{\mathrm{E}}{{\mathrm{r}}_{\mathrm{f}}}\sqrt{\frac{\left(1-\mathsf{\epsilon }\right)\left(1-{\mathsf{\epsilon }}^{\prime }\right)}{2\mathsf{\pi }\mathrm{RM}}}(\frac{{\mathrm{P}}_{\mathrm{sat}}-{\mathrm{P}}_{\mathrm{v}}}{\sqrt{{\mathrm{T}}_{\mathrm{s}}}})$$

(11)

where ε and ε′ are the porosity of fabric with and without water, respectively, and r_f is the fiber diameter. When the clothing materials were exposed to extremely hot or cold experimental conditions, the water frosting or boiling process had a significant effect on the heat and moisture transfer in the clothing materials [77,78].

5.2. Absorption and Desorption

Most fibrous materials, such as wool and cotton, are characterized by good hygroscopic properties. The absorbing process is a chemical reaction that leads to the variation of molecular energy. The latent heat equation on the absorption and desorption of the fiber was first presented by Henry based on a representative elemental volume [44]. It was supposed that there was a transient equilibrium between the fiber and the neighboring air. In addition, the values for the hygroscopic capacity were assumed to be linearly proportional to the temperature and air humidity. Therefore, the equation of moisture adsorption rate is written as,

$${\mathsf{\Gamma }}_{\mathrm{f}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=\mathrm{const}+{\mathrm{a}}_1{\mathrm{C}}_{\mathrm{a}}+{\mathrm{a}}_2\mathrm{T}$$

(12)

where Γ_f is the absorption/desorption rate of the fiber, C_f is the concentration of water vapor in the fibers, C_a is the concentration of water vapor in the air filling the inter-fiber void space, and a₁ and a₂ are both experimental estimating constants. However, compared to the experimental data, the prediction results showed great errors because the simple model of the sorption relation differed significantly from the actual sorption principle. Since then, Nordon and David [45] carried out experimental studies to investigate the relationship between the moisture content of fiber and the relative humidity. The corresponding formulation on the hygroscopic rate of fiber is established as below,

$${\mathsf{\Gamma }}_{\mathrm{f}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}{=\mathsf{\epsilon }\mathsf{{\rm K}}}_1{(\mathrm{H}}_{\mathrm{a}}-{\mathrm{H}}_{\mathrm{f}}{\left)\right(1-\exp (\mathsf{{\rm K}}}_2{\mid \mathrm{H}}_{\mathrm{a}}-{\mathrm{H}}_{\mathrm{f}}\mid ))$$

(13)

where ε is the porosity of the fiber, H_a and H_f are the relative humidity of the void space of fabrics and fibers, respectively, and K₁ and K₂ are both experimental estimating constants. Even though the improved model simulated the sorption process of fiber to some extent, it was not suitable to predict the long-time sorption. This was because the effect of the sorption-desorption kinetics of the fiber on the hygroscopic process was ignored in the model. Furthermore, the physical mechanisms of sorption-desorption of the fiber were ignored in the model.

Actually, the hygroscopic properties of fibers should be further differentiated for strongly and weakly hydrophilic fibers. Concerning the strongly hydrophilic fibers (such as wool and cotton), the moisture sorption process was divided into two stages by considering the absorption kinetics of fiber [79]. In the first stage, the moisture sorption process was simulated on the basis of the Fickian diffusion with a constant diffusion coefficient. In the second stage, the absorbed water could bring about changes in the fiber’s structure so that the rate of moisture absorption had a decreasing trend [80]. The findings of the experimental tests revealed an exponential relationship for the second-stage sorption of wool fibers. The two-stage model of sorption rate was derived and improved by Li and Holcombe [46], and Li and Luo [81,82]. The rate of moisture sorption for the two stages depended on the initial moisture content of fiber and the sorption duration, which is given by [46],

$${\mathsf{\Gamma }}_{\mathrm{f}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=\left(1-\mathsf{\alpha }\right){\mathrm{R}}_1+{\mathsf{\alpha }\mathrm{R}}_2$$

(14)

where R₁ and R₂ are, respectively, the moisture adsorption rates of the first-stage and second-stage, and α is a proportion of adsorption in the second stage. The sorption rate for the first stage was calculated by the Crank’s truncated solution which has a strict time restriction and needs long computation times. The second-stage sorption rate was obtained by an empirical equation, depending on the local relative humidity, the ambient temperature, and the sorption history of the fiber. However, it was hard to determine these parameters for simulating all stages of moisture adsorption. For simplifying the numerical calculation and increasing the application range on the model of moisture sorption, a new numerical methodology for the moisture sorption in the fibers was developed by Li [81]. A uniform diffusion equation and two sets of variable diffusion coefficients were employed to simulate the sorption process of a fiber:

$$\begin{array}{cc}\hfill \{& \begin{array}{}\mathrm{(15)}& {\mathsf{\Gamma }}_{\mathrm{f}}=\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{t}}=\frac{\partial }{\mathrm{r}\partial \mathrm{r}}({\mathrm{rD}}_{\mathrm{f}}\left(\mathrm{x},\mathrm{t}\right)\frac{\partial {\mathrm{C}}_{\mathrm{f}}}{\partial \mathrm{r}})\hfill \mathrm{(16)}& {\mathrm{C}}_{\mathrm{fs}}\left(\mathrm{x},{\mathrm{R}}_{\mathrm{f}},\mathrm{t}\right)=\mathrm{f}\left({\mathrm{H}}_{\mathrm{a}}\left(\mathrm{x},\mathrm{t}\right),\mathrm{T}\left(\mathrm{x},\mathrm{t}\right)\right)\hfill \end{array}\end{array}$$

$${\mathrm{D}}_{\mathrm{f}}\left(\mathrm{x},\mathrm{t}\right)=\{\begin{array}{cc}\left(1.04+68.2{\mathrm{W}}_{\mathrm{c}}-1342.5924{\mathrm{W}}_{\mathrm{c}}{}^2\right)\times {10}^{-14}\hfill & \mathrm{t}<540 \mathrm{s}\\ 1.616405\left(1-\exp (-18.16323\exp (-28{\mathrm{W}}_{\mathrm{c}}\right)))\times {10}^{-14}\hfill & \mathrm{t}>540 \mathrm{s}\end{array}$$

(17)

where r is the radial coordinate of a fiber, D_f is the diffusion coefficient of water vapor in the fiber for different stages, C_fs is the concentration of water vapor on the fiber’s surface, f is the nonlinear function equation, and W_c is the moisture content within the fiber of the fabric. The predicted results of the new model were compared with the experimental results, the previous two-stage model, and the Nordon-David model, as shown in Figure 6 [81]. It was clear that the simulative results outperformed the other two models and were in good accordance with the experimental results.

Instead, for the fibers of weakly hygroscopic properties (such as polyester and polyamide fiber), the process of moisture sorption was assumed as a pure Fickian diffusion [82] and could be simulated using the first-stage model of Li and Luo [81]. For the blended fabrics, the sorption rate of the water vapor showed an increase with the rising of the blending ratio of hydrophilic fiber [83]. However, the sorption of liquid water was ignored in the previous process of moisture sorption. Thus, Le et al. [73] proposed a model for simulating the absorption of water vapor and liquid water. The sorption rate equation is given below:

$${\mathsf{\Gamma }}_{\mathrm{f}}={\mathsf{\Gamma }}_{\mathrm{gs}}+{\mathsf{\Gamma }}_{\mathrm{ls}}={\mathrm{h}}_{\mathrm{m}}{\mathsf{\alpha }}_{\mathrm{s}}{\mathsf{\gamma }}_{\mathrm{gs}}\left({\mathrm{R}}_{\mathrm{f},\mathrm{ep}}-{\mathrm{R}}_{\mathrm{f}}\right)+{\mathrm{h}}_{\mathrm{m}}{\mathsf{\alpha }}_{\mathrm{s}}{\mathsf{\gamma }}_{\mathrm{ls}}\frac{{\mathsf{\epsilon }}_{\mathrm{l}}}{{\mathsf{\epsilon }}_{\mathrm{l}}{}^{\mathrm{cr}}}(\frac{{\mathrm{R}}_{\mathrm{f},\mathrm{ep}}}{{\mathrm{R}}_{\mathrm{f}}}-1)$$

(18)

where h_m is the mass transfer coefficient, α_s is the specific surface area per unit volume, γ_ls is the percentage of free water absorbed by the fiber, ε_l is the volume fraction of the liquid water, ε_l^cr is the critical value of the liquid fraction at which the liquid phase becomes mobile, R_f,ep is the equilibrium fiber regain at the fiber surface, R_f is the instantaneous fiber regain. Generally, the phase change and absorption/desorption were greatly determined by the fabric’s properties (such as fiber’s diameter, pore size, and hygroscopicity), the moisture content, and the environmental conditions [8,84]. Some influencing factors, such as convection and gravity, should be further considered in the coupled heat and moisture transfer.

6. Application of the Sustainable Method

The sustainable method is an effective tool to explore the mechanism associated with heat and moisture transfer and predict clothing performance in various environments. Besides, it can be used to design the parameters of clothing materials for improving personal thermal and moisture management. In the following paragraphs, some examples of applications are introduced.

6.1. Clothing for Extremely Cold Environments

The numerical model can represent the heat and moisture transfer in clothing materials and provide insights into the functional design of clothing for extremely cold conditions. The dynamic thermal and moisture comfort of clothing is significantly influenced by the water sorption of the fiber. An improved two-stage sorption model was developed by Li and Holcombe [46] to investigate the effect of fiber hygroscopicity on the subjective perception of coolness and dampness of clothing [85,86], and the moisture buffering of clothing during wearing [87]. A typical three-layer clothing system with a thin-inner fabric, a thick fibrous batting, and a thin-outer fabric was selected as a clothing sample for developing the heat and moisture transfer model [68,75]. The effects of positions of different battings and water condensation on thermal comfort were analyzed using the developed models. The results showed that the hygroscopic battings placed in the inner region and the non-hygroscopic battings placed in the outer region of the clothing assembly improved thermal comfort. Shen et al. [88,89] developed a 3D numerical model of heat and flow transfer through cold protective clothing for analyzing the effects of ambient temperature, air velocity, and clothing thickness on thermal insulation. Some important conclusions on the performance design of cold protective clothing were obtained. In order to analyze the behaviors of heat transfer and thermal regulation for electrically heated footwear, Liu et al. [90] recently developed a heat transfer model in electrically heated footwear in a severely cold environment. It was found that the mode of temperature control for the human skin had better thermal regulative performance and less energy consumption than the mode of temperature control for the heating pad.

6.2. Clothing for Thermal Hazardous Environments

Workers in fire-fighting, the petrochemical industry, and emergency rescue, usually encounter multiple thermal hazards, including flash fire, high-intensity thermal radiation, hot gases, contact with hot objects, hot liquid splashes and hot steam, etc. [91,92,93,94]. The heat and moisture transfer model in thermal protective clothing was developed quickly in recent decades, despite the fact that some experimental studies, such as bench-top tests and flame manikin tests, were used to evaluate the thermal protective performance of the clothing or fabric. The numerical model can be employed to predict the time to cause skin burn and conduct a parameter study. The predictive procedure based on the developed model is illustrated in Figure 7. The air gap model between the clothing and human body, the skin heat transfer model, and the Henriques burn model were integrated into the clothing model to calculate the burn time and skin temperature [95]. By changing the boundary conditions of the external environment, the heat and moisture model was employed to simulate different exposure conditions, such as flash fire [12,29], and high-level and low-level thermal radiations [96,97,98]. Some factors influencing the thermal protective performance of clothing were evaluated using the heat and moisture transfer models. The effect of moisture within the protective clothing on the radiative and conductive heat transfer was assessed by Fu et al. [23]. A stored thermal model was developed by Su et al. [30] to analyze the transmitted and stored heat transfer within protective clothing. Besides, the fabric properties, the air gap size, and the applied compression were analyzed to improve the thermal protective performance provided by the clothing.

6.3. Development of Heating and Cooling Textiles

Another category was the development of smart clothing for improving personal thermal management (PTM) by understanding the mechanism associated with heat and moisture transfer in clothing materials [99,100]. An energy storage model aiming at a new type of protective clothing with embedded phase change materials was presented [101,102,103,104,105]. The model was used to investigate the different thicknesses of the PCM layer, the melting state of PCM, and its position conditions combined in the clothing. It was reported that the most effective position for a PCM layer was near the outside of the suit [102]. Based on the understanding of the radiative heat transfer in porous materials, Cui et al. developed radiative heating textiles with the reflection of body IR [106], and radiative emission of the outer fabric [107]. It was found that the nanoporous metalized PE textile, by increasing the reflection of body IR and decreasing the radiative emission of the outer fabric, greatly outperforms other radiative heating textiles by more than 3 °C in the decrease of set-point. Based on a similar mechanism of radiative heat transfer, radiative cooling textiles were developed by Tong et al. [108], and Cui et al. [109,110] by analyzing the required visible and IR properties. A minimum IR transmittance and a maximum IR reflectance were obtained to design infrared-transparent visible-opaque fabrics (ITVOF). In addition, it is possible to improve the air/vapor permeability and mechanical properties by understanding the moisture transfer. The fiber extrusion and industrial knitting/weaving technology were used by Peng et al. [111] to produce a nano-PE textile with great cooling power, impressive wearability, and durability. The nano-PE textile is able to be mass-produced for industrial applications. Tao et al. [112] also proposed scalable industrial textile manufacturing routes for the hierarchical-morphology metafabrics, as shown in Figure 8C. The woven metafabrics provide a better cooling effect than the nano-PE fabrics proposed by Peng et al. [111], meanwhile exhibiting excellent mechanical strength, waterproofness, and breathability. This study predicts the arrival of industrial applications for radiative heating and cooling textiles.

The design of heat conduction in the clothing materials is crucial to the PTM. For conductive heating textiles, the aerogel with air-like low thermal conductivity [113], and the biomimetic fibers [114] were widely used to improve heat conductive pathways, showing great potential in thermal insulation applications (see Figure 8D). For conductive cooling textiles, Hu and co-workers [100] used highly aligned boron nitride/poly(vinyl alcohol) composite fibers to develop a thermally conductive textile by the scalable three-dimensional printing method. The textile effectively conducts the body heat away to the environment for satisfying the personal cooling requirement. Furthermore, Peng et al. [115] proposed an integrated cooling textile of heat conduction and sweat transportation, showing an excellent cooling rate and moisture permeability (see Figure 8E).

Figure 8. Design mechanism of heat transfer in textile materials for the PTM. (A) Schematic diagram of radiative heating textile [107]. (B) Design principles of radiative cooling textile [109]. (C) Schematic of the layered structure of the dual-mode textile [112]. (D) Schematic description of the fabrication of KNF aerogel fibers [114]. (E) Structure design and working mechanism of integrated cooling textile of heat conduction and sweat transportation [115]. (F) Design principles of an IR gating textile [116].

Figure 8. Design mechanism of heat transfer in textile materials for the PTM. (A) Schematic diagram of radiative heating textile [107]. (B) Design principles of radiative cooling textile [109]. (C) Schematic of the layered structure of the dual-mode textile [112]. (D) Schematic description of the fabrication of KNF aerogel fibers [114]. (E) Structure design and working mechanism of integrated cooling textile of heat conduction and sweat transportation [115]. (F) Design principles of an IR gating textile [116].

7. Summary and Outlook

The increasing pressure on the development of new clothing products for human thermal comfort and safety in cold, moderate, and extremely hot environments has prompted wide attention. The sustainable evaluation of heat and moisture transfer in clothing materials was required. The heat and moisture transfer model can represent the dynamic change of temperature, water vapor, liquid water, and bounding water that contributes to the analysis of the heat and moisture transfer mechanism in clothing materials. The parameter study of the model provides new insights and methods for the functional design of clothing materials used for fire-fighting, outdoor sports, indoor office and farm work, etc. Here, three conclusions are outlined to further promote the future study, development, and application of sustainable methods in clothing materials.

(1)

The current heat and moisture transfer models mostly focused on the one-dimensional transfer in the clothing material, while the development of the multi-dimensional models remained an exploratory stage. The multi-dimensional transfer model should be further proposed to provide a framework for simulating the radiative and convective heat transfer, diffusion, and convection of liquid water and gas, capillary transport of liquids, sorption phenomena, and phase changes. Furthermore, the multi-dimensional transfer model should consider the effects of clothing structure and human geometrical morphology for adapting the local difference of heat and moisture transfer.

(2)

The model of heat and moisture transfer provides new sights and methods for the improved design of clothing performance and human thermal comfort. In contrast to the limited use of cold protective clothing, it was clear that the heat and moisture transfer models had the widest application in clothing for thermal hazardous environments. In addition, the application of heat transfer models in smart textiles and clothing gradually attracted a lot of attention. Some heating and cooling textiles were developed by changing the energy storage and designing the pathway of radiative and conductive heat transfer. In the future, the moisture transfer model should be used to design smart regulative clothing for improving personal moisture management. Besides, the performance of other smart textiles (such as dual-mode PTM textiles and shape memory textiles) should be further improved by using the heat and moisture transfer models.

(3)

Although the sustainable methods were popularly applied to the understanding of mechanisms, product development, and performance evaluation, these sustainable methods were difficult in the wide application in the market due to their complexity and confidentiality. It is necessary to develop a sharing and easy-to-operate platform for market application. In addition, it was hard to obtain the optimal parameters for developing the clothing materials aimed at different environmental conditions. The inverse problem in the heat and moisture transfer models should be conducted to obtain the optimal parameters for performance improvement of the clothing materials.