Analysing the impact of cloth fabrics on skin temperature during and after exercise using an FDM model

This study presents a 1D finite difference model that examines the influence of cloth fabrics on skin temperature during and after exercise, considering the complex nature of the human body and its susceptibility to infections and viruses. The aim is to design comfortable, high-quality fabrics that minimize potential issues caused by body temperature fluctuations. The model incorporates various physical, physiological, and thermal parameters of cloth to develop protective clothing suitable for exercise. Numerical results were compared to previous studies that analyzed skin temperature without clothing to validate the model’s accuracy. The findings indicate a minimal difference in skin temperature when wearing cotton and polyester cloth, with polyester fabric demonstrating superior characteristics such as stretchability, durability, and sweat resistance. The thermal information obtained from this model can be utilized to design appropriate clothing for diverse weather conditions, ultimately enhancing the performance and comfort of athletes, military personnel, and individuals engaged in physically demanding work. Additionally, the model can aid in developing thermal stress protocols for infection treatment and provide guidelines for physical activity to promote healthy living. This research contributes to the field of materials research by offering valuable insights into the design and development of protective clothing for exercise. By understanding the impact of cloth fabrics on skin temperature, advancements can be made in creating clothing that optimizes human comfort and performance.


Introduction
Over the last decade, exercise clothing has become increasingly popular. Exercise enthusiasts are advertised clothes that keep them cool and dry when exercising in hot weather. Keeping thermal balance in a heated environment is crucial for preserving life and preventing heart ailments and vital for preventing performance degradation during exercise. Numerous textile experts have examined clothing fabrics designed for enhanced variability. During human-environment interaction, clothing plays an important role. Figure 1 shows the heat exchange between the clothed human body and the environment. The figure shows that heat is transferred from the human body to the environment through conduction, convection and evaporation. Still, cloth acts as a barrier to transfer the heat from the body to the environment or environment to the body. Rather than studying how clothing permits the heat exchange between the wearer and his environment, fashion and technological developments directly influence clothing design. However, the study must comprehend the connection between textile materials and human physiological processes to enhance wearer comfort and performance. The thermoregulation system kicks in to bring our body temperature back to normal after a workout, removing heat from the body [1]. The blood carries heat from different parts of your body to the skin and subsequently out into the surroundings. The main challenge during exercise in both warm and cold environments is the dissipation of the heat generated by muscular activity. The balance between heat acquisition from the environment, heat generation from metabolism, and heat loss through evaporation, radiation, conduction and convection is crucial To identify the crucial factors influencing clothing comfort during physical activity, Davis et al experimented [1]. Raccugliaa et al experimented to determine the critical factors that affect clothing comfort during physical exercise [7]. Gavin et al experimented with investigating the improvement of temperature regulation during exercise in moderate heat using clothing made from different fibers [19].
There are no known theoretical investigations in the existing literature concerning the impact of cloth fabrics on skin layer temperature during and immediately after exercise. Various experimental works were documented to investigate fabric's effect on heat transfer through the human body. But no work is done in the case of exercise. Some of the experimental work described in the literature for the study of the effect of cloth material on the human body during exercise. Nevertheless, no work has been done to study the impact of cloth on skin layer temperature during exercise in different environmental conditions. Some of the mathematical models reported in existing literature for analyzing the temperature distribution in the human skin layer without wearing cloth. But none of the models analyses the temperature distribution in a skin layer wearing cloth.
This study proposed a mathematical model to analyze the temperature distribution of the skin layer of the human body wearing cloth during and immediately after exercise. A one-dimensional unsteady state bioheat equation with a cloth system is used to measure the distribution of temperature in the skin layer wearing cloth during and immediately after exercise. Many clothing and physiological parameters have been taken to analyze the skin temperature in different environmental conditions. It is presumed that there is an insignificant amount of air gap between the protective layer and the skin surface, maintaining the continuity of heat flux at the interface.
The rest of this paper is organized as follows. Section 2 details the clothing material used in this study. Section 3 introduces the mathematical model to analyze the temperature distribution in the outer skin layer. Section 4 presents the solution of the model by FDM. Section 5 presents the secondary data used in this study. Section 6 shows the temperature profile of Skin layers. Section 7 shows the model validation. Section 8 summarizes the paper.

Clothing material for exercise
A person feels tired, worn out, sore, and possibly soaked in sweat after a hard workout. A person's feelings may vary after exercising, depending on the workout attire. The type of fabric used to make clothing is one of several aspects that might influence the comfort level of the attire. For workout clothes, generally consider two main factors: breathability and management of moisture. Although fit and feel are also crucial, it's necessary to understand how perspiration and heat influence the fabric of exercise clothing. Many fabrics are used in workout clothes, but in this study, the most common fabrics, polyester and cotton, have been taken in analyzing the effect of cloth on the human body. Polyester is mostly used fabric of workouts in any weather. Polyester has the excellent quality, that is wrinkle-resistant, and wicks away moisture. Additionally, it is light and breathable, allowing your perspiration to pass through the material and keep you dry for a long time [6]. The cotton fabric is used in regular-intensity workouts, yoga, weight training, daily wear and other low-sweat activities. Cotton fabric is also breathable, moisture-wicking, lightweight and durable [20]. The study in this paper analyses the temperature distribution in the human outer skin layer wearing different types of cloth materials during and after exercise. The following two types of clothing made from knitted fabrics are used in the study:

Made from cotton fibers
Among exercise clothing fabrics, cotton and polyester are most commonly used. Table 1 show the fabric properties of popular moisture-wicking garments for exercise. The current investigation is conducted for skin layers along the clothing made from different fibres. The core body and skin layers mainly have two components of the human body [22]. Subcutaneous tissue, epidermis, and dermis are the three sub-layers of the skin. The Skin-clothing hierarchy is shown in figure 2. In this figure l 1 , l 2 , l 3 and l 4 represent the subcutaneous tissue, dermis layer, epidermis layer and clothing layer. The subcutaneous tissue is the deepest layer of the skin. It is made up of adipose (fat) tissue, blood vessels, and nerves. The subcutaneous tissue is an insulating layer, helping regulate body temperature and providing cushioning and support. The Dermis layer is the middle layer of the skin, located beneath the epidermis. It is thicker than the epidermis and contains various structures like blood vessels, hair follicles, sweat glands, and sebaceous glands. Epidermis is the outermost layer of the skin. It acts as a protective barrier against external elements. Figure 2 represents the epidermis as a thin outer layer. The last layer in this figure represents the clothing layer covering the skin. The clothing layer provides an additional protective barrier, insulation, and aesthetic function to the skin clothing system. Blood vessels are present in both layersthe dermis and the subcutaneous tissue. The epidermis layer does not contain Blood vessels. Blood temperature and Blood flow have an impact on layer temperature variations. In this study, the total thickness of the skin with a cloth layer is taken 0.6 cm. The thickness of the skin and clothing layer is given in the table 2. The blood flow and metabolic activity in the subcutaneous tissue layer are assumed to be constant. As a result, subcutaneous tissues have the maximum heat conductivity, metabolic activity, and blood flow, whereas the epidermis has the lowest. Due to the absence of blood vessels in the epidermis, there is no blood flow, so there is hardly any metabolic activity. As a result, metabolic activity and blood flow rate are considered as negligible and thermal conductivity is assumed to be a constant.
The study was conducted using the following two cases: Case 1 A person is doing exercises for 20 min. The body generates metabolic energy when he starts exercising to keep the blood flowing. As a result, the flow of blood M̅ and metabolic activity P will be at their lowest at time t = 0, increase with time (i.e. for t > 0 ), and then become constant after a specific amount of time. At the time t = ∞, the blood flow and metabolic activities will be at their peak. Therefore, we expect that the rate of blood mass flow M̅ (t) and metabolic activity P(t) will vary exponentially with time: Figure 2. Skin-clothing hierarchy. also, P(t) = P min for t = 0 and P(t) = P max for t = ∞ Case 2 It is considered that at time t = 0, the person was initially engaged in physical activity, and at time t = ∞, he is at rest. The metabolic activity and blood flow are both at their peak at time t = 0. When t > 0, they will continue to fall until they attain their steady state condition. Therefore, we assume that the metabolic activity and blood mass flow rate in the skin layers will vary exponentially with time:

Proposed mathematical model
The equation of the bioheat transfer model explains how conduction, perfusion, and metabolism influence heat transfer. During exercise, the body generates extra heat energy, which is then released to the environment through its mechanisms. The bioheat equation with metabolic heat generation and clothing system is written as Where ρ, c, k is density, specific heat and thermal conductivity of tissue respectively. P denotes source of heat generation and T a is the temperature of arterial blood. m b and c b are the rate of blood mass flow and specific heat of blood. T skin represents skin temperature and T cl represents temperature of cloth. The last term P cl is given by Where A cl = A b f cl , f cl is the clothing area factor, A b is the surface area of clothed human body and k cl is the thermal conductivity of cloth. Heat Transfer Equation for skin layers: The unsteady state heat equation for the skin layer is given by On the left side, the first term represents the total heat storage, and on the right side, the first, second, and third terms represent diffusion, perfusion, and metabolic heat generation source, respectively.
Heat Transfer Equation for clothing layer: The blood perfusion rate and heat generation source of the body is negligible in the equation for clothing. Therefore, the equation for the clothing layer is given by Where ρ, c ̅ , k is the density, specific heat and thermal conductivity of clothing, respectively. Boundary conditions For the boundary condition, x represents the skin layers, and t denotes time. Boundary condition at x = l 0 (body core) The current study assumes that the heat stress produced by physical activity is not severe enough to affect the body's core temperature. Thus, the body core is maintained at 37°C.
Boundary condition at x = l 3 (skin surface) for unclothed body During the exercise period, skin layer's outer surface is exposed to the environment. Therefore, heat flux is dissipated for x = l 3 , and heat is lost via conduction, radiation, convection and evaporation from the outer surface. Thus the mixed boundary condition is used to calculate the net heat flux.
L and E represent latent heat and sweat evaporation rate, respectively. T ∞ represents atmosphere temperature and h represents coefficient of heat transfer. Boundary condition at x = l 4 (clothing surface) for clothed body During the exercise, the skin layer's outer surface is exposed to the environment. Therefore, heat flux is dissipated for x = l, and heat is lost via conduction, convection, radiation, and evaporation from the outer surface. Thus the mixed boundary condition is used to calculate the net heat flux [24,25].

Inner Boundary Condition
The inner boundary is maintained at a uniform 33°C. The condition at the inner boundary is given by: The FDM is used to evaluate the governing equation. In order to solve the model of equation (1), we take the following actions presented in figure 3: Construction of finite difference scheme: To analyze the temperature distribution at various points of the skin clothing layers, firstly discretized, the human body wearing cloth into N equal parts shown in figure 4. The temperature increases from the core body towards the skin's surface temperature. The governing equation is evaluated by the FDM at (i, n) grid point is provided by The central difference is used for writing the right side term, and the forward difference is used for writing the left side term. Using equations (9), (2) as: Simplify the equation The equation for human body wearing cloth is written by FDM as:

Data collection
The study analyses the effect of cotton or polyester fabric cloth on the outer skin layer of the human body during and immediately after exercise. At different ambient temperatures, the rate of basal metabolic, rate of sweat evaporating and blood flow mass at the same skin layers are determined differently; however, the thermal conductivity of the skin layers is defined differently for each layer.
To evaluate the skin temperature during and after exercise, physiological and physical parameters like the sweat evaporation rate (E), metabolic rate (P) and blood mass flow rate (M) are used shown in table 3. The data is collected from online sources and research papers. The effect of skin and clothing parameters in tables 4 and 5 has been considered for numerical simulation. With surrounding temperatures of T a = 15°C, 23°C, 33°C, calculations have been performed in two possible cases.

Results
A study is conducted to examine the temperature distribution in the outer skin layer of the human body wearing cloth and the effect of different types of clothing construction on thermal balance, and comfort during and after exercise. The study has analyzed how sweat evaporation, ambient temperatures and cloth material affect the human body's temperature distribution using the above parameters.

Effect of cloth
In this study, the temperature distribution in the outer skin of the human body wearing cloth is evaluated for both the cases during and immediately after exercise. Two types of fabric have been taken to assess the effect of cloth material on the thermal comfort of the human body during and after exercise. This study used two types of cloth material to evaluate the temperature distribution in the outer skin of the human body. Firstly, the model analyzed the temperature distribution in an unclothed human body to validate the model with previous work, then analyzed the skin temperature of a human body wearing cloth made of different fibres. The temperature distributions were measured in a skin layer of the human body wearing cloth made of two types of fibre cotton and polyester, during and after exercise. The graphs of temperature distribution in the human body wearing clothes made from different fibres have been plotted. The graph represents the temperature plotted against time. Figure 5 shows the temperature distribution in the outer skin of the human body wearing two types of cloth at ambient temperatures of 15°C, 23°C, 33°C, with varying sweat evaporation rates.
In the second case, initially, the individual is doing the exercise. Then he comes to rest. Figure 6 depicts the temperature distribution of the outer layer of the human body's skin while wearing cloth made from polyester and cotton fibers after exercise, under ambient temperatures of 15°C, 23°C, 33°C, with varying sweat evaporation rates. The x-axis of each graph represents time, while the y-axis represents temperature. Each graph consists of two lines representing the effect of polyester and cotton cloth. The graphs identify trends and patterns in how cloth materials interact with the surrounding environment and the body's cooling mechanisms. The skin layer's initial temperature is 37°C. From all the graphs of figure 6, it is observed that the temperature of the skin layers begins to decrease immediately after exercise. After 10 min, the temperature of the skin layers returns to its normal level. After exercise ceases, the body initiates a cooling-down process to restore its temperature to a normal level. This happens due to the body's thermoregulatory mechanisms, such as increased sweating and vasodilation of blood vessels near the skin's surface, which aid in dissipating heat and reducing skin temperature. These graphs show the minor difference in outer skin temperature wearing cotton and polyester cloth. The temperature of the outer layer of the skin wearing polyester is slightly higher than the temperature of the outer layer of the skin wearing cotton cloth.

Effect of ambient temperature
The temperature of the surrounding environment affects the temperature of the human body. During exercise, hot weather produces extra heat stress in the human body. At the higher temperature of the environment, the evaporation occurs in a body. For analyzing the effect of surrounding temperature on the temperature of the outer skin layer wearing different cloth during and after exercise, 23°C and 33°C are used as ambient temperatures.

Effect of ambient temperature on outer skin temperature
Firstly the study analyzed the effect of ambient temperature on the skin layer without wearing cloth to compare with previous studies, then examined the effect of ambient temperature on skin temperature wearing cloth. Table 6 shows the temperature of the skin's outer layer of a human body without wearing cloth and then wearing two types of fibres cotton and polyester made cloth during exercise at different ambient temperatures. In the case of without wearing cloth, the result obtained from the model is perfectly matched with the previous model [23].
In figures 5(c) and (e), the time period is plotted against the temperature in the outer skin layer of the human body wearing cloth with sweat evaporation rate 0.00048 g cm −2 min −1 .  From the graphs 5c, 5e and table 6, it is observed that the temperature of the outer skin of the human body wearing cotton cloth has more temperature by 0.73°C at ambient temperature 33°C for E = 0.00048 g cm −2 min −1 during exercise than the temperatures at 23°C. And the temperature of the skin's outer layer of the human body wearing polyester cloth has more temperature by 0.72°C at ambient temperature 33°C for E = 0.00048 g cm −2 min −1 during exercise than the temperatures at 23°C.

Effect of ambient temperature on outer skin temperature of the clothed body after exercise
In the second case, the person is initially doing the exercise and then comes to the rest. Twenty minutes after exercise, the temperatures of the outer skin layer were measured at different environmental temperatures for the same sweat evaporation rate. Table 7 shows the temperature of the skin's outer layer of the human body wearing two types of fibres cotton and polyester made cloth after exercise at different ambient temperatures. The present table 7 shows temperatures of the outer skin layer clothed body after exercise at various ambient temperatures. In figures 6(c) and (e), the time period is plotted against the temperature in the skin layers with a cloth immediately after the exercise with sweat evaporation rate 0.00048 g cm −2 M −1 in −1 .
From figure 6 of graphs 6c and 6e and table 7, it is observed that the temperature of the outer skin of human body wearing cotton cloth has more temperature by 0.74°C at ambient temperature 33°C for Figure 6. Estimation of temperature distribution in outer skin layers of the human body wearing cloth during exercise at ambient temperature of 15°C, 23°C, 33°C at different sweat evaporation rates. E = 0.00048 g cm −2 min −1 during exercise than the temperatures at 23°C. And the temperature of skin's outer layer of the human body wearing polyester cloth has more temperature by 0.73°C at ambient temperature 33°C for E = 0.00048 g cm −2 min −1 than the temperatures at 23°C during exercise. It was observed that the ambient temperature affects the outer skin temperature of the human body wearing cloth made of polyester or cotton.

Effect of sweat evaporation
Sweating helps cool the human body down. The value of sweating is taken differently at different ambient temperatures to analyze the effect of sweating on the skin's outer layer temperature of the human clothed body during and after exercise.

Effect of sweat evaporation on skin temperature during exercise
Calculated numerical results and skin temperature graphs have been plotted at different sweat evaporation rates.
In the case of skin temperature without wearing cloth, the table shows the comparison between the present result with previous work [23], and it was observed that the results are almost the same with the previous work. In figures 5(b) and (c) of the graphs, the time period is plotted against the temperature in the outer skin layer of the clothed body during exercise. The figures and table show that the skin temperature wearing both fabrics decreases as sweat evaporation increases. The maximum temperature in skin layer wearing cotton cloth is 36°C at E = 0 g cm −2 min −1 and 33.74°C at E = 0.00048 g cm −2 min −1 during exercise. The maximum temperature in skin layer wearing polyester cloth is 36.01°C at E = 0 g cm −2 min −1 and 33.79°C at E = 0.00048 g cm −2 min −1 during exercise. Results show that the skin's outer layer temperature of the human body wearing cloth made of polyester is a little higher than that of the skin of the human body wearing cloth made of cotton.

Effect of sweat evaporation on skin temperature after exercise
In the second case, the individual first exercises and then comes to rest. When measuring the temperature distribution in subcutaneous tissues, dermis, and epidermis after exercise, the value of sweat evaporation is calculated differently at various ambient temperatures. The graphs of the time period versus the temperature in the skin's outer layer of the human body wearing cotton and polyester cloth after exercise are shown in figures 6(b) and (c).
According to the figures, there is a minor difference between the temperature profiles of outer skin layers wearing clothes made of cotton and polyester fibres. The temperature in the outer skin layer wearing cloth made of polyester fiber is 0.01 more than the temperature in skin layer wearing cloth made from cotton fibers at ambient temperature 23°C and E = 0.00048 g cm −2 . min. Also, the temperature in the outer skin layer wearing cloth made of polyester fiber is 0.04 more than the temperature in the skin layer wearing cloth made from cotton fibers at ambient temperature 33°C and E = 0.00048 g cm −2 . min. These figures and table9 represent that the outer skin's temperature decreases while the evaporation of sweat increases.

Comparative analysis
This study analyses the effect of cloth fabric on skin layer temperature during and immediately after exercise. For analyzing the effect of cloth on skin layer temperature, firstly analyzed the skin temperature without wearing cloth during exercise. The temperature of skin layers with and without cloth during and after exercise has not been experimentally investigated in previous studies. These investigations have not been validated because of a lack of corresponding experimental data. Although some models have been developed to analyze the skin temperature without wearing cloth during exercise. Shrestha et al has used the bioheat equation to analyze the temperature distribution in the skin layer without cloth by FEM [23]. In the present study, the physiological parameters have been taken similarly to shrestha's study. The results of the proposed model have been compared with the previous model [23]. Tables 6 and 8 show the comparison between the skin layer's temperature based on different ambient temperatures and rates of sweat vaporization, respectively. Shresth's model and the current model agree to a reasonable extent. The outcomes of this model for the skin layer without clothing align with those of the preceding model's analysis. Apart from the compared parameters, the study includes estimating skin temperature wearing cloth during and after exercise. Thus this makes the model more holistic to provide more specific predictions than other specific models.

Conclusion
Regular exercise is essential for overall fitness, health and mental well-being. The clothes used during exercise can have a pretty big impact on physical and mental performance. The Mathematical model built for the distribution of temperature in the outer skin layer of the human body wearing cloth made from different fibers during and after exercise using FDM was used to forecast the impact of thermal stress. The effect of various thermal and physiological parameters of the human body and cloth has been considered to analyze the temperature profile in the outer skin layer. The temperature profiles of the skin layer wearing cotton and polyester cloth have been evaluated for both the case during and immediately after exercise. It was observed from the results that as increasing ambient temperature, the temperature in the skin layer rises during and after exercise. The skin layer can regulate its temperature by generating the necessary sweat from the body when the environment is high during exercise. In the case of after exercise, the heat is transferred more in the form of sweat. Exercise has a significant impact on the body's temperature. There is a minor difference in skin temperatures wearing cotton and polyester cloth. Cotton quickly absorbs the body's sweat and keeps it cool, but it is not stretchable and shows sweats. Therefore, polyester is better while having more temperature because it is stretchable, durable, and not showing sweat. These mathematical models can forecast how thermal stressors will impact how much an individual exercises and rests. The model has been compared with the previous studies to find the model's accuracy. It was observed that the good agreement between these models. Additionally, heat stress protocols required for infection treatment and physical activity recommendations for healthy lifestyles can be created using the thermal data from such models. But in the case of skin disease patients, polyester can harm Table 8. Comparison of skin layers temperatures between E = 0 g cm −2 min −1 and E = 0.00048 g cm −2 min −1 at T a = 23°C during exercise.
Outer skin temperature without wearing cloth the skin. In the future, this model can be implemented for skin disease patients. Also, the thermal information acquired from this model can be used to design clothes for skin disease patients. The model can help optimize the fibers to design cloth for skin disease patients. The data used in this study was taken from previous research, and the model used in this study can be implemented by collecting real-time data from the gym. These models can be enhanced to collect temperature data of human organs engaged in physical activity. Additionally, the model can be improved in the future to analyze the impact of different intensity exercises during exercise or other activities. The model can also be extended to higher dimensions.