ZHANG Wenhuan(張文歡)， LI Jun(李 俊), 2*

1 College of Fashion and Design, Donghua University, Shanghai 200051, China

2 Key Laboratory of Clothing Design and Technology, Ministry of Education, Donghua University, Shanghai 200051, China

Abstract: For improving the evaluative accuracy of thermal protective clothing performance, the estimated methods of thermal response of skin and the human body were comprehensively described and analyzed. This study reviewed the one-dimensional (1D) and multi-dimensional heat transfer models of the skin heat transfer model, including the corresponding heat and moisture transfer. Further, it investigated the influence of moisture transfer in vivo heat transfer. Moreover, the thermo-physiological model with active regulation was analyzed, especially in the local extremes, such as fingers and toes. Additionally, future research trends are discussed in estimating thermal protective performance. In developing the thermal protective model, it is essential to consider the geometric structure, local heat thermoregulation of extremities, and mass transfer inside the skin.

Key words: thermal response; thermo-physiological model; human skin; bioheat model; mass transfer

Introduction

Firefighters often encounter multiple thermal hazards, such as flame fire, high-level thermal radiation, hot gases, and hot liquid splashes in the firefighting rescue[1-4]. The thermal protective clothing ensembles could protect the human body by minimizing and preventing skin burn or heat strain. It can effectively avoid direct contact between the human body and the external environment and slow the transfer speed of environmental heat flux transfer to the skin surface[5-6]. The heat and mass transfer performance of clothing ensembles could be assessed by human and physical experiment tests[5,7]. The physical experiment is more widely used because human trials have potential risks for the subjects and obvious ethical issues[8-9].

Two physical measuring methods have been used to study skin temperature changes and assess skin burn degrees of local skin: hot plate instrumented of fabric and full-size manikin[10-11]. The evaluation process is first to establish the external thermal environment. Then the skin surface temperature or heat flow is obtained through the skin simulant sensor, which is used as the boundary condition or input parameter of the skin burn simulation model to predict skin burn degree and accomplish thermal protection performance evaluation[12-14]. Therefore, the rationality of numerical computations with bioheat models is directly related to the accuracy of prediction results.

The core of mathematical model prediction is to solve the heat transfer inside human skin and obtain the heat flux on the skin surface. An analytical bioheat model was initially developed from the Pennes model with blood perfusion, which differs from the heat conduction model applied in metal materials. The one-dimensional (1D) finite-difference model and two-dimensional (2D) finite element bioheat model were developed by Ng and Chua[15], and they compared these two models to explore the applicability of 1D. It illustrated that the heat transfer is similar between the two models. Moreover, Shenetal.[16]developed a coupled heat and moisture transfer model to examine the effect of physiological sweat on skin heat transfer, followed by a revised heat and moisture transfer model established by Fuetal.[17]. However, the above models only consider the passive heat transfer of skin, which is more suit for exposure to the flash fire in a short time. The skin can play a role in thermal regulation to control human skin temperature, especially in hot temperatures and low-level radiation. The thermoregulation models were widely used to assess human comfort and apply test thermal protective performance, which could provide more comprehensive information about the human body for emergency rescue.

In this paper, the 1D and multi-dimensional heat transfer models, coupled heat and mass transfer of internal skin were summarized. Furthermore, the human thermoregulation model was reviewed and analyzed. In addition, the future trend of the heat transfer simulation of human skin was concluded. The research will help understand the heat transfer mechanism of the human body and local internal skin. This also could provide guidelines for the thermal protection assessment and the complete standards.

1 Heat Transfer Model of Human Skin

Under low-level radiation exposure, thermal skin response estimation focuses on the skin burn degree prediction. The primary premise of skin burn prediction is obtaining the skin surface or internal temperature of skin. The surface accumulative heat flux can be calculated based on the received data, which also be applied to predicting skin burn injury according to various skin burn predictive models[17-18]. Therefore, the heat transfer model of human skin is critical in providing internal skin thermal information and assessing skin burn degree. According to the dimension of numerical simulation, the heat transfer model is divided into 1D and multi-dimensional heat transfer numerical simulation.

1.1 1D heat transfer model

1.1.1Fourierheatconductionequation

The temperature field inside the skin reflects skin temperature distribution in space and time. The classic heat conduction phenomenon is described by the partial differential equation combined with Fourier’s law and energy conservation law, as shown in

(1)

whereρ,cp, andkare the density, specific heat, and thermal conductivity of human skin, respectively;T(x,t) is the temperature of the skin layer at depthxand timet.

The heat conduction equation has been widely used in skin burn evaluation and standardized. However, this method only uses the skin as a rigid body. It does not consider the influence of the internal tissue structure of local skin, such as blood flow and metabolism rate.

There is a particular delay response for the external heat flux in the human skin compared to metal materials, with a low internal heat transfer coefficient and a high thermal capacity. Non-Fourier heat transfer models have been proposed, considering the thermal delay of the human body, including the thermal wave model of bioheat transfer (TWMBT) and the dual-phase lag model of bioheat transfer (DPLMBT)[19-20]. These models broke through the assumption that the heat transfer velocity in the medium was infinite, taking into account the thermal relaxation time required for the dynamic balance of heat transfer.

The calculated method of the TWMBT model is shown in

(2)

whereρb,cp,b, andTbare the blood density, specific heat, and temperature, respectively;wbis the blood perfusion rate;Qmandqmare the heat generated by physiology (metabolism) and related heat flux, respectively.Qrandqrare the heat generated by spatial distribution (spatial heating) and relevant heat flux, respectively.τis the thermal relaxation time of the medium.

The formula of the DPLMBT model is shown in

(Tb-T)+qr+qm+

(3)

whereτtandτqare the thermal relaxation time of the medium and the heterogeneous medium’s microstructure interaction, respectively.

Although the thermal wave model considers the thermal relaxation behavior and conforms to the second law of irreversible thermodynamics[21-22], there are many controversies in describing the rationality of rapid heat transfer under micro-scale action. These thermal wave models only illustrated the time microscale action of heat transfer of the human skin but did not consider the relationship between heat transfer and space.

1.1.2Pennesbioheattransfermodel

Given the shortcomings of the heat conduction equation in simulating human body thermal-physiological regulation, Torvi and Dale[23]introduced the Pennes bioheat equation, as shown in Eq.(4), to distinguish heat transfer between the human body and physical materials.

wbρbcp,b(Tb-T(x,t))+Qm,

(4)

The model was developed based on assumptions[22-23]. (1) The skin heat transfer is 1D along with the thickness. (2) The thermophysical properties of each layer of skin tissue are constant, and each layer is different. (3) The blood temperature is constant, equal to the core temperature of the human body. (4) The local blood flow rate remains constant.

Some studies have shown that blood perfusion can be ignored in short-term, high-intensity radiative heat exposure conditions. However, blood perfusion is still necessary for low-level radiative conditions[22]. This is because the reaction time of human blood perfusion is 20 s, which far exceeds the time of skin burn in low-level radiation conditions. Additionally, the effect of metabolic rate was simplified in the Pennes bioheat equation. In practice, the skin surface temperature, relative humidity (RH), and the microclimate RH between the skin surface and inner clothing layer are influenced by metabolic heat flux, which is the crucial heat transfer parameter in assessing the thermal response of the human body[24].

1.2 Multi-dimensional heat transfer model

The 2D heat transfer model containing different properties of each layer of human skin was constructed to predict skin burn degrees accurately compared to the previous 1D model. The finite difference and finite element methods were applied to solve the internal heat transfer model[25]. The results showed that the temperature change was the same in the above two models, suggesting that the 1D model could effectively evaluate skin burn injury. In addition to the radiant heat exposure and flash fire, this method also could assess the injury threshold for the hot steam and hot water splash exposure condition[26].

Moreover, the three-dimensional (3D) skin heat transfer model was established and refined the effect of convection and heat dissipation of blood on skin heat transfer[27]in the medical field. Based on the consideration of blood perfusion, metabolic heat production, and conduction heat transfer of human tissues in the Pennes bioheat transfer model, the blood perfusion rate was suggested to function the temperature difference between arteries and veins. The temperatures of arteries and veins were assumed to be the human core and local tissue temperature, respectively. However, it has been found that the effect of intravascular reflux on heat transfer needs to be considered when the diameter is higher than 50 μm[27]. Thus, Zareetal.[27]constructed a 3D skin heat transfer model, refined the effect of blood convection and heat dissipation on skin heat transfer, explored the convective heat transfer among blood, blood vessels, and trans-vascular tissues in radiative conditions, and optimized the predictive results of skin burns. However, the corresponding 3D model is not applied to testing thermal protective clothing and establishing relative standards.

2 Coupled Heat and Mass Transfer Model of Skin

The thermal protective performance is significantly influenced by moisture, which is contributed by the high humidity environment and body sweat[28]. This could be attributed to that moisture could change thermo-physical properties, such as thermal conductivity, specific heat capacity, and optical properties (including radiant absorption coefficient and transmissivity)[26-27]. Moreover, the skin tissues can absorb or desorb moisture through micropores that change their thermal properties[28-30]. The thermal conductivity of water is 0.61 W/(m·K) (at 25 ℃), higher than the values of the epidermis and dermis, which are about 0.225 W/(m·K) and 0.523 W/(m·K), respectively[31]. Shenetal.[16]developed a heat and mass transfer model in multi-layer skin tissues to investigate the effect of moisture content, as shown in Eq. (5). The results revealed that water vaporization and diffusion heat loss could cool down the epidermis layer. In contrast, blood perfusion and water diffusion can heat the subcutaneous tissue. The results also demonstrated that the model of skin heat flux considering moisture could be used to evaluate the thermal protective performance.

wbρbcp,b(Tb-T(x,t))+Qm-Qd-Qv,

(5)

whereQdandQvare heat loss of water diffusion and water vaporization, respectively.

However, experimental studies have shown that the skin burn degree will be out of order in high temperatures and humidity[26]. This may be attributed to the high internal water content of the human skin with the evaporation of moisture in the external environment. However, this disorder phenomenon is only described qualitatively and lacks quantified studies. Furthermore, the relevant model is still unable to simulate anomalous phenomena.

3 Thermoregulation Model of Human Body

In addition to the passive response of human skin to the external environment, there is an internal active regulation process, which directly leads to changes in the skin surface temperature collected in the first step, and affects the internal temperature of skin and skin burn injury assessment.

Adding a temperature control system to adjust the skin surface temperature had been applied in the thermal comfort research, using a human thermal-physiological regulative model to control sweating thermal manikin or numerical manikin[32]. The representative models are the Fiala and the UC-Berkely models[33-35]. However, the limbs are widely simplified into cylinders, truncated cones, and rectangles without considering the actual shape. The volume-specific surface area in the limbs, especially hands and feet, is much smaller than the average trunk and the entire body[36]. And the blood flow rate in the fingers and toes varies greatly in hot and cold environments. Nagasakaetal.[37]reported that the maximum values has 600 times more blood flow than the minimum in fingers. The fold changes in blood flow through the fingers are unparalleled in any hand area. The maximum blood flow in the human trunk is only 56 times the minimum[38]. Blood flow is essential in transferring heat to body parts such as the human body, especially in extreme regions away from the core areas, such as the chest and stomach[39]. The finger blood vessels may constrict to reduce heat transfer into the body through the heated hand when the human body is hyperthermic.

4 Conclusions

Although numerical methods have been developed to explore the heat distribution of internal skin and assess skin burn injury, there are some limitations due to technical difficulties. In the future, the realistic geometric surfaces of the extreme, such as fingers and toes, should be considered comprehensively in establishing a numerical model, especially in 3D models. This could provide more information about the convective and radiative heat transfer due to the spatial relationship between the skin surface and the environment. Furthermore, the influence of continuous perspiration on the heat and mass transfer of skin should be analyzed comprehensively.

In summary, the present predicted results with the heat transfer model deviate from reality under specific conditions. Thus, it is necessary to establish the expected model with more realistic geometric surfaces, active thermal regulationinvivo, and mass transfer inside the skin. This could provide more accurate methods for evaluating the thermal protection performance of clothing and explain more mechanisms of coupled heat and mass transfer inside the skin. In addition, the progress of the numerical simulation method above will lay a foundation for revising the standard.