Numerical study of the air gap between fire-protective clothing and the skin

Abstract

The analysis of the air gap between fire-protective clothing and the skin plays a crucial role in evaluating the protective performance of the clothing. However, the more accurate the analysis of the air gap, the more complex the air-gap model. This article introduces a novel air-gap model that stands halfway in terms of accuracy and complexity between other two models that already exist in the literature. A comparison between the performances of fire-protective clothing predicted by using the three air-gap models is discussed in this article. Different parameters that affect heat transfer within the air gap and hence the protective performance of the clothing were studied to assess the novel air-gap model compared with the other two models. Despite its simplicity, the novel air-gap model predicted the performance of fire-protective clothing as accurately as the most realistic model.

Introduction

Workers in many fields and industries such as petroleum and petrochemical industries, firefighting, and even race car driving rely on protective clothing to protect themselves from fire exposure. Exposure to fire can result in skin burn injuries that range from first-degree to third-degree burns, depending on the intensity and duration of exposure. The type of protective clothing varies from one application to another, depending on the probability and type of exposure. Nevertheless, the typical protective clothing system consists of at least one fire-resistant fabric, the human skin and an air gap between the fabric and the skin. Evaluating the thermal protective performance (TPP) of the clothing is accomplished by estimating the total energy transfer through the clothing that causes burn injury to the human skin on the other side of the clothing. Bench top tests [1–4] were used in evaluating the TPP of the clothing against a variety of different types of exposure. For example, according to ASTM D 4108 [2], the fabric specimen is exposed to flame contact from a Meker burner, while ASTM F 1939 [3] employs a set of quartz tubes to produce a purely radiant exposure. In addition, NFPA 1971 [4] uses a Meker burner and quartz tubes to produce both convective and radiant exposures. On the other hand, manikin tests [5] are used to evaluate the TPP of the whole garment at different locations of the manikin body.

Modeling of the thermal performance of protective clothing has been extensively reported in the literature during the past decade. Torvi and co-workers [6,7] and Zhu and Zhang [8] modeled heat transfer in a single layer of a fire-resistant fabric during local flame and radiant exposure tests, respectively. Mell and Lawson [9] modeled heat transfer in firefighters’ clothing during radiant exposure. Song et al. [10] modeled coupled heat and mass transfer in firefighters’ clothing during a local flame test. Zhiying et al. [11] tested the TPP and moisture transport of firefighter’s clothing. Li and Zhu [12] developed a mathematical model for moisture and heat transfer coupled with phase change materials in porous textiles. Mercer and Sidhu [13] investigated the performance of protective clothing with embedded phase change material.

Pennes’s model [14] was extensively used in the literature to model heat transfer in the human skin. Ng and Chua [15] developed and compared one-dimensional and two-dimensional numerical codes to predict the state of skin burns. Jiang et al. [16] developed a one-dimensional multi-layer model to predict the effects of thermal physical properties and geometrical dimensions on the transient temperature and injury distributions in the skin. Most of these models employed the burn integral of Henrique and Moritz [17] to estimate times to receive burn injuries.

The air gap between protective clothing and the skin plays an important role in the protective performance of the clothing since the energy transfer through the air gap determines the level of exposure on the skin. This role has been addressed in the literature by many researchers. Torvi and co-workers [6,18] investigated the influence of the air gap width on the protective performance of a single layer fire-resistant fabric during a contact flame bench top test. Sawcyn and Torvi [19] and Talukdar et al. [20] attempted to improve the modeling of the air gap in bench top tests of protective fabrics. Ghazy and Bergstrom [21] introduced a more realistic analysis for the transient heat transfer in the air gap between protective clothing and the skin. Ghazy and Bergstrom [22] further extended this analysis to the air gaps between the fabric layers in firefighters’ protective clothing. The three-dimensional body scanning technology was used [23–26] to determine the width and distribution of air gaps between the protective garment and the manikin body and the influence of these gaps on the protective performance of the garment.

The size of the air gap between the clothing and the skin determines the modes of energy transfer within the air gap. Torvi and co-workers [6,18] demonstrated numerically and by flow visualization that convection and radiation heat transfer modes occur within the air gaps of the contact flame bench top test for gap widths that are bigger than 6.4 mm (1/4 in.), while energy transfers by conduction and radiation modes for smaller gaps. In addition, thermal radiation was shown to be the dominant mode of heat transfer within the air gaps regardless of size [6,7,18–21]. Moreover, the more accurate the analysis of the air gap, the closer is the evaluation of the protective performance of the clothing to its actual value. Nevertheless, a small improvement in the accuracy of evaluating the protective performance of the clothing may require more complex calculations.

Given this context, this article assesses the effect of the air gap analysis on the evaluation of the performance of protective clothing during fire exposure. The article holds a comparison between two extremes in modeling the air gap between protective clothing and the skin: a simple model (SM) that uses approximate analysis for the air gap and a realistic model that accounts for the combined conduction–radiation heat transfer in the gap. Unlike the SM that ignores the interaction between the air gap and thermal radiation through the gap, the realistic model deals with the gap as a radiation participating medium that absorbs and emits thermal radiation. Furthermore, this article introduces a simplified conduction–radiation model (SCRM) that stands halfway between the two models as an attempt to balance between the accuracy and complexity in modeling the air gap in protective clothing. In addition, the performance of protective clothing was predicted by the three models and compared for different parameters that affect heat transfer through the air gap such as the air gap absorption coefficient, air gap width and fabric thickness.

Problem formulation

A typical protective clothing system that consists of a single layer of Kevlar®/PBI fire-resistant fabric, the human skin and an air gap between the fabric and the skin is shown in Figure 1. The human skin consists of the epidermis, dermis and subcutaneous layers, where blood perfusion takes place in the latter two layers. The fabric is exposed to a flame contact with a nominal heat flux of about 83 kW/m² to simulate flash fire exposure. Energy is transferred by both convection and radiation from the flame to the fabric. A portion of this energy is stored inside the fabric, raising its temperature and causing thermochemical reactions within the fabric, while another portion of this energy is transferred by radiation from the fabric to the ambient environment. For air gap widths that are equal or less than the air gap width of the standard TPP test [2] of 6.4 mm (1/4 in.), energy transfers by both conduction and radiation from the backside of the fabric to the skin, raising the skin temperature and potentially causing skin burn injuries. After exposure ends, energy transfers by convection and radiation from the fabric to the ambient environment.

Figure 1.

The protective clothing system schematic diagram.

Heat transfer in the fire-resistant fabric

The energy equation for the Kevlar®/PBI fabric is expressed [6,21,27] as

$\rho C^A(T)\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k(T)\frac{\partial T}{\partial y})+\gamma \sigma {\varepsilon }_g{T}_g^4\exp (-\gamma y)\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}0<t\le t_{\exp }$

(1a)

$\rho c_P(T)\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k(T)\frac{\partial T}{\partial y})\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>t_{\exp }$

(1b)

where ρ and k are the fabric density and thermal conductivity, respectively, σ is the Stefan–Boltzmann constant, ${\varepsilon }_g$ is the hot gas emissivity, T_g is the hot gas temperature (K), γ is the extinction coefficient of the fabric, $C^A$ is the fabric apparent heat capacity [6,7] that accounts for the evaporation of the moisture enclosed in the fabric’s pores and the energy consumed by the thromochemical reactions in the fabric such as fabric pyrolysis and $t_{\exp }$ is the exposure duration.

The boundary conditions for the fabric energy equation are as follows

$-k_{\mathrm{fab}}(T)\frac{\partial T_{\mathrm{fab}}}{\partial y}{|}_{y=0}=h_{\mathrm{fl}}(T_g-T_{\mathrm{fab}(y=0)})-\sigma {\varepsilon }_{\mathrm{fab}1}(1-{\varepsilon }_g)(T_{\mathrm{fab}(y=0)}^4-T_{\mathrm{amb}}^4)t>0$

(2)

$-k_{\mathrm{fab}}(T)\frac{\partial T_{\mathrm{fab}}}{\partial y}{|}_{y=L_{\mathrm{fab}}}=q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}-k_{\mathrm{air}}(T)\frac{\partial T_{\mathrm{air}}}{\partial y}{|}_{y=L_{\mathrm{fab}}}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0$

(3)

where $h_{\mathrm{fl}}$ is the convective heat transfer coefficient from the flame to the fabric, ${\varepsilon }_{\mathrm{fab}1}$ is the fabric exposed surface emissivity, $T_{\mathrm{amb}}$ is the ambient temperature (300 K) and $k_{\mathrm{air}}$ is the air gap thermal conductivity. $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}$ is the emitted radiation from the fabric backside surface, which varies according to the analysis of the thermal radiation through the air gap.

The fabric initial condition is

$T_{\mathrm{fab}}(y,t=0)=T_{\mathrm{amb}}$

(4)

Heat transfer in the human skin

The bioheat equation developed by Pennes [14] was employed to model heat transfer in the skin tissues. The energy equations for the three layers (epidermis, dermis and subcutaneous) of the skin are written as

$(\rho c_P){}_{\mathrm{ep}}\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k_{\mathrm{ep}}\frac{\partial T}{\partial y})$

(5)

$(\rho c_P){}_{\mathrm{ds}}\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k_{\mathrm{ds}}\frac{\partial T}{\partial y})+(\rho c_P){}_b{\omega }_b(T_{\mathrm{cr}}-T)$

(6)

$(\rho c_P){}_{\mathrm{sc}}\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k_{\mathrm{sc}}\frac{\partial T}{\partial y})+(\rho c_P){}_b{\omega }_b(T_{\mathrm{cr}}-T)$

(7)

where ${\omega }_b$ is the blood perfusion rate within the dermis and subcutaneous layers, $T_{\mathrm{cr}}$ is the human core body temperature and ρ,c_P and k have their conventional meaning.

The skin boundary conditions are

$-k_{\mathrm{ep}}(T)\frac{\partial T_{\mathrm{ep}}}{\partial y}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}=q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}-k_{\mathrm{air}}(T)\frac{\partial T_{\mathrm{air}}}{\partial y}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0$

(8)

$T_{\mathrm{sc}}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}+L_{\mathrm{ep}}+L_{\mathrm{ds}}+L_{\mathrm{sc}}}=T_{\mathrm{cr}}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0$

(9)

where $L_{\mathrm{ep}}$ , $L_{\mathrm{ds}}$ and $L_{\mathrm{sc}}$ are the widths of the epidermis, dermis and subcutaneous layers, respectively, and $T_{\mathrm{cr}}$ is the core body temperature. The radiation heat flux at the air–skin interface, $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}$ , varies as well according to the air gap analysis. The continuity of temperature and heat flux represents the inner boundary conditions between the three layers of the skin.

The initial condition of the skin is introduced by a linear temperature distribution between 32.5°C at the epidermis surface and 37°C at the subcutaneous base (core body temperature). When the basal layer (interface between the epidermis and the dermis layers) temperature reaches 44°C, skin burn injury takes place. The integral of Henrique and Moritz [17] was employed to predict times to receive skin burn injuries as follows

$\varphi ={\int }_0^{t}P\exp (-\frac{\Delta E}{\mathrm{RT}})dt$

(10)

where ϕ is a quantitative measure of skin damage, P is a pre-exponential factor, $\Delta E$ is the activation energy of the skin and R is the ideal gas constant. The basal layer temperature is used in the integral to predict times to receive first- and second-degree burns while the dermal base (interface between the dermis and subcutaneous layers) temperature is used to predict times to receive third-degree burns.

Heat transfer in the air gap

There are three approaches considered here to model the conduction and radiation heat transfer within the air gap between protective clothing and the skin. The essential differences between the three approaches are the accuracy in modeling the thermal radiation through the gap and the coupling between the two modes of heat transfer – conduction and radiation – within the gap.

Simple model

Most studies reported in the literature [6–8,10,11,18,19,23,24] used a relatively simple model for the air gap between the fabric and the skin. For example, they decoupled the conduction and radiation heat transfer through the air gap and instead assumed steady-state conduction and only surface radiation heat transfer within the air gap. The conduction and radiation heat transfer within the gap are introduced by

$k_{\mathrm{air}}(T)\frac{\partial T_{\mathrm{air}}}{\partial y}{|}_{y=L_{\mathrm{fab}}}=k_{\mathrm{air}}(T)\frac{\partial T_{\mathrm{air}}}{\partial y}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}=k_{\mathrm{air}}(T)\frac{T_{\mathrm{fab}}{|}_{y=L_{\mathrm{fab}}}-T_{\mathrm{ep}}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}}{L_{\mathrm{air}}}$

(11)

$q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}=q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}=\frac{\sigma (T_{\mathrm{fab}}^4{|}_{y=L_{\mathrm{fab}}}-T_{\mathrm{ep}}^4{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}})}{\frac{1}{{\varepsilon }_{\mathrm{fab}2}}+\frac{1}{{\varepsilon }_{\mathrm{ep}}}-1}$

(12)

where ${\varepsilon }_{\mathrm{fab}2}$ and ${\varepsilon }_{\mathrm{ep}}$ are the fabric backside surface emissivity and the epidermis surface emissivity, respectively, and the radiation heat fluxes $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}$ and $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}$ are employed in equations (3) and (8), respectively. All studies in the literature that utilized the SM disregarded the variation in the thermal conductivity of the air gap with temperature. However, this parameter was considered in this article to preclude its effect when comparing between the three air-gap models.

Combined conduction–radiation model

A second approach to model the air gap between protective clothing and the skin was developed by Ghazy and Bergstrom [21]. They dealt with the air gap as a radiation participating medium that absorbs and emits thermal radiation, where the conduction and radiation heat transfer within the gap was coupled by the air gap energy equation as follows

$\rho (T)c_P(T)\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k(T)\frac{\partial T}{\partial y})-\frac{\partial q{″}_R}{\partial y}$

(13)

The boundary conditions for the air gap are obtained from the continuity of temperature between the air gap and both the fabric and the skin (epidermis) surface as follows

$T_{\mathrm{air}}{|}_{y=L_{\mathrm{fab}}}=T_{\mathrm{fab}}{|}_{y=L_{\mathrm{fab}}}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0$

(14)

$T_{\mathrm{air}}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}=T_{\mathrm{ep}}{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}t>0$

(15)

The air gap initial condition is

$T_{\mathrm{air}}(y,t=0)=T_{\mathrm{amb}}$

(16)

In order to estimate the divergence of radiative heat flux through the air gap $\frac{\partial q{″}_R}{\partial y}$ and the radiation heat fluxes on both sides of the air gap, $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}$ and $q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}$ , the radiative transfer equation (RTE) for the air gap has to be solved along with its boundary conditions as follows.

The RTE for the air gap as a gray, absorbing and emitting medium [28] is written as

$\frac{\mathrm{dI}(\overrightarrow{r},\stackrel{\wedge }{s})}{\mathrm{ds}}=-\kappa (\genfrac{}{}{0ex}{}{\rightharpoonup }{r})I(\genfrac{}{}{0ex}{}{\rightharpoonup }{r},\stackrel{\wedge }{s})+\kappa (\genfrac{}{}{0ex}{}{\rightharpoonup }{r})I_b(\genfrac{}{}{0ex}{}{\rightharpoonup }{r})$

(17)

where I is the radiation intensity, which varies with the spatial position $\genfrac{}{}{0ex}{}{\rightharpoonup }{r}$ and the angular direction $\stackrel{\wedge }{s}$ , κ is the air gap absorption coefficient, s is the geometric distance and I_b is the black body intensity.

The boundary conditions for the air gap RTE are written as

$I_{\mathrm{fab}}(\overrightarrow{r},\stackrel{\wedge }{s})={\varepsilon }_{\mathrm{fab}2}(\overrightarrow{r})I_{b,\mathrm{fab}}(\overrightarrow{r})+\frac{{\rho }_{\mathrm{fab}2}(\overrightarrow{r})}{\pi }{\int }_{\stackrel{\wedge }{s}\text{'}·\stackrel{\wedge }{n}<0}I(\overrightarrow{r},\stackrel{\wedge }{s})|\stackrel{\wedge }{s}\text{'}·\stackrel{\wedge }{n}|d\Omega \text{'}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\mathrm{at}y=L_{\mathrm{fab}}$

(18)

$I_{\mathrm{ep}}(\overrightarrow{r},\stackrel{\wedge }{s})={\varepsilon }_{\mathrm{ep}}(\overrightarrow{r})I_{b,\mathrm{ep}}(\overrightarrow{r})+\frac{{\rho }_{\mathrm{ep}}(\overrightarrow{r})}{\pi }{\int }_{\stackrel{\wedge }{s}\text{'}·\stackrel{\wedge }{n}<0}I(\overrightarrow{r},\stackrel{\wedge }{s})|\stackrel{\wedge }{s}\text{'}·\stackrel{\wedge }{n}|d\Omega \text{'}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\mathrm{at}y=L_{\mathrm{fab}}+L_{\mathrm{air}}$

(19)

where ${\varepsilon }_{\mathrm{fab}2}$ and ${\rho }_{\mathrm{fab}2}$ are the fabric backside emissivity and reflectivity, respectively, ${\varepsilon }_{\mathrm{ep}}$ and ρ_ep are the epidermis surface emissivity and reflectivity, respectively, $\stackrel{\wedge }{s}\text{'}$ is the reflected ray unit direction, $\stackrel{\wedge }{n}$ is the unit normal to the surface and $d\Omega \text{'}$ is the solid angle containing the reflected ray. The numerical solution of RTE along with its boundary conditions can be found in the study of Chai and Patankar [29].

The divergence of radiative heat flux in equation (13) is calculated as

$\frac{\partial q{″}_R}{\partial y}=\kappa (4\pi I_b(\overrightarrow{r})-G(\overrightarrow{r}))$

(20)

The incident radiation $G(\overrightarrow{r})$ is defined as

$G(\overrightarrow{r})={\int }_{4\pi }I(\overrightarrow{r},\stackrel{\wedge }{s})d\Omega$

(21)

The radiation heat fluxes on both sides of the air gap (equations (3) and (8)) are calculated as

$q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}={\int }_{4\pi }I(\overrightarrow{r},\stackrel{\wedge }{s})(\stackrel{\wedge }{s}·{\stackrel{\wedge }{e}}_y)d\Omega {|}_{y=L_{\mathrm{fab}}}$

(22)

$q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}={\int }_{4\pi }I(\overrightarrow{r},\stackrel{\wedge }{s})(\stackrel{\wedge }{s}·{\stackrel{\wedge }{e}}_y)d\Omega {|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}$

(23)

Simplified conduction–radiation model

This model deals with the air gap as a radiation participating medium that only absorbs thermal radiation. The ability of the air gap to emit thermal radiation was disregarded while its ability to absorb thermal radiation was considered via the exponential decay that is introduced by Beer’s law [30]. The conduction and radiation heat transfer within the air gap is coupled by the air gap energy equation as follows

$\rho (T)c_P(T)\frac{\partial T}{\partial t}=\frac{\partial }{\partial y}(k(T)\frac{\partial T}{\partial y})-\frac{\partial }{\partial y}q{″}_R(y)$

(24)

where $q{″}_R(y)$ is the radiation heat flux within the air gap, which is derived by Beer’s law as

$q{″}_R(y)=q{″}_R{|}_{y=L_{\mathrm{fab}}}\exp (-\kappa y)$

(25)

where κ is the air gap absorption coefficient and $q{″}_R{|}_{y=L_{\mathrm{fab}}}$ is the radiation heat flux emitted from the fabric backside, which is calculated as

$q{″}_R{|}_{y=L_{\mathrm{fab}}}=\frac{\sigma (T_{\mathrm{fab}}^4{|}_{y=L_{\mathrm{fab}}}-T_{\mathrm{ep}}^4{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}})}{\frac{1}{{\varepsilon }_{\mathrm{fab}2}}+\frac{1}{{\varepsilon }_{\mathrm{ep}}}-1}$

(26)

where ${\varepsilon }_{\mathrm{fab}2}$ is the fabric backside emissivity and ${\varepsilon }_{\mathrm{ep}}$ is the epidermis surface emissivity.

The boundary and initial conditions for the air gap energy equation (equation (24)) are introduced by equations (14)–(16), similar to the case of the combined conduction–radiation model (CCRM). The radiation heat fluxes on both sides of the air gap (equations (3) and (8)) are estimated as follows

$q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}=\frac{\sigma (T_{\mathrm{fab}}^4{|}_{y=L_{\mathrm{fab}}}-T_{\mathrm{ep}}^4{|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}})}{\frac{1}{{\varepsilon }_{\mathrm{fab}2}}+\frac{1}{{\varepsilon }_{\mathrm{ep}}}-1}$

(27)

$q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}+L_{\mathrm{air}}}=q{″}_y(\overrightarrow{r}){|}_{y=L_{\mathrm{fab}}}\exp (-\kappa L_{\mathrm{air}})$

(28)

where $L_{\mathrm{air}}$ is the air gap width. Equations (26) and (27) are basically the same as equation (12).

Results and discussion

The energy equations for the fabric, air gap and skin were solved along with their boundary conditions by the finite volume method [31] using the Gauss–Seidel point-by-point iterative scheme. For each time step, temperatures from the previous time step were used as initial values for the iteration loop. Then, new temperatures were calculated by visiting each control volume starting from the fabric surface to the subcutaneous base. When convergence was achieved, the basal layer and the dermal base temperatures were used in Henriques’ integral (equation (10)) to predict times to receive skin burns.

The fabric and hot gas parameters used in the simulation are listed in Table 1, while the human skin thermophysical properties are listed in Table 2. The simulation assumed an exposure of 10 s followed by 90 s of cool down. The three models were assigned the same values for the time step and grid sizes in order to eliminate their effect when comparing between the models. Comparisons were held between the novel model–SCRM–and the other two models that already exist in the literature to investigate how capable the novel model is in accurately predicting the clothing performance.

Table 1.

Kevlar®/PBI and burner parameters [21].

Property		Value
Lfab	Fabric thickness	0.6 mm
Wfab	Fabric width	0.05 m (2 in.)
ρfab	Fabric density	323 kg/m3
γfab	Fabric extinction factor	0.01
ɛfab	Fabric emissivity	0.9
τfab	Fabric transmissivity	0.01
Tg	Hot gases temperature	2000 K
ɛg	Hot gases emissivity	0.02
hfl	Flame convective heat transfer coefficient	40 W/m2K

Table 2.

Human skin thermophysical properties [21].

Property	Epidermis	Dermis	Subcutaneous	Blood
Thickness (m)	8 × 10−5	2 × 10−3	1 × 10−2	–
Density (kg/m3)	1200	1200	1000	1060
Specific heat (J/kg°C)	3598	3222	2760	3770
Thermal conductivity (W/m°C)	0.255	0.523	0.167	–
Blood perfusion rate (m3/s)/m3 tissue	–	–	–	1.25 × 10−3

The SM decouples the conduction and radiation heat transfer within the air gap while the other two models combined them. In order to justify the influence of only coupling the conduction and radiation heat transfer within the air gap on predicting the performance of protective clothing, simulations were first carried out for the CCRM and SCRM using an air gap absorption coefficient of 0 m⁻¹ while the SM implicitly assumes a zero air gap absorption coefficient by considering only the surface radiation through the air gap.

A comparison between the three air-gap models in predicting the temperature distributions within the gap is shown in Figure 2. The temperatures predicted by the CCRM and SCRM are identical for the fabric backside, air gap center and epidermis surface. Despite the big difference in the number of calculations required by both models, the only physical difference between the two models is the way that the air gap interacts with thermal radiation. This interaction is related to the absorption coefficient of the gap. Therefore, the two models behave the same way for the case of a zero air gap absorption coefficient. In addition, the figure shows that the SM over-predicted the temperature of the fabric backside, while it under-predicted the temperatures of the air gap center and epidermis surface. Moreover, the discrepancy between the predictions made by the SM and those made by the other two models is evident at the air gap center. This discrepancy is attributed to the decoupling between conduction and radiation heat transfer within the air gap that the SM assumes.

Figure 2.

Comparison between the temperatures predicted by the three air-gap models at three locations in the air gap: (a) fabric backside, (b) the air gap center and (c) epidermis surface.

More insight can be acquired from the energy transfer within the gap. Figure 3 shows a comparison between the three models in predicting the conduction and radiation heat fluxes within the air gap (the case of a zero absorption coefficient). The conduction and radiation heat transfer predicted by the CCRM and SCRM are identical, which is consistent with the temperature distributions shown in Figure 2. In addition, the decoupling between the conduction and radiation heat transfer that is assumed by the SM caused the SM to underestimate the conduction heat flux and overestimate the radiation heat flux within the gap. Furthermore, the deviation in predicting the conduction heat flux is about double that of the radiation heat flux.

Figure 3.

Comparison between the predictions made by the three models for the energy transfer within the air gap: (a) conduction heat flux at the fabric–air interface and (b) radiation heat flux emitted from the fabric backside surface.

The influence of a variation in the air gap absorption coefficient on skin burn predictions made by the three models is shown in Table 3. In fact, a variation in the absorption coefficient of the gap is related to a variation in the concentration of the combustion products in the gap, which result from the pyrolysis of the fabric. Table 3 shows that the SM predicted skin burn injuries to take place later that did the other two models, especially third-degree burn injuries. In addition, since the SM does not account for the variation in the absorption coefficient of the gap, it produces a sole set of times to skin burn injuries. On the other hand, the SCRM precisely predicted times to first- and second degree-burns compared with the CCRM; however, there is a deviation between times to third-degree burns predicted by the two models. This deviation increases as the air gap absorption coefficient increases. The reason for that is the SCRM ignored the thermal radiation emitted by the gap, which increases as the absorption coefficient increases. Nevertheless, the two models are identical when the air gap absorption coefficient is equal to zero.

Table 3.

Influence of the air gap absorption coefficient on skin burn predictions.

Air gap absorption coefficient (m−1)	Time to receive skin burn (s)
	Simple model			Combined conduction– radiation model			Simplified conduction– radiation model
	First degree	Second degree	Third degree	First degree	Second degree	Third degree	First degree	Second degree	Third degree
0	5.6	5.8	79.4	5.5	5.7	39.6	5.5	5.7	39.6
5	5.5	5.8	42.3	5.5	5.8	42.3
10	5.5	5.8	45.7	5.5	5.8	45.9
15	5.6	5.8	50.8	5.6	5.8	51.3
20	5.6	5.9	59.4	5.6	5.9	61.1

The air gap width is another parameter that affects the performance of protective clothing and responds directly to the air-gap model. Table 4 shows the influence of a variation in the air gap width on skin burn predictions made by the three models. The SM under-predicted times to skin burn injuries, especially for third-degree burns. The discrepancy between times to burn injuries predicted by this model and those predicted by the other two models increases with the increase in the air gap width. That is because the SM ignores the interaction of the gap with thermal radiation, which strengthens as the gap width increases due to the increase in the volume of the gases inside the gap. On the other hand, the SCRM precisely predicted times to skin burns for different air gap widths compared with the CCRM. However, there is an insignificant discrepancy between times to third-degree burns predicted by the two models.

Table 4.

Influence of the air gap width on skin burn predictions.

Air gap width (mm)	Time to receive skin burn (s)
	Simple model			Combined conduction– radiation model			Simplified conduction– radiation model
	First degree	Second degree	Third degree	First degree	Second degree	Third degree	First degree	Second degree	Third degree
1	4.2	4.3	18.3	4.2	4.3	18.3	4.2	4.3	18.5
2	4.8	5	22.6	4.8	5	22.7	4.8	5	22.9
3	5	5.3	26.2	5.1	5.3	26.6	5.1	5.3	26.7
4	5.2	5.4	29.8	5.3	5.5	30.5	5.3	5.5	30.6
5	5.3	5.5	33.4	5.4	5.6	34.8	5.4	5.6	34.9
6	5.4	5.6	37.4	5.5	5.7	40.1	5.5	5.7	40.1

The level of energy transfer from the backside of the fabric to the skin through the air gap is related to the fabric thickness. The energy transfer within the gap by both conduction and radiation decreases as the fabric thickness increases. The influence of a variation in the fabric thickness on skin burn predictions made by the three models is shown in Table 5. The SM under-predicted times to skin burn injuries compared with the other two models, especially for third-degree burns. The deviation between the predictions made by the SM and the other two models increases as the fabric thickness increases. Moreover, for the simulation parameters considered in this study, unlike the other two models, the SM predicted third-degree burns to take place if the fabric thickness is increased to 0.7 mm. On the other hand, the SCRM over-predicted times to skin burn injuries compared with the CCRM.

Table 5.

Influence of the fabric thickness on skin burn predictions.

Fabric thickness (mm)	Time to receive skin burn (s)
	Simple model			Combined conduction– radiation model			Simplified conduction– radiation model
	First degree	Second degree	Third degree	First degree	Second degree	Third degree	First degree	Second degree	Third degree
0.6	5.4	5.7	38.9	5.5	5.8	42.3	5.5	5.8	42.3
0.65	5.7	6	49.5	5.8	6.1	59.3	5.8	6.1	60.6
0.7	6.1	6.3	72.4	6.1	6.4	6.1	6.4
0.9	7.4	7.7	7.4	7.8	7.5	7.8
1.2	9.5	9.9	9.5	9.9	9.6	10
1.5	12	12.6	12	12.7	12.1	12.8
1.8	17	19.7	17	20	17.4	20.2

The SM was shown to be inappropriate for predicting the performance of protective clothing. On the other hand, the SCRM, although less complex than the CCRM, predicts the performance of protective clothing almost as accurately as the CCRM. The SCRM, as a novel model, can be a possible replacement for the CCRM as an accurate but less complex model.

Conclusions

The effect of the air-gap model between protective clothing and the skin in evaluating the clothing performance during fire exposure was studied numerically. This article introduces a novel air-gap model–SCRM–that balances between the accuracy and complexity in modeling the air gap between protective clothing and the skin. The performance of protective clothing was investigated by the SCRM and compared with that predicted by the other two air-gap models–SM and CCRM–from the literature. Skin burn predictions made by the three models for different values for the air gap absorption coefficient, air gap width and fabric thickness were compared. The decoupling between the conduction and radiation heat transfers within the air gap that the SM assumes caused it to over-predict the temperature of the fabric backside and under-predict the temperatures of the air gap center and epidermis surface compared with the other two models, with an air gap absorption coefficient of 0 m⁻¹. The SCRM over-predicts times to third-degree burns for different values of the air gap absorption coefficient compared with the CCRM. This deviation in predicting times to third-degree burns increases as the air gap absorption coefficient increases. The SCRM predicts times to skin burns almost the same as does the CCRM for different air gap widths while the SM under-predicts times to skin burn injuries, especially for third-degree burns. For different fabric thicknesses, the SM under-predicts times to skin burns while the SCRM over-predicts times to skin burns for different fabric thicknesses compared with the CCRM.

In general, the SCRM produces skin burn predictions that are very close to those produced by the CCRM as compared with the SM. That makes the SCRM, as a simple and accurate model, a potential replacement for both the SM and CCRM. Nevertheless, caution should be exercised for the minimal over-prediction in times to skin burns made by the SCRM, especially for third-degree burns.