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O R IGINA L

Patirop Chitrphiromsri Andrey V. Kuznetsov

Modeling heat and moisture transport in firefighter

protective clothing during flash fire exposure

Received: 11 April 2003 / Published online: 27 May 2004 Springer-Verlag 2004

Abstract In this paper, a model of heat and moisturetransport in firefighter protective clothing during a flashfire exposure is presented. The aim of this study is toinvestigate the effect of coupled heat and moisture

transport on the protective performance of the garment.Computational results show the distribution of temper-ature and moisture content in the fabric during theexposure to the flash fire as well as during the cool-downperiod. Moreover, the duration of the exposure duringwhich the garment protects the firefighter from gettingsecond and third degree burns from the flash fire expo-sure is numerically predicted. A complete model for thefire-fabric-air gap-skin system is presented.

List of symbolsA surface area [m2]

cp specific heat at constant pressure [J kg1 K1]Da diffusivity of water vapor in the air [m

2 s1]Deff effective diffusivity of the gas phase in the

fabric [m2 s1]Dsolid effective diffusivity of bound water in the

solid phase [m2 s1]df average fiber diameter [m]F view factorg gravitational acceleration [9.81 m s2]hc convective heat transfer coefficient [W m

2

K1]hm convective mass transfer coefficient [m s

1]k thermal conductivity [W m1 K1]

L thickness [m]m_ sv water vapor mass flux out of the fiber [kg

m3 s1]

M molecular weight [kg kmol1]Nu Nusselt numberp pressure [Pa]P frequency factor (pre-exponential factor)

[s1]qair,cond/conv

heat flux by conduction/convection from thefabric to the human skin across the air gap[W m2]

qair,rad heat flux by radiation from the fabric to thehuman skin across the air gap [W m2]

qconv convective heat flux from the flame to thefabric [W m2]

qrad incident radiation heat flux from the flameonto the fabric [W m2]

R universal gas constant [8.315 103 J kmol1

K1]Rf,/=0.65 fabric regain at 65% relative humidity

Rf,skin equilibrium regain at the fiber surfaceRf,total total fiber regainRa Rayleigh numberT temperature [K]t time [s]

Greek symbolsa thermal diffusivity of the air [m2s1]b thermal expansion coefficient of the air [K1]x linear horizontal coordinate [m]DE activation energy for skin [J kmol1]Dhl enthalpy of transition from bound water to free

liquid water [J kg-1]

Dhvap enthalpy of evaporation per unit mass [J kg-1]DT temperature difference across the air gap [K]d thickness of the air gap [m] volume fraction~e emissivity/ relative humidityc extinction coefficient of the fabric [m1]m kinematic viscosity of the air [m2s1]q density [kg m3]r Stefan-Boltzman constant [5.670 108W m2

K4]

P. Chitrphiromsri A. V. Kuznetsov (&)Department of Mechanical and Aerospace Engineering,North Carolina State University, Campus Box 7916,Raleigh, NC 27695-7910, USAE-mail: avkuznet@eos.ncsu.edu

Heat Mass Transfer (2005) 41: 206215DOI 10.1007/s00231-004-0504-x

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~s transmissivity of the fabrics fabric tortuosityW quantitative measure of burn damagexb blood perfusion [0.00125 m

3s1m3tissue]

Subscripts0 initial statea dry air

art arterialamb ambient airblood bloodbw bound waterds dry solideff effectiveeq equilibriumfab fabricfl flameg hot gasesgap air gaps saturationskin human skin

v water vaporw waterc gas phaser solid phase

1 Introduction

Every year many firefighters are injured as a result ofexposure to a flash fire. In order to prevent or minimizethe burn injuries, thermal protective clothing must be

properly designed. In developing thermal protectivematerials, such as firefighter garments, researchers tra-ditionally focus on heat transfer in fabrics subjected toflash fire conditions. However, moisture transport infabrics and its effect on protective performance of thegarment has not been studied in sufficient detail. In thispaper, a model that couples heat and moisture transportis developed.

Protective fabric can be treated as a porous medium.There are many existing models for the analysis ofmultiphase transport in porous media. Vafai and So zen[1] summarized and compared these models. One of themodels, which is suitable for fabrics subjected to inten-

sive heat, is Gibsons model [2]. However, Gibsonsmodel does not account for radiation heat transferwithin the fabric layer. Torvi [3] developed a heattransfer model, which accounts for the radiative heattransfer through a fabric.

The present study is aimed at developing a model toanalyze heat and moisture transport in protectiveclothing. Combining Gibson and Torvis models makesit possible to account for the thermal response of thefabric. The skin model developed by Pennes [4] is uti-lized to predict tissue burn injuries, which are evaluated

based on the approach suggested by Henriques andMoritz [5].

2 Problem description

A schematic diagram of heat and moisture transport infirefighter garments as well as heat transfer in human

skin and tissue is displayed in Figure 1. The garmentconsists of three fabric layers, which are the outer shell,the moisture barrier, and the thermal liner. The config-uration of each garment layer is shown in Figure 1. Thehuman skin can also be divided into three layers, such asepidermis, dermis, and subcutaneous, as shown in Fig-ure 1.

3 Heat transfer model in fabric

Gibson [2] applied Whitakers theory [6] of coupledheat and mass transfer through porous media to de-

rive a set of equations for modeling heat and masstransfer through textile materials. He assumed thatfabric can be modeled as a hygroscopic porous media.He modeled the material as a mixture of a solid phaseconsisting of solid (e.g., polymer or cotton) fibers plusbound water absorbed by the polymer matrix, a liquidphase consisting of free liquid water, and a gaseousphase consisting of water vapor plus inert air. Themodel accounts for heat transfer by conduction in allphases, convection in the gas and liquid phases, andlatent heat release due to phase change from liquid tovapor phase.

Torvi [3] assumed that convective heat flux only ap-

plies to the surface of the fabric but radiative heat fluxcan penetrate through the fabric up to a certain depth.

Based on the above assumptions, the energy balancein the infinitesimal element of fabric can be written in theform of a differential equation. The partial differentialequation is developed for the temperature distribution ina composite fabric layer by combining Gibson andTorvis models. Therefore, the energy equation is mod-eled based on Gibsons model plus the penetratingradiation term, which is described by Torvis model [3].Thermal properties of all phases are accounted for in themodel based on the relations given by Gibson [2].Radiative heat transfer in the fabric is accounted for by

introducing in the energy equation a source term similarto that of Torvis model [3]. For simplicity, the gas phaseconvection contributions due to pressure differences,which can arise either due to body movement or due toexternal air movement (wind), are neglected. Moreover,it is assumed that if there is any extra liquid sweat whichbuilds up on the skin surface, it will either drip off orwick into the fabric and then will be absorbed by thefabric fibers and become bound water. In the otherwords, free liquid water exists neither on the surface ofthe skin nor in the fabric layer.

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Energy equation

qcp@T

@t Dhl Dhvap _msv

@

@xkeff

@T

@x

c q00rade

cx

1

where q is the effective density of the fabric, cp theeffective specific heat of the fabric, T is the temperature,t is the time, Dhl is the enthalpy of transition from

the bound water to the free liquid water, Dhvap is theenthalpy of evaporation per unit mass,

_msv

is the mass flux of vapor out of the fiber (or into thefiber if _msv is negative), x is the linear horizontal coor-dinate, keff is the effective thermal conductivity of thefabric, c is the extinction coefficient of the fabric, andqrad is the incident radiation heat flux from the flameonto the fabric.

The effective density of the fabric, q, can be calcu-lated [2] as:

q ebwqw edsqds ecqv qa 2

where bw is the volume fraction of the water dissolved inthe solid phase, qw is the density of the liquid water, ds isthe volume fraction of the dry solid fiber (assumed to beconstant), qds is the density of the dry solid, c is thevolume fraction of the gas phase, qv is the intrinsicdensity of the water vapor, and qa is the intrinsic densityof the dry air.

The effective specific heat of the fabric, cp, can becalculated [2] as:

cp ebwqwcpw edsqdscpds ecqvcpv qacpa

q

3

where (cp)w is the specific heat of the liquid water, (cp)dsis the specific heat of the dry solid, (cp)v is the specificheat of the water vapor, and (cp)a is the specific heat ofthe dry air.

The enthalpy of transition from the bound water tothe free liquid water state, Dhl, can be presented [2] as:

Dhl 1:95 1051 /

1

0:2 /

1

1:05 /

!

4

where / is the relative humidity defined as:

/ pv

ps5

In equation (5), pv is the partial pressure of the watervapor and ps is the saturation vapor pressure, which is afunction of T only.

The saturation vapor pressure, ps, is calculated [2] as:

ps 614:3 e xp 17:06T 273:15

T 40:25

!& '6

The enthalpy of vaporization per unit mass, Dhvap, canbe calculated [2] as:

Dhvap 2:792 106 160T 3:43T2 7

The mass flux of the vapor out of the fiber, _msv, is cal-culated [2] as:

_msv Dsolidqdsd2f

Rf;total Rf;skin 8

where Dsolid is the effective diffusivity of bound water inthe solid phase, df is the average fiber diameter, Rf,total isthe total fiber regain, and Rf,skin is the equilibrium regainat the fiber surface.

Definitions of the physical properties of the fabric aregiven in Morton and Hearles work [7]. The fiber regain,Rf, can be represented as:

Rf ebwqwedsqds

9

The total fiber regain, Rf,total, is calculated by usingthe volume fraction of the bound water, bw, obtainedfrom the solid phase continuity equation, which willbe discussed later on in this paper. In the samemanner, the equilibrium regain at the fiber surface,Rf,skin, can be calculated by using the equilibriumvolume fraction of bound water, bw,eq, obtained fromthe sorption relation, which will be provided later onin this paper.

The effective thermal conductivity of the fabric, keff,can be calculated [2] as:

Fig. 1 Schematic diagram of heat and moisture transport in theprotective clothing and the human skin

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keff kc1 ebw edskr eckceckr 1 ebw edskc

& '10

where kc is the thermal conductivity of the gas phase andkr is the thermal conductivity of the solid phase.

The thermal conductivity of the gas phase, kc, can becalculated [2] as:

kc

kvqv kaqa

qv qa

11

where kv is the thermal conductivity of the saturatedwater vapor and ka is the thermal conductivity of the dryair.

The thermal conductivity of the solid phase, kr, canbe calculated [2] as:

kr kwqwebw kdsqdsedsqwebw qdseds

12

where kw is the thermal conductivity of the liquid waterand kds is the thermal conductivity of the dry solid.

The extinction coefficient, c, that characterizes the

decrease of thermal radiation as it penetrates deeper intothe fabric, is given [3] as:

c ln~s

Lfab13

where ~s is the transmissivity of the fabric and Lfab is thefabric thickness. It is assumed that radiation penetratesthrough the outer layer of the fabric only.

The incident radiation heat flux coming from theflame to the fabric, q00rad, is found [3] as:

q00rad r~egT4g T

4fab r~efabFfabamb1 ~egT

4fab T

4amb

14where r is the Stefan-Boltzman constant, ~eg is theemissivity of the hot gases, Tg is the temperature of thehot gases, Tfab is the temperature at the outside surfaceof the fabric, ~efab is the emissivity of the fabric, Ffabamb isthe view factor accounting for the geometry of the fabricwith respect to the ambient, and Tamb is the temperatureof the ambient air. Since this paper considers a 1Dmodel, the view factor, Ffabamb, is set to unity.

Solid phase continuity equation

qw @@tebw _msv 0 15

Gas phase diffusivity equation

@

@tecqv _msv

@

@xDeff

@qv@x

16

where Deff is the effective diffusivity of the gas phase inthe fabric, which is defined [2] as:

Deff Daec

s17

In equation (17), Da is the diffusivity of water vapor inthe air and s is the fabric tortuosity.

The diffusivity of the water vapor in the air, Da, iscalculated [2] as:

Da 2:23 105 T

273:15

1:75

18

Volume fraction constraint

ec ebw eds 1 19

Sorption relation [2]

ebw;eq 0:578Rf;/0:65 edsqdsqw

/

1

0:321 /

1

1:262 /

!20

where Rf,/=0.65 is the fabric regain at 65% relativehumidity.

Thermodynamic relations

pa pc pv 21

pa qaR

MaT 22

pv qvR

MvT 23

where pa is the partial pressure of the air, pc is the

total gas pressure, R is the universal gas constant, Mais the molecular weight of the air, and Mv is themolecular weight of the water vapor.

Initial Conditions

Tx; t 0 T0x 24

/x; t 0 /0x 25

ebwx; t 0 ebw0x 26

where To is the initial temperature, /o is the initial rel-ative humidity, and bwo is the initial volume fraction ofthe bound water.

Boundary Conditions for the Fabric

keff@T

@x

x0

q00conv q00rad

x0

27

keff@T

@x

xLfab

q00air;rad q00air;cond=conv

xLfab

28

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hmqv;amb qvx0 Deff@qv@x

x0

29

hmqv;air qvxLfab Deff@qv@x

xLfab

30

where qconv is the convective heat flux from the flameto the fabric, qair,rad is the heat flux by radiation from

the fabric to the human skin across the air gap,qair,cond/conv is the heat flux by conduction/convectionfrom the fabric to the human skin across the air gap,hm is the convective mass transfer coefficient, qv,amb isthe density of water vapor in the ambient air, andqv,air is the density of water vapor in the air gap.

The radiation and convection heat fluxes can befound [3] as:

q00conv q00radx0 hc;flTg Tfab 31

where hc, fl is the convective heat transfer coefficientbetween the flame and the outer surface of the fabric.

The heat flux by radiation from the fabric to the

human skin across the air gap is given by [3]:

q00air;rad

xLfab

rT4fab T

4skin

AskinAfab

1~efab~efab

1Ffabskin

1~eskin

~eskin

32

where Tskin is the temperature at the outside surface ofthe human skin, Askin is the surface area of the humanskin, Afab is the surface area of the fabric, Ffabskin is theview factor accounting for the geometry of the fabricwith respect to the human skin (set to unity because themodel is one-dimensional), and ~eskin is the emissivity ofthe human skin.

The heat flux by conduction/convection from thefabric to the human skin across the air gap is given by [3]:

q00air;cond=conv

xLfab

hc;gapTfab Tskin 33

where hc,gap is the convective heat transfer coefficient ofthe air due to conduction and natural convection in theair gap. hc,gap can be found [3] as:

hc;gap NukairT

Lgap34

where Nu is the Nusselt number; kair(T) is the thermalconductivity of the air, which is a function of T only;

and Lgap is the thickness of the air gap.

4 Heat transfer model in the skin

The Pennes model [4] is used to model heat transfer inthe living tissue. The skin is divided into three layers,namely, the epidermis, the dermis, and the subcutaneousregion. Blood perfusion applies only to the latter tworegions. The model is based on the assumption that there

is an energy exchange between the blood vessels and thesurrounding tissue. According to the Pennes model, thetotal heat transfer by the flowing blood is proportionalto its volumetric flow rate and the temperature differencebetween the blood and the tissue.

Bio-heat transfer equation

qcpskin@T

@t r kskinrT qcpbloodxbTart T

35

where qskin is the density of the human skin, (cp)skin is thespecific heat of the human skin, kskin is the thermalconductivity of the human skin, qblood is the density ofthe human blood, (cp)blood is the specific heat of thehuman blood, xb is the blood perfusion, and Tart is thearterial temperature.

Boundary Conditions for the Skin

kskin@T

@xxLfabLgap

q00air;rad q00air;cond=conv

xLfabLgap

36

TjxLfabLgapLskin Tart 37

where Lskin is the thickness of the human skin.

5 Natural convection in the air gap betweenthe fabric and the skin

For modeling the thermal response of firefighter pro-tective clothing exposed to flash fire, the convective heat

transfer in the air gap between the fabric and the skin issimulated as a natural convection in a vertical enclosure,which is heated from one side. Catton [8] summarizedthe Nusselt number correlations for the air in a longvertical enclosure heated from one side. The relationbased on Denny and Clevers work [9] is given as:

Nu 1:0; Ra 1713

0:112Ra;0:294 Ra > 1713

&38

where Ra is the Rayleigh number defined as:

Ra gbDTd3

am

39

In equation (39), g is the gravitational acceleration, b isthe thermal expansion coefficient of the air, DT is thetemperature difference across the air gap, d isthe thickness of the air gap, a is the thermal diffusivity ofthe air, and v is the kinematic viscosity of the air.

From the above expression, natural convection willcontribute to heat transfer across the enclosure when theRayleigh number is greater than 1713. The maximumRayleigh number, Ra, for all computed cases of theThermal Protective Performance (TPP) test was 1123.

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Therefore, for the case computed in this paper, theRayleigh number is always smaller than 1713, whichmeans that natural convection is negligible. Therefore,radiation and conduction heat transfer will be domi-nating heat transfer mechanisms across the air gap.

6 Tissue burn injury model

The tissue burn injury model is based on the work byHenriques and Moritz [5]. Thermal damage occurs whenthe temperature at the interface between the epidermisand dermis in the human skin (called the basal layer, cf.Fig. 1) rises above 44 C. The destruction rate of thegrowing layer can be modeled by a first order chemicalreaction. Arrhenius rate equation can be used to esti-mate the rate of tissue damage:

dX

dt Pexp

DE

RT

40

where W is a quantitative measure of the burn damage at

the interface or at any depth in the dermis, P is thefrequency factor or pre-exponential factor (s1), and DEis the activation energy for skin.

The above equation can be integrated over the timeinterval when the temperature at the interface is above44 C:

X

Zt

0

Pexp DE

RT

dt 41

For predicting the first and second degree burns, thetemperature at the interface between the epidermis anddermis in the human skin must be used as T in equa-tion (41). First degree burn occurs when the value of theburn integral, W, reaches 0.53 at this interface, whilesecond degree burn happens when W attains 1.0 at thesame interface. For predicting third degree burns, thetemperature at the interface between the dermis and thesub-cutaneous layer (called the dermal base, cf. Fig. 1)must be used as T in equation (41). The third degreeburn occurs when W attains 1.0 at this interface. Thesetissue burn damage criteria can be used once appropriatevalues of P and DE are provided. These values weresuggested by Weaver and Stoll [10] for the basal layerand by Takata and et al. [11] for the dermal base.

7 Numerical procedure

In this work, the finite difference method (Patankar [12]and Tannehill, et al. [13]) is used to solve the differ-ential equations (equations (1), (15), (16), and (35)),which are the energy equation for the fabric, the solidphase continuity equation, the gas phase diffusivityequation, and the bio-heat transfer equation for theskin, respectively. The Crank-Nicholson scheme is used

to discretize the transient partial differential equations.Due to non-linearities in this system, the Gauss-Seidelpoint-by-point iterative scheme is used to solve theseequations. In order to avoid divergence of the iterationmethod, the underrelaxation procedure is utilized. Thevalue of the underrelaxation parameter is 0.8. Thesolution procedure is as follows. All variables areknown at the initial state, then the program marchesforward in given time increments. The variables at theprevious time step are used as guessed values for thevariables at the current time step. The new values ofvariables are computed by visiting each grid point in acertain order. Then the iterations are repeated until thechanges in the solutions become smaller than 106.Next, after the temperature profile in multiple layers ofskin is obtained, Henriques burn integral (equa-tion (41)) is used to calculate the maximum durationsof the flash fire exposure before the human skin can getsecond and third degree burns.

8 Results and discussion

The thermophysical/geometrical properties of the fabricutilized in the computations are listed in Table 1. Theradiation parameters used in the computations, whichare given by Torvi [3], are listed in Table 2. The ther-mophysical/geometrical properties of the human skin,which are given by Torvi and Dale [14], are listed inTable 3. Thermal properties of the flame and theambient air, and the initial data of the fabric and the airgap are listed in Table 4.

The nominal thickness of the air gap for the standardTPP test [15] is 0.00635 m (1/4). Computations areperformed for the duration of a flash fire exposure of 4

seconds. After the fire is off, computations continue untilthe time reaches 60 seconds. The temperature of the hotgas and the ambient temperature gradually decreaseafter 4 seconds of burning. Figure 2 depicts the tem-perature distributions in the fabric at different momentsof time. The x coordinate in this figure (and in Figs. 37)shows the distance from the outer surface of the fabric(the surface that is exposed to fire). The temperature atthe outer surface of the fabric increases very fast com-pared to that at the inner surface of the fabric while thegarment is exposed to the intensive flash fire. In the samemanner, the temperature at the outside surface of thefabric reduces very fast compared to that at the inside

surface of the fabric during the cool-down phase of theprocess (after the burn). Figure 3 displays the tempera-ture distributions in the human skin and tissue at dif-ferent moments of time. The origination point of the xaxis is at the outer surface of the fabric, the x axis isdirected inside the human tissue. According to Tables 1and 4, the first skin layer begins at the distance of0.00885 m from the outer surface of the fabric. The skintemperature keeps increasing even when the fire is off.This is because of the energy accumulated within thefabric and the air gap during the fire exposure. There-

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fore, skin burns may occur not only during the 4 secondsof the flash fire exposure, but also after the exposurebecause of the heat accumulated in the garment. Fig-ure 4 shows distributions of the fiber regain in the fabricat different moments of time. Figure 5 illustrates distri-butions of the moisture content in the fabric at differentmoments of time. The regain is defined as the ratio of themass of absorbed water in the fabric to the mass of dryfabric. Similarly, the moisture content is defined as theratio of the mass of absorbed water in the fabric to themass of wet fabric. Therefore, by their definitions, both

the fiber regain and the moisture content are related,hence both graphs have the same trend. The garment isin the equilibrium state in the beginning. Then the dif-ference in properties of the three fabric layers causesjumps in the fiber regain and the moisture content at theinterfaces and these are shown in Figs. 4 and 5. Both thefiber regain and the moisture content in the fabric de-crease during the 4-second flash fire exposure and theystill keep decreasing until they reach their minimumvalues, which correspond to an equilibrium state atthose temperature and humidity conditions. If the

cooling time is long enough, both fiber regain andmoisture content in the fabric will go back to what theywere at the initial state. Figure 6 shows distributions ofthe relative humidity in the fabric at different momentsof time. The relative humidity in the outer layer of thegarment drops very fast when it is exposed to the flashfire. In the latter layers of the garment, the relativehumidity increases. This means that the moisture ispushed from the outside fabric layer to the inside fabriclayer and then into the air gap because of the tempera-ture gradient. After the temperatures at the outer surface

Table 1 Thermophysical/geometrical properties of thefabric

Property Outer Shell:60/40KEVLAR / NOMEXblend at 7.0 oz/yd2

Moisture Barrier:Breathable PTFEfilm on NOMEXE89TM

Thermal Liner:Aramid batt quiltedto 3.2 oz/yd2

NOMEX

qds[kg m3] 286 250 220

(cp)ds[J kg1 K1] 1005 1150 1300

kds[W m1K1] 0.080 0.050 0.052

L [m] 0.700 103 0.850 103 0.950 103

ds 0.336 0.409 0.360Rf 0.055 0.056 0.041s 2.12 2.49 1.82Dsolid/df

2 [s1] 3.44 102 2.69 102 4.81 102

Table 2 Radiation parameters

Property Fabric Flame Skin

~e 0.9 0.02 0.94~T 0.01

Table 3 Thermophysical/geometrical properties of the human skin

Property Epidermis Dermis Subcutaneous Blood

q[kg m3] 1200 1200 1000 1060cp[J kg

1 K1] 3600 3400 3060 3770k [W m1 K1] 0.255 0.523 0.167 L [m] 8 105 2 103 1 102 xb [m

3 s1 m3] 1.25 103

Tarterial [C] 37.0Tsurface [C] 34.0

Table 4 The initial conditions for the fabric and the air gap of theTPP test, and the thermal properties of the flame and the ambient

air

T0,fab [C] 40.0/0,fab 0.50/0,airgap 0.50/

0.50Tg[K] 2000hm,airgap [m s

1] 0.021hm,[m s

1] 0.021Tamb[C] 30.0

pc[N m2] 1.01325 105

Lgap[m] 6.35 103

hc,fl [W m2 K1] 120.0

Fig. 2 Temperature distributions in the fabric at different momentsof time

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and the inner surface of the fabric become low enough,

the relative humidity starts growing back to its initialdistribution. Figure 7 depicts distribution of the vapordensity in the fabric at different moments of time. Thevapor density increases because the temperature in-creases and causes the phase transition from the boundwater to the water vapor. In addition, Fig. 7 shows thatthe moisture moves from the outer shell to the moisturebarrier and then to the thermal liner (cf. Fig. 1) becauseof the temperature gradient. Figure 8 shows the calcu-lated fabric weight per unit area versus time. The fabricweight decreases because the fabric loses the moisture to

the air gap. Figure 9 displays the calculated vapor den-

sity in the air gap versus time. The vapor density in theair gap increases because the air gap gains the moisturefrom the fabric. However, the vapor density will de-crease and the fabric weight will increase when thetemperature in the garment is again low enough, whichwill cause the moisture transport to go backwards.Figure 10 presents the calculated relative humidity in theair gap versus time. Because the relative temperatureincrease is slower than the relative moisture density in-crease, one can see that the relative humidity in the airgap increases slightly and then drops rapidly. When the

Fig. 3 Temperature distributions in the human skin and tissue atdifferent moments of time

Fig. 4 Distributions of the fiber regain in the fabric at differentmoments of time

Fig. 5 Distributions of the moisture content in the fabric atdifferent moments of time

Fig. 6 Distributions of the relative humidity in the fabric atdifferent moments of time

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temperature increases, the saturation pressure also in-creases. Therefore, the relative humidity in the air gapreduces even though the moisture content in the air gap

increases.The thickness of the air gap between the garment and

the body depends on the particular location on the hu-man body. Table 5 shows that the maximum air gapoccurs for the leg and the minimum air gap occurs forthe shoulder. These values of the air gaps are based onrepresentative scans performed by Song [16]. The max-imum durations of the flash fire exposure before thehuman skin gets second and third degree burns at dif-ferent locations on the human body are given in Table 5.This table shows that the distribution of the air gap

Table 5 Maximum durations of the flash fire exposure before get-ting the second and third degree burns at different locations on thehuman body

Location Air gapthickness(mm)

Maximum exposuretime for seconddegree burn (sec)

Maximumexposuretime for thirddegree burn (sec)

TPP test 6.35(or 1/4)

5.95 19.63

Arm 6.58 5.99 19.70Front 10.21 6.20 20.10Back 5.93 5.86 19.51Leg 18.50 6.27 20.20Shoulder 1.60 3.66 15.91

Fig. 7 Distributions of the vapor density in the fabric at differentmoments of time

Fig. 8 Calculated fabric weight per unit area versus time

Fig. 9 Calculated vapor density in the air gap versus time

Fig. 10 Calculated relative humidity in the air gap versus time

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thickness affects the maximum durations of the flash fireexposure before getting the second and third degreeburns.

9 Conclusions

The coupled heat and moisture transport in firefighterprotective clothing during flash fire exposure is investi-gated numerically. It is shown that the obtained com-prehensive model of heat and moisture transport can beused to estimate the thermal response of protectivefabric. The distributions of temperature and moisturecontent in the fabric and the human skin during flash fireexposure can be obtained. Maximum durations of theflash fire exposure exceeding which would result in thesecond degree burn and the third degree burn can alsobe predicted.

Acknowledgements The support provided by the National TextileCenter is gratefully acknowledged. Helpful discussions with Profs.R. L. Barker, H. Hamouda, and Drs. D. B. Thomson and G. Song

are greatly appreciated.

References

1. Vafai K, So zen M (1990) A comparative analysis of multiphasetransport models in porous media. Ann Rev Heat Transfer 3:145162

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