NISTIR 6881

Thermal Performance of Fire Fighters’ Protective Clothing.

1. Numerical Study of Transient Heat and Water Vapor Transfer

Kuldeep Prasad

William Twilley

J. Randall Lawson
NISTIR 6881

Thermal Performance of Fire Fighters’ Protective Clothing.

1. Numerical Study of Transient Heat and Water Vapor Transfer

Kuldeep Prasad

William Twilley

J. Randall Lawson

Fire Research Division

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8660

August 2002

UNITED STATES OF AMERICA

DEPARTMENT OF COMMERCE

U.S. DEPARTMENT OF COMMERCE

Donald L. Evans, Secretary

TECHNOLOGY ADMINISTRATION

Phillip J. Bond, Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Arden L. Bement, Jr., Director

Sponsored in part by:

FEDERAL EMERGENCY MANAGEMENT ADMINISTRATION

Joe M. Allbaugh, Director

U.S. FIRE ADMINISTRATION

R. David Paulison, Administrator
Contents

1 Abstract 1

2 Introduction 1

3 Detailed Model of Transient Heat and Moisture Transfer Through Cloth 3

4 Approximate Model of Transient Heat and Moisture Transfer Through Cloth 6

5 Thermal Radiation Model 8

6 Numerical Model 11

6.1 Initial Conditions, Boundary Condition and Interface Conditions . . . . . . . . . . . . . . . 11

7 Results and Discussion 12

7.1 Heat and Mass Transfer through a Wet Thermal Liner . . . . . . . . . . . . . . . . . . . . . 12

7.2 Time Dependent Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7.3 Boundary Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7.4 Wet Turnout Coat Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

8 Concluding Remarks 25

9 Directions for Future Research Activities 26

10 Acknowledgments 28

References 29
List of Figures

1 Schematic cross-section of a three layered firefighter protective clothing ensemble surrounded

by ambient air. Radiative fluxes incident on material boundaries have been indicated. . . . . 9

2 Grid spacing and dimensions for a one-dimensional control volume used in the model for

fire fighter protective clothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Schematic of an Aralite thermal liner consisting of Kevlar batting quilted to an Aramid face

cloth used for studying heat and moisture transfer. The batting and face cloth are 0 265 cm

and 0 025 cm thick, respectively and are separted by a 0 075 cm thick air gap. . . . . . . . . 13

4 Comparison of numerical and experimental results of temperature history at the front and

back faces of the Arlaite thermal liner. The batting is subjected to an incident flux of 2 5

kW m

2

for 750 s, followed by a cool down period of 100 s. . . . . . . . . . . . . . . . . . 14

5 Comparison of numerically predicted temperature histories for the dry and wet thermal liners. For each case, numerical results have been shown for the front face and the back face. . 15

6 Temperature time histories at the various fabric - air interfaces. The total weight of water

(g) in the fabric is plotted as a function of time for the Aralite thermal liner subjected to an

incident radiative flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Simulation results at time t 0 s for a wet thermal liner subjected to an external incident

flux 2 

5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 18

8 Simulation results at time t 100 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 19

9 Simulation results at time t 200 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 20

10 Simulation results at time t 300 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 21

11 Simulation results at time t 400 s for a wet thermal liner subjected to an external incident

flux 2 

5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 22

12 Simulation results at time t 500 s for a wet thermal liner subjected to an external incident

flux 2 

5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 23

13 Simulation results at time t 800 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the thermal liner. . . . 24

14 Numerical predictions of convective heat flux at the boundaries (front and back faces) as a

function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
15 Numerical predictions of radiative heat flux at the boundaries (front and back faces) as a

function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

16 Numerical predictions of moisture mass flux at the boundaries (front and back faces) as a

function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

17 Schematic of a typical three layered turnout coat used as firefighter protective clothing,

subjected to an incident radiative flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

18 Comparison of numerically predicted temperature histories for the dry and wet turnout coat.

For each case, numerical results have been shown for the front and back faces. The mass

loss curve during evaporation of water from the turnout coat has also been shown on the Y2

axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

19 Simulation results at time t 100 s for a wet turnout coat subjected to an external incident

flux of 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the turnout coat. . . . . 30

20 Simulation results at time t 600 s for a wet turnout coat subjected to an external incident

flux of 2 

5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure),

moisture content (bottom left sub-figure) and dry / wet density (bottom right sub-figure) has

been shown as a function of distance measured from the front face of the turnout coat. . . . . 31
1 Abstract

This study is the first in a series of reports on understanding the performance of fire fighter clothing, in

protecting skin from thermal injury that results from exposure to high intensity thermal radiation. A detailed

mathematical model is constructed to study transient heat and moisture transfer through multi-layered fabric

assemblies with or without air gaps. The model accounts for changes in thermodynamic and transport

properties of the fabric due to the presence of moisture. Numerical simulations are performed to study heat

and mass transport through wet thermal liners (used in fire fighter protective clothing) when subjected to a

radiative heat flux from a gas fired radiant panel. Results were found to compare well with experimental

measurements. The numerical solutions are further analyzed to provide a detailed physical understanding

of the governing processes. Moisture in the cloth tends to vaporise upon heating and part of it recondenses

in the interior of the cloth. It was observed that the temperature of the fabric layers and total heat flux to the

skin is significantly influenced by the amount of moisture and the distribution of moisture in the protective

clothing. Finally, simulations are performed for a wet turnout coat assembly to demonstrate the flexibility

of the model for designing fire fighter protective clothing.

2 Introduction

During fire fighting, fire fighters are subjected to a variety of fire conditions. Fire fighters can be burned by

radiant energy that is produced by a fire and localized flame contact exposure. The most common exposure

is to low level radiant heat flux over prolonged periods of time. Fire fighters working in these conditions,

often sweat profusely, which leads to accumulation of moisture in the turnout garment. Fire fighters can

also become wet when they are doused by water from a hose spray. Fire fighters have received second

degree burns while working in these “wet” conditions. The presence of moisture in protective clothing can

significantly change the garment’s protective performance [1]. Wet garments exhibit higher heat transfer

rates than dry garments. Evaporation and condensation of the moisture and the energy associated with

phase change can affect the temperature and energy flux to the skin surface. Burn injuries can result from

heating and evaporation of moisture trapped within one’s protective clothing. These injuries are generally

referred to as scald injury or steam burns. A numerical tool for studying moisture transport through a

thermally irradiated fire fighters’ protective clothing is critical in preventing burn injury and in designing

new protective gear. Such a tool can also provide information regarding the heat capacity of the protective

garment to fire fighters and will assist them in understanding the thermal response of the protective gear to

different fire scenarios.

The thermal performance of fire fighters’ protective clothing has been a point of interest and discussion

for several decades. Many of these discussions are based on fire services field experience. A great deal still

needs to be done in terms of detailed scientific analysis for predicting the thermal performance of protective clothing throughout the range of fire environments normally faced by a fire fighter. At a fundamental

level, this problem can be viewed as the study of heat and mass (moisture) transfer through porous textile

fabrics. Combined heat and mass transfer with phase change in a porous medium is a process which occurs

frequently in nature as well as in various engineering endeavors. Drying and humidification in chemical

processes and in climate control or movement of moisture in the soil are examples. Such processes have

therefore been widely studied by agricultural, civil, chemical and petroleum engineers.

Heat and mass transfer in wet porous media are coupled in a complicated way. The structure of the solid

matrix varies widely in shape. There is, in general, a distribution of void sizes, and the structures may also

be locally irregular. Energy transport in such a medium occurs by conduction in all of the phases as well as

by convection within the liquid and gas phases. Mass transport occurs within the voids of the medium. In an

unsaturated state these voids are partially filled with a liquid, whereas the rest of the voids contain some gas.

1
For the analysis of wet fire fighter fabrics, the liquid is water and the gas is air. Evaporation or condensation

occurs at the interface between the water and air so that the air is mixed with water vapor. A flow of the

mixture of air and vapor may be caused by external forces, for instance, by an imposed pressure difference.

The vapor will also move relative to the gas by diffusion from regions where the partial pressure of the vapor

is higher to those where it is lower. The partial pressure of vapor at the interface to the liquid is determined

by the sorption isotherm, which makes it dependent on moisture content as well as on temperature. The

saturation pressure is also different on a curved surface from that on a plane one and is influenced by the

presence of air. The flow of liquid is caused by external forces, like imposed pressure differences, gravity

and internal forces like capillary, intermolecular and osmotic forces.

A detailed study of the transport processes occurring within the solid matrix and in the voids is complicated even for a regularly shaped matrix and is impossible for the irregular shaped configurations that exist

in general, in porous media. The normal approach in an analysis is, therefore, to treat the media involved

as continua. The energy and mass flux then have to be described by constitutive equations. The various

driving forces involved make the constitutive equations quite complicated. The difficulty in handling them

is aggravated by the fact that the transport properties involved vary strongly with the structure of the porous

medium, the moisture content, and the temperature.

Simultaneous differential equations for the transfer of heat and moisture in porous media under the

combined influence of gravity and gradients of temperature and moisture content were developed by D. A.

De Vries [2]. These equations are a generalization of those derived by Philip et al. [3]. Eckert and Faghri

[4] have performed a general analysis of moisture migration in a slab of an unsaturated porous material for

a condition where the temperature of one surface is suddenly increased to a higher value whereas the temperature of the other surface is maintained constant. Udell [5], [6] has derived a general, one-dimensional,

steady-state model describing the heat and mass transfer within a homogeneous porous medium, saturated

with a wetting liquid, its vapor and a non-condensible gas. The effects of gas diffusion, phase change, conduction, liquid and vapor transport, capillarity, and gravity are included. The analysis is based on a general

thermodynamic description of the unique equilibrium states characteristic of liquid wetting porous media.

Bouddour et al. [7] have provided a systematic, rigorous and unified treatment of the governing equations

for simultaneous heat and mass transfer within a wide range of porous media.

Some work has also been done in the area of coupled diffusion of moisture and heat in hygroscopic

textile materials. Gibson [8] has given a review of numerical modeling of convection, diffusion and phase

changes in textiles. The paper summarizes current and past work aimed at utilizing CFD techniques for

clothing applications. It was shown that water in a hygroscopic porous textile may exist in vapor or liquid

form in the pore spaces. Phase changes associated with water include liquid evaporation/condensation in

the pore spaces and sorption/desorption from polymer fibers. Additional factors such as swelling of solid

polymer due to water and heat of sorption was incorporated into the appropriate conservation and transport equations. Nordon and David [9] have attempted to solve the non-linear differential equations which

describe coupled diffusion of heat and mass (moisture) in hygroscopic textile materials. In addition to the

diffusion equations, a rate equation was introduced describing the rate of exchange of moisture between the

solid (textile fibers) and the gas phase. The predictions compared favorably with experimental observations

on wool bales and wool fabrics [10]. Farnworth [11] has developed a simple (algebraic) model of combined

heat and water vapor transport in clothing. Transport by forced convection was not included in this model.

The calculations were performed in a time dependent mode and compared to experiments performed on a

sweating hot plate in a nonsteady state mode. Much of this work [8]-[11] was performed for single layers

of cotton or wool fabrics and is not directly relevant to fire fighter protective clothing. Bamford and Boydell

[12] have developed a finite difference burn injury evaluation code (ICARUS) for evaluating time to seconddegree burns caused by thermal radiation. ICARUS models the heat transfer between the clothing layers

with associated air gaps and a multilayered skin model. The model does not account for moisture transport

through the protective clothing.

2
Recently, the Building and Fire Research Laboratory (BFRL) at the National Institute of Standards and

Technology (NIST) has developed a physics-based computational model for predicting the thermal performance of dry fire fighters protective clothing [13]. This model successfully predicted heat transfer through

clothing and provided insight into how the garment would respond to radiative heat flux exposures. This

first step in the development of predictive methods for protective clothing helped to advance the science

and holds promise, but is only one of the many elements required for accurate prediction of thermal performance across the broad use range of these garment systems. In this work, we extend the model to study the

thermal performance of fire fighters’ protective clothing under wet conditions. Section 3 gives a detailed

discussion of the mathematical formulation for transient heat and moisture transfer through porous clothing. This model accounts for variation in thermodynamic and transport properties due to the presence of

moisture on the fabric. A simplified form of the equations are derived by making assumptions appropriate

for fire fighter protective clothing (Section 4). The thermal radiation model is briefly discussed in Section 5,

followed by the the numerical implementation of the model. A brief section has been included to discuss the

initial, boundary and interface conditions. Numerical simulation results are reported for a wet thermal liner

in Section 7. These results are compared with experimental data. The results have been analyzed to obtain a

detailed understanding of the various physical processes. Finally, we discuss the conclusions (Section 8) that

we have derived from this project and our detailed recommendations for future research activities (Section

9).

3 Detailed Model of Transient Heat and Moisture Transfer Through Cloth

Before proceeding to formulate the present problem of heat and moisture transfer, when the outer layer of

cloth is irradiated by high intensity thermal radiation, several important assumptions can be made to simplify

the formulation 

Mass transfer of moisture is caused by molecular diffusion and bulk flow of vapor through the gas

volume surrounding the cloth fibers (inter-fiber void space), but not by diffusion on the surface or

through pores in the cloth fibers (capillary action). 

The local moisture content (moisture regain) of the cloth is at all times in equilibrium with the partial

pressure of water vapor at the temperature of the local gas in the voids. It is assumed that the rate of

equilibration is much faster than the vapor diffusion process. 

Volume changes of the fibers due to the changing moisture content are neglected. 

Heat and mass transport are one-dimensional, and is along the thickness of the fabric layers. There is

no lateral transport.

Consider a small volume element of a slab of homogeneously packed textile material of unit area and of

thickness ∆X. The equation for conservation of mass and energy will be expressed in terms of unit volume

of the textile-air mixture. Water vapor is free to convect and diffuse through the interfiber void space and to

be sorbed or desorbed by the fibers. Water vapor can accumulate in the unit element both in the void space

and in the fibers. The total mass balance continuity equation for water vapor species (gas and liquid phase)

can be written as

∂

∂t



ρo 1  f  M

W1  ∂∂t 

fCX1 	  f

∂

∂x Cv X1  f

∂

∂x

D12C

∂X1

∂x 
 (1)

where

3
f = volume fraction of voids in the cloth,

ρo = density of cellulosic fiber (g/cm3),

M = local moisture content (moisture regain),

weight of water per unit weight of dry cloth (g/g),

W1 = molecular weight of water vapor (g/mol),

C = molar concentration (mol/cm3),

v = molar averaged velocity (cm/s),

D12 = coefficient of binary diffusion between water vapor and air (cm2/s),

X1 = volume fraction of water vapor.

The first term on the left hand side represents the accumulation of water in the fibers. Note that ρo 1  f  is

the dry density of the cloth and is different from ρo, the density of the cellulosic fiber. The second term on

the left hand side represents the accumulation of water vapor in the inter-fiber void space. The accumulation

of water inside the control volume can change due to bulk flow of vapor (first term on the right hand side)

and molecular diffusion (second term on the right hand side) through the gas volume surrounding the cloth

fibers.

Similarly the continuity equation for air can be written as

∂

∂t 

fCX2 	  f

∂

∂x Cv X2   f

∂

∂x

D21C

∂X2

∂x  


(2)

where, X2 is the volume fraction of air. Note, that subscript 1 refers to water vapor and subscript 2 refers

to air. Equations 1 and 2 have to be solved subject to the constraint equation, that the sum of the volume

fraction is equal to one (X1 X2 1).

Conservation of energy for the control volume can be stated as

∂

∂t



ρo 1  f  MH1

W1  

∂

∂t 

ρo 1  f  Hc 	 

∂

∂t 

fC X1h1 X2h2 	 



∂

∂x   kc 

kw  kc  f  

∂T

∂x  f

∂

∂x

Cv



X1h1 X2h2 	   f

∂

∂x

D12C

∂X1

∂x

h1  D21C

∂X2

∂x

h2  

∂qR

∂x 


(3)

where1,

H1 = Molal Enthalpy of liquid water (erg/mol),

Hc = Enthalpy of fabric (erg/g),

h1 = Molal Enthalpy of water vapor (erg/mol),

h2 = Molal Enthalpy of air (ergs/mol),

kc = Thermal Conductivity of fabric (erg/cm/s/K),

kw = Thermal Conductivity of liquid water (erg/cm/s/K),

f  = Volume fraction of liquid water,

qR = Radiative Flux.

The left hand side of the energy equation is the rate of accumulation of enthalpy in the control volume. The

first term on the left hand side is the contribution due to change in enthalpy of liquid water, the second term is

1The policy of the National Institute of Standards and Technology is to use SI units of measurement in all its publications. In

this document, however, the CGS system of units is sometimes used because of the scales and ranges of the quantities and the wide

use of such units in the fire modeling field. For clarification, erg=10 

7

J, dyne = 10

5 Pa.

4
due to the fabric and the last term is due to water vapor air mixture that is present in the control volume. The

first term on the right hand side (Equation 2) shows the net rate of heat addition due to thermal conduction

into the control volume. The second term on the right hand side represents the net rate of influx of enthalpy

by convection, while the third term shows contribution due to molecular diffusion in the inter-fiber void

space. The last term on the right hand side of Equation 2, represents the net rate of heat added due to the

incident radiative flux on the control volume. This term will be discussed in more detail in section 5.

Since f  , the volume fraction of liquid water in the control volume is equal to ρo 1  f  M 

ρw, the total

thermal conductivity kT can be defined as

kT kc 

kw  kc  

ρo 1  f  M

ρw  


(4)

where, ρw is the density of the liquid water (g/cm3). The total thermal conductivity is a volume weighted

measure of thermal conductivity of cloth and of liquid water. Thermal conductivity of water is 23 times

that of air, so the contribution to kT from air and water vapor are assumed to be negligible. Thus, the total

thermal conductivity increases linearly with moisture regain M, in agreement with experiments by Schneider

and Hoschke [14].

To progress any further, we must somehow relate the moisture content M of the fabric to the water

vapor volume fraction X1 in the gas phase. If the gas flows slowly through the pores, then the cloth and gas

phase will stand in approximate local equilibrium at all times. This assumption [15] allows us to neglect the

detailed kinetics of adsorption in favor of standard equilibrium thermodynamics, and to assume a definite

functional relationship such as

M Φ T 


X1  (5)

This relationship is known as an adsorption isotherm [16] and it relates the moisture content M to water

vapor volume fraction X1, and is a function of temperature [17], [18]. The adsorption isotherm was measured

experimentally for a few fire fighter protective clothing fabrics using the HYDEN Adsorption Analyzer2.

Finally, we close the system of equations using the equation of state

P CRoT 
(6)

where, Ro is the Universal gas constant (8 

314 107erg/mol/K).

Using equations 1, 2, 3, 5 and 6 along with constraint equations and appropriate initial and boundary

conditions, one can obtain a solution of temperature T, moisture regain M, the volume fractions X1 and

X2 and the molar density C as a function of distance x and time t. The mathematical solution of the set

of equations based on a realistic model of movement of water vapor, by molecular diffusion and bulk flow,

through cloth, when subjected to an external radiation source, is challenging. The complexity of the problem,

arises from the fact that there is no simple way to evaluate the bulk flow velocity of water vapor through the

inter-fiber void spaces, when the cloth is heated to over 100 0C in a very short time (fraction of a second),

at very high radiation intensity. Instead of solving the Navier-Stokes equations in the void spaces, the bulk

flow velocity can be calculated simply from the local gradient in total pressure of the system and can be

expressed using Darcy’s momentum equation

v 

K

μ 

∂P

∂x 


(7)

where,

2Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the materials

used and the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute

of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the

purpose.

5
P = Total Pressure (dyn/cm2

),

μ = Fluid viscosity,

K = Fabric permeability (cm2).

However, at very high radiation intensities, the flow of vapor due to the total pressure gradient will exceed

that transferred by diffusion and a theory based solely on diffusion will break down under those conditions.

Note, that Darcy’s momentum equation provides a linear relationship that is characteristic of Stokes flow

(viscous flow domination over inertial force) and is not valid at high velocities. More importantly, the

external flow field generated by the fire which surrounds the fire fighter must be known a priori, and imposed

as a boundary condition on the present analysis (which is limited to the fabric and air gaps). Experiments

have also shown that at moderately high radiation intensities, fabrics in contact with skin cannot withstand

more than a few second exposure without being scorched. Any theory that is expected to describe such

a situation adequately must also include the effect of cloth decomposition or chemical reaction, which is

still beyond our present ability. Besides, most fire fighter injuries (second degree burns) take place at low

to medium incident intensities when there is little or no thermal degradation of their protective gear. We

next develop an approximate model of heat and mass transfer through porous cloth valid for low to medium

intensities, assuming that the gas flows slowly through the cloth and that adsorption isotherms relating

moisture content to vapor pressure are valid.

4 Approximate Model of Transient Heat and Moisture Transfer Through

Cloth

Multiplying equations 1 and 2 by h1 and h2 respectively, and then adding them together we obtain,

h1

∂

∂t



ρcM

fW1 

CX1 h2

∂

∂t 

CX2 	 h1

∂

∂x Cv X1  h2

∂

∂x Cv X2   h1

∂

∂x

D12C

∂X1

∂x   h2

∂

∂x

D21C

∂X2

∂x 
 (8)

where, ρc ρo 1  f  is the dry density of the fabric. Subtracting equation 8 from equation 3, we obtain

H1  h1 

∂

∂t



ρcM

W1  



ρcM

W1 

∂H1

∂t 

∂

∂t 

ρcHc 	 fC



X1

∂h1

∂t 

X2

∂h2

∂t  



∂

∂x  kT

∂T

∂x  fCv



X1

∂h1

∂x 

X2

∂h2

∂x 



fD12C



∂X1

∂x

∂h1

∂x 

∂X2

∂x

∂h2

∂x  

∂qR

∂x



(9)

The enthalpies can be defined as follows

h1 c1T 


h2 c2T 


H1 C1T ∆H 




Hc CcT 
(10)

where,

c1 = molal heat capacity of water vapor (erg/mol/K),

c2 = molal heat capacity of air (erg/mol/K),

C1 = molal heat capacity of liquid water (erg/mol/K),

Cc = mass heat capacity of fabric (erg/g/K),

∆H  = Heat of Adsorption (erg/mol).

6
Substituting the above in equation 9, and assuming that the heat capacities are independent of temperature,

we obtain



∆H  

C1  c1  T 

ρc

W1 

∂M

∂t 

 

ρcMC1

W1 

ρcCc fC X1c1 X2c2  

∂T

∂t 



∂

∂x  kT

∂T

∂x  fCv



X1c1 X2c2 	

∂T

∂x



fD12C



∂X1

∂x

c1 

∂X2

∂x

c2 

∂h2

∂x 

∂qR

∂x



(11)

In order to derive the approximate model for transient heat and moisture transfer through cloth, we

make an additional assumption that, sensible heat transfer in the vapor phase is negligible compared with

heat conduction through the cloth and with the latent heat effects of adsorption and desorption of water on

the cloth fibers. With this assumption, the energy conservation equation (Eq. 11) simplifies to

ρc∆H

∂M

∂t 

 

ρcMC1

W1 

ρcCc 

∂T

∂t 

∂

∂x  kT

∂T

∂x 

∂qR

∂x 


(12)

where, ∆H ∆H  W1 is the heat of adsorption per unit mass (erg/g). Furthermore, if we define the total density of the control volume ρ ρc 1 

M 




and the total heat capacity of the control volume CT Cc 

MC1 W1

1M 


then the energy equation (equation 12) can be expressed simply as

ρCT

∂T

∂t 

∂

∂x  kT

∂T

∂x 

∂qR

∂x  ρc∆H

∂M

∂t



(13)

The final form of the energy equation (Eq. 13) simply states that the increase in heat content of the material

inside the control volume (textile fabric, air, water and water vapor) is equal to the net amount of heat

entering by conduction plus the contribution due to radiative heating of the volume plus the heat evolved

as water vapor is adsorbed inside the control volume. Note, that the total heat capacity CT is a non-linear

function of the moisture content M, and has contributions from the heat capacity of dry fabric and that of

liquid water. Both thermal conductivity kT and heat capacity increase substantially with moisture regain,

however, thermal diffusivity kT ρCT shows a minor variation with moisture regain.

Simplification of the mass conservation equation requires an estimation of the bulk flow velocity term.

As mentioned earlier, we have restricted our attention to the problem of transient heat and moisture transfer

through fabrics subjected to low or medium radiation intensities. We now assume that the volume of air

flowing through the fabric is negligible compared with that of the water vapor due to desorption and adsorption of water to and from the cloth fibers. Air is assumed to be a stagnant layer through which water vapor

flows. Thus if the rate of transfer for the air species is set to zero, we obtain

Cv X2  CD12

∂X2

∂x 0 (14)

Since X1 X2 1, we obtain

Cv 



CD12

1  X1 

∂X1

∂x

(15)

Substituting 15 in equation 1, the continuity equation for water can be re-written as

ρc

W1

∂M

∂t 

fC

∂X1

∂t  f

∂

∂x



D12C

1  X1 

∂X1

∂x 
 (16)

7
Replacing volume fraction X1 by fractional partial pressure p

P we obtain

ρc

f

∂M

∂t 

ρgW1

PW

∂p

∂t 

∂

∂x

  

W1D12

RoT 1  pP  

∂p

∂x  


(17)

where, p is the vapor pressure and ρg is the gas density (g/cm3) defined as

ρg CW PW 

RoT  

(18)

W is the mean molecular weight of the system. If we further define the mass diffusion coefficient, D as

D 

D12W1

RoT 1  pP 

(19)

then the final form of the mass continuity equation can be re-written as

ρc

f

∂M

∂t 

ρgW1

PW

∂p

∂t 

∂

∂x

D

∂p

∂x 

(20)

The mass continuity equation (Eq. 20) states that the net amount of vapor entering the control volume by

diffusion is equal to the increase in moisture in air plus the increase in the moisture content of the fibers. The

mass continuity equation (Eq. 20), the energy conservation equation (Eq. 13) along with the equilibrium

relationship (Eq. 5) are numerically solved in each fabric layer and air gap to obtain the three unknown

variables (moisture content M, temperature T and vapor pressure p). Note, that the equilibrium relationship

can be easily expressed in terms of vapor pressure p, instead of the the volume fraction X1. The gas density

ρg is obtained from the equation of state 18. The numerical techniques used to solve the equations are

discussed in Section 6.

5 Thermal Radiation Model

To obtain the temperature distribution throughout the protective clothing ensemble both the energy equation

(Eq. 13) and the radiative heat transfer equation (in some approximation) must be solved. The thermal

radiation model described here, is an extension of the model developed by Mell and Lawson [13] for fire

fighter protective clothing. We assume, that within a material layer, the contribution to radiative flux from

self emission is much smaller than that due to the absorption of the externally incident flux. The major

radiative flux incident on the boundaries of a material layer are assumed to be due to :

1. the external incident heat flux on the outer garment layer. This contributes to the forward incident

fluxes and the backward incident fluxes on the inner gas/solid boundaries, if reflection occurs.

2. interlayer (across air layers) radiative flux and its reflection. This occurs when the material surfaces

bounding the air layers have different temperatures and contributes to both the forward and backward

incident flux.

With regards to 1, only the backward reflection of radiation due to the external flux is calculated. Also in

the present model, the net flux, which is found by integrating over all the wavelengths is considered [19].

Under these assumptions, the net radiative flux qx 

l at a distance x measured from the left boundary, within

material layer l can be obtained from the Beer-Lambert law, and can be expressed as

qx 

l q

i

l

eκlx 

q

i

l

eκl 

dl x 




(21)

8
qe

σε3(T3

4

-T∝

4

)

qe,3

i,-

σε1(T∝

4

-T1

4

) q2-3

q2-3

qe,1

i,+

qe,1

i,+

qe,1

i,+

qe,3

q i,+

e,1

i,+

qe,1

i,-

qe,2

i,+

qe,2

i,-

q1-2

q1-2

Layer 1 Layer 2 Layer 3

Figure 1: Schematic cross-section of a three layered firefighter protective clothing ensemble surrounded by

ambient air. Radiative fluxes incident on material boundaries have been indicated.

where, q

i

l

and q

i

l

are the fluxes incident on the left and right side, respectively, of material layer l, κlis the

absorption coefficient of layer l and dlis the thickness of material layer l.

The absorptivity of a fabric layer, α, is related to it transmissivity, τ, and reflectivity r, through

α 

r τ 1 (22)

The absorption coefficient κlis assumed constant within the material layer l, and can be determined from

the transmissivity and reflectivity of the fabric layer as

κl 

1

dl

ln 

1  rl

τl 


(23)

where, dlis the thickness of the fabric layer l.

The fluxes incident on the left and right hand side of the material boundary are from two sources:

the external radiation source (qe) and the interlayer flux denoted as q12 for fabric layers 1 and 2. These

fluxes have been depicted in Figure 1 for a three layered clothing assembly surrounded by ambient air of

temperature T∞.

9
The contribution to the incident boundary flux due to the external flux are as follows:

Fabric Layer 1 (24)

q

i

e 1 qe 1  r1 

q

i

e 1 qer2 1  r1  e

κ1d1 

Fabric Layer 2 (25)

q

i

e 2 qe 1  r2 

1  r1  e

κ1d1 

q

i

e 2 qer3 1  r2 

1  r1  e

κ1d1 κ2d2 

Fabric Layer 3 (26)

q

i

e 3 qe 1  r3 

1  r2 1  r1  e

κ1d1 κ2d2 

q

i

e 3 0

The net interlayer radiative flux is computed using the result for plane parallel plates with isotropic

scattering, diffusively reflecting boundaries separated by nonparticipating air [13]. With this assumption

q12 integrated over all wavelengths is

q12 

σ ε1T

4

1 

r1ε2T

4

2 

1  r1r2 

σ ε2T

4

2 

r2ε1T

4

1 

1  r1r2

(27)

Thus, the net incident flux on the the left side of a material layer l=2 (for example) is the sum of the two

contributions

q

i  

2 q

i  

e 2 

q12 (28)

This incident flux is used in equation 21 for computing the net radiative flux and subsequently in the energy

equation 13.

L C R

Left Face

l

Right Face

r

∆x

δr

+

δl

δr

δr

-

Figure 2: Grid spacing and dimensions for a one-dimensional control volume used in the model for fire

fighter protective clothing.

10
6 Numerical Model

The partial differential equations expressing conservation of energy (Eq. 13) and the mass continuity equation (Eq. 20) derived in the previous section were discretized using a control volume approach to derive the

finite difference form of the equations. The method of discretization ensures local energy and mass conservation and requires approximation of only first order derivatives (rather than higher order derivatives).

An arbitrary control volume surrounding grid point C (at the center of the control volume is shown in

Figure 2. Control volume faces are marked by dashed lines, the left face is denoted by l and the right face

by r. Note that the material interfaces are at the control volume interfaces. Grid points to the left and right

of C are denoted by L and R, respectively. The control volumes centered around C, L and R may not be of

the same size, i.e.

δl δr δx (29)

The goal of the numerical procedure is to predict the temperature T, vapor presure P and moisture

content M at the cell centers. It is assumed that these quantities vary linearly within the control volume. The

coefficient of the various terms are computed at the cell center and are assumed to be constant within each

cell.

Integrating equation 13 over the control volume centered around C gives

r

l

ρCT

∂T

∂t

dxdA kT

∂T

∂x 







r

l

dA qR 

r

l

dA  r

l

ρc∆H

∂M

∂t

dxdA 

(30)

The first order derivates in the conduction flux term are obtained by assuming that T varies linearly with the

control volume. Care is taken to ensure that the flux is continuous at the cell interfaces. Similarly, integrating

equation 20 results in

r

l

ρc

f

∂M

∂t

dxdA  r

l

ρgW1

PW

∂p

∂t

dxdA D

∂p

∂x 







r

l

dxdA (31)

The discretized form of the above equations are solved for each material layer and air gap. A second

order explicit Runge-Kutta scheme was used for time stepping [13]. Although the stability characteristics

of these methods are more restrictive than implicit methods, explicit Runge-Kutta techniques result in more

accurate solutions than implicit schemes of comparable order.

6.1 Initial Conditions, Boundary Condition and Interface Conditions

A unique solution to the governing equations requires the specification of initial and boundary conditions.

The initial temperature distribution in the fabric layers and the air gap has to be specified. Normally, room

temperature values are specified as measured in the laboratory. The initial moisture distribution inside the

fabric layers is also specified as an initial condition. The vapor pressure within the fabric layer is then

computed from the equilibrium relationship. Temperature and vapor pressure in the air gap are normally

specified at room temperature and relative humidity. The incident radiative flux as a function of time must

also be specified to start the calculations.

Boundary conditions must be specified at the edges of the computational domain. This includes specification of temperature and vapor pressure or relative humidity at the right and left edges of the computational

domain. Besides specification of initial and boundary conditions, specialized interface conditions have to be

formulated at the gas / solid boundaries. There are two types of gas / solid boundaries, according to whether

or not convective heat and mass transfer is present. It is assumed that the air gaps between the fabric layers are small enough and the velocity boundary layer does not develop fully within the air gaps. The heat

transfer in these air gaps and the adjoining material layers is by conduction only while mass transfer is by

11
diffusion only. Convective heat and mass transfer are very important at the outer surface of the turnout coat

exposed to the ambient atmosphere.

The surface heat transfer coefficient hc, was obtained from the Nusselt number through empirical correlation of free convection on a vertical plate [20], [21]

hc Nu

kG

L 


(32)

where, Nu is the Nusselt number, kG is the thermal conductivity and L is the characteristic length. Correlations appropriate for both laminar and turbulent flow were used depending on the magnitude of the Rayleigh

number. The surface mass transfer coefficient mc was obtained from the heat transfer coefficient hc by

assuming that the ratio of Schmidt to Prandtl numbers is unity. Thus,

hc

mc PCvapor

M

Mw 


(33)

where, P is the total pressure, Cvapor is the specific heat of humid air and M Mw is the ratio of mean

molecular weight of gas to that of water. These correlations are obtained from work done by Carslaw and

Jaegar [22]. The surface heat and mass transfer coefficients are used in estimating the heat and mass fluxes

at the boundaries of the garment as discussed earlier.

7 Results and Discussion

In order to demonstrate the effect of moisture on wet fire fighter protective clothing, a series of simulations

and experiments were performed. We next describe these simulations and compare them with available

experimental data.

The presence of moisture in the fabric and the amount of moisture affects the local density, and thermodynamic properties (heat capacity) as well as transport properties (thermal conductivity and diffusivity).

Moisture changes the propagation of the thermal wave into the fabric layer, since some energy is used in

heating up the moisture and in the evaporation process. Water vapor can also condense on the fabric and

this further affects the temperature distribution. As a result, the moisture distribution inside the fabric layer

is an important input quantity for the numerical simulation. Note that we are assuming moisture distribution

varies only along the thickness of the fabric layers (one-dimensional problem).

The numerical model is relatively flexible, in that any initial moisture distribution can be specified for

each fabric layer as an input from the experimental configuration. Experimentally, determining the moisture

distribution within the fabric layers is a challenging task. In the experiments, a known quantity of water was

sprayed on the front and back sides of the fabric layers with the hope that this would produce a uniform

distribution of moisture in all of the fabric layers. The use of a single fabric layer instead of multiple

fabric layer garments, allows us to control and prescribe the moisture content and moisture distribution in

a more precise manner. Since detailed comparison of numerical and experimental results require a better

understanding of moisture distribution inside the various fabric layers, it was decided to initially restrict

this study to single fabric layers. The thermal liner was chosen for this single fabric layer study becuase

it absorbs water more readily as compared to the moisture barrier. Also, since the thermal liner is slightly

thicker, the thermocouples could be attached more precisely on the front and back faces.

7.1 Heat and Mass Transfer through a Wet Thermal Liner

The thermal liner that was used in this analysis is commonly known as ARALITE, manufactured by Southern

Mills. The Aralite thermal liner is a needle-bonded Kevlar batting quilted to a dyed aramid face cloth.

12
Thermal Liner

B

a

t

tin

g

F

a

c

e

Clo

t

h

Air

G

a

p

External

Incident

Flux

X

Convective Heat

and Mass Transfer

Convective Heat

and Mass Transfer

Figure 3: Schematic of an Aralite thermal liner consisting of Kevlar batting quilted to an Aramid face cloth

used for studying heat and moisture transfer. The batting and face cloth are 0 265 cm and 0 025 cm thick,

respectively and are separted by a 0 075 cm thick air gap.

The open structure of this material provides a high insulation value and is a commonly used fire fighter

turnout suit material. To perform a simulation, the thickness, density, conductivity, specific heat and the

optical properties of transmissivity and reflectivity were needed. These properties measured and tabulated

by Lawson et al. [23] and were used in our calculation.

Figure 3 shows a schematic of the thermal liner consisting of a batting and face cloth. An air gap (1

mm thick) separates the batting from the face cloth. In the experiments, the batting is subject to an external

incident flux of 2.5 kW/m2starting at t 0 s. The external flux is applied until 750 s. The simulation is extended to 850 s to allow the fabrics to cool down. A uniform void fraction value of 0 

7 for the batting and 0 2

for the face cloth was used. The void fraction is obtained by measuring the compressed and uncompressed

(normal loft) thickness of the fabric layer. The thermal liner does not have a clear, planar edge and therefore, thickness measurements in the uncompressed state are difficult. In the compressed state, thickness was

found to vary with the pressure and it was unclear if the fiber structure was changed during compression.

In the experiments, two thermocouples are located on the thermal liner. One thermocouple is on the

thermal batting and faces the radiant panel. This face is also referred to as the front face or the left face.

Another thermocouple is placed on the Aramid face cloth facing away from the radiant panel. This face is

referred to as the back face or the right face. Convective heat and mass transfer occur at the front and back

13
0 200 400 600 800

20

30

40

50

60

70

80

90

100

110

120

Front Surface

Back Surface

Numerical Results

Experimental Data

Front Surface

Back Surface

Time (s)

T

e

m

p

e

r

atu

r

e (

o

C)

0 200 400 600 800

20

30

40

50

60

70

80

90

100

110

120

Figure 4: Comparison of numerical and experimental results of temperature history at the front and back

faces of the Arlaite thermal liner. The batting is subjected to an incident flux of 2 5 kW m

2

for 750 s,

followed by a cool down period of 100 s.

faces, which are open to the atmosphere. It is assumed that the air gap which is approximately 1 mm thick

does not allow for a fully developed boundary layer. As a result conductive heat transfer is still the more

dominant heat transfer mechanism as opposed to convective heat transfer. It is thus assumed in the present

analysis that heat and mass transfer between the fabric layer and the air gaps (between the fabric layers) is

by diffusive processes alone. Convective heat and mass transfer are active only on the fabric faces that are

open to the atmosphere.

Figure 4 shows temperature as a function of time for the front and back faces of the thermal liner

when subjected to a radiative heat flux of 2 

5 kW/m2. The numerical results are shown as lines while the

experimental data are shown as symbols only. The initial temperature of the fabric is approximately 25 oC .

As the thermal liner is exposed to a radiative flux of 2 

5 kW/m2at t 0 s, the temperature of the front and

back face start rising sharply. The rate of rise for the front face is higher than that for the back face. This is

because the front face is exposed directly to the radiant panel. Only a small fraction of this radiant energy is

transmitted and heats up the rear face. The numerically predicted profiles follow the experimental data very

closely (error is within 5 %) in this region. Energy is also conducted to the rear face, but this is a relatively

slow process. During this initial transient, negligible amount of water has evaporated and the energy is used

in heating up the fabric and moisture - air mixture.

14
The sharp initial transient is followed by a region where temperature are almost constant. The front

face stabilizes at approximately 52 oC for approximately 200 s, while the back face temperature stabilizes

at approximately 45 oC until 400  420 s. This feature is also observed in the experimental data. In fact, the

experimental data show a very slight decrease in temperature. The experimental data shows that the front

face temperature reaches approximately 52 oC and then drops to 50 oC , while the rear face reaches as high

as 45 oC and then cools down to 41  42 oC . In fact the numerical data also indicates a temperature drop of

approximately 0 2  0 5

oC , which is difficult to observe on this plot (Figure 4).

The stabilization in temperature indicates that the incident energy is being used to evaporate the moisture. The amount of moisture being evaporated can be computed approximately by dividing the incident

energy flux by the heat of evaporation. The length of this plateau region depends on the amount of water in

the fabric. If the amount of water on the front face of the fabric is less, the plateau region will be shorter. If

there is more water on the front face, the plateau region will be proportionately longer.

0 200 400 600 800

30

40

50

60

70

80

90

100

110

TIME(s)

T

e

m

p

e

r

atu

r

e (

o

C)

0 200 400 600 800

30

40

50

60

70

80

90

100

110

Dry Thermal Liner Wet Thermal Liner

Front Surface

Back Surface Back Surface

Front Surface

Figure 5: Comparison of numerically predicted temperature histories for the dry and wet thermal liners. For

each case, numerical results have been shown for the front face and the back face.

At approximately 200 s into the simulation, the temperature of the front face starts rising again, indicating that the front face is completely dry. The back face temperature starts rising at 400  410 s indicating

that the entire fabric is completely dry. Once the back face is completely dry, the temperature starts rising

sharply again until a steady state condition is reached. The experimental results indicate that the temperature

does not rise as sharply as the numerical result. The temperature at the back face stabilizes at approximately

15
TIME(s)

T

e

m

p

e

r

atu

r

e (

o

C)

T

otal w

eig

ht of w

ate

r in fa

b

ric (g)

0 200 400 600 800

30

40

50

60

70

80

90

100

110

5

10

15

20

T4

T4

T3

T2

T1

T1

T2

T3

Total weight of

water

Figure 6: Temperature time histories at the various fabric - air interfaces. The total weight of water (g) in

the fabric is plotted as a function of time for the Aralite thermal liner subjected to an incident radiative flux.

90 oC . The temperature at the front face also starts rising once the front face has completely dried but

the rate of rise is relatively small. This rate of temperature increase is smaller than the rate at which the

temperature at the back face increases. This rate of temperature increase is also much smaller than the rate

of temperature rise from 25 oC to 50 oC (see Figure 4) at the front face. At 200 s into the simulation, only

the front face of the fabric is dry, but there is still water present inside the fabric. The temperature of this

portion of the fabric (which is wet) is low which results in conductive heat losses from the front face of the

fabric. These conductive losses are higher than what one would expect, if the entire fabric was dry, since the

thermal conductively of the wet fabric is higher than that of the dry fabric. Due to these higher conductive

heat losses the temperature of the front face rises at a slower rate. In fact the moisture distribution inside

the fabric layer can influence the slope of the temperature time curve in this region. Simulations where a

different distribution of moisture was assumed resulted in vastly different slopes. The slope of this curve

can therefore be used to obtain some information on the moisture distribution inside the fabric. When the

entire fabric is completely dry, at 400 s into the simulation, the temperature starts rising again at a faster

rate. The temperature of the front face stabilizes finally at 115 oC . During the period from 600 s to 750

s the temperatures of the front and the back faces remain constant. This indicates that a balance has been

reached between the energy flowing into the fabric and convective heat losses at the boundaries. At t 750

s into the simulation, the radiative flux from the radiant panel was cut off, which results in a rapid drop in

16
temperature of the front and rear faces, consistent with the experimental data.

Our results clearly indicate that there is good qualitative agreement between the numerical predictions

and thermocouple measurements.

Figure 5 shows a comparison for a thermal liner that is initially completely dry and a wet thermal liner.

For each case, the temperature time curves for the front and back faces of the thermal liner have been shown.

The wet thermal liner results are duplicated from Figure 4 for comparison with the dry case. For the dry

thermal liner, the temperature at the front face increases sharply from 25 oC over a period of 30  40 s and

then stabilizes at the steady state value of 115 oC . The temperature of the back face rises less sharply than

that of the front face, and this temperature stabilizes at approximately 90 oC . The final temperatures (before

the radiative heating is cut-off) are the same for the dry and wet thermal liners. This figure clearly shows the

effect of moisture on reducing the temperature at the front and rear faces.

Figure 6 shows the temperatures at all the four interfaces as a function of time. The numerically computed mass loss in grams has also been plotted as a function of time on the Y2 axis. The mass loss curve

shows the amount of liquid water that is present in the fabric. It is an integrated value over the entire thickness of the fabric. At t 0 s, the results indicate approximately 24 g of water. During the first 30 to 40 s

of the simulation, there is very little evaporation of water and the mass loss curve is almost flat. From 40

to 400 s, the total weight of water in the fabric reduces linearly with time. At t 450 s, all the water has

evaporated from the fabric. These observations compared well with the numerically computed temperature

histories in the thermal liner. After the radiation has been cut-off, small amounts of water is absorbed back

into the fabric, from the surrounding atmosphere. This explains the small increase in mass loss curve after

t 750 s.

7.2 Time Dependent Simulations

Figures 7-13 shows time dependent simulation results for a wet thermal liner subjected to an external incident flux. Each figure shows results at a specific time. Each figure has four sub-figures. In the top left

sub figure, temperature (

oC ) as a function of distance has been shown. The distance is measured from the

front face of the thermal liner. Dotted lines have been drawn to indicate the location of the interface. The

batting material lies between 0 0 and 0 265 cm. The air-gap is between 0 265  0 34 cm and the face cloth

is between 0 34  0 365 cm. The upper right figure shows the vapor pressure (P) in dyn/cm2as a function of

distance. The moisture content M has been shown in the lower left figure while the lower right figure shows

the dry fabric density and the wet fabric density as a function of distance.

Figure 7 shows results at time t 0 s and thus represent the initial conditions. The temperature is

uniform everywhere at 25 oC . The moisture content M shows the assumed moisture distribution in the

batting and the face cloth. The resulting density distribution that is initially imposed on the fabric is also

shown. The moisture distribution shows a moisture content of 3 

0 at the front face. This moisture content

drops linearly to a value of 1 5 over the thickness of the batting. The moisture content in the face cloth

is set at a constant value of 0 2. In the experiments, water is sprayed on the front and back faces of the

fabric. Most of the water sprayed on the front face stays on the front face and we assume a linear decrease

in the amount of water as a function of distance. The difference between wet fabric and dry fabric weight

distribution clearly illustrates the initial water distribution in the batting. Note that the batting is a relatively

thick material with very high void fraction. The water sprayed on the back face is assumed to be uniformly

distributed over the face cloth. This distribution of water in the face cloth is reasonable because the face

cloth is very thin as compared to the thermal batting.

Figure 8 shows results at 100 s into the simulation. The thermal liner is now being radiatively heated

from an external source. The temperature has increased to approximately 50 oC , but is almost uniform

over the thickness of the liner. The temperature at the back face is only slightly less than that at the front

face. The vapor pressure has increased significantly above its initial value and is close to the saturated

17
Time = 0.0 seconds

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Figure 7: Simulation results at time t 0 s for a wet thermal liner subjected to an external incident flux 2 5

kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content (bottom

left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of distance

measured from the front face of the thermal liner.

vapor pressure (relative humidity=100 %).The moisture content of the fabrics when subjected to a 100 %

humidity environment at room temperature is approximately 0 

08. Since the actual moisture content at

t 100 s is much larger than 0 

08, at each point in the fabric, we expect the vapor pressure to be very close

to the saturated vapor pressure. The vapor pressure is higher at the front face and then gradually decreases

across the thickness, showing the dependence of vapor pressure on temperature. The moisture content curve

indicates that some of the moisture from the front of the fabric has evaporated, which decreases the moisture

content. The water vapor that is produced because of the evaporation process can now diffuse towards the

front face or towards the back face. The diffusion process depends on the gradient of partial pressure P.

Also note that convective heat transfer at the front face is continuously removing energy from the fabric.

Depending on the vapor pressure of the ambient atmosphere, convective mass transfer can add or remove

moisture from the front and rear faces.

Figure 9 shows simulation results at 200 s. The temperature and vapor pressure curves have not changed

significantly from their value at 100 s (Figure 8). The moisture content curve indicates significant evaporation at the front face. This results in wet fabric density approaching the dry fabric density. We also notice

moisture absorbed from the environment at the front face. Higher moisture content levels at the interface

18
Time = 100.0 seconds

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Figure 8: Simulation results at time t 100 s for a wet thermal liner subjected to an external incident flux 2 5

kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content (bottom

left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of distance

measured from the front face of the thermal liner.

between the air gap and the face cloth is indicative of condensation at the face cloth.

At 300 s after the onset of external radiation (Figure 10), we start observing an increase in the temperature at the front face to approximately 70 oC . The vapor pressure curve shows a peak at 0 

1 cm. The

moisture content curve indicates that the front half of the batting material is dry. This is also manifested

in the fact that the wet fabric density approaches the dry fabric density. Notice that the peak in the vapor

pressure curve coincides with an increase in moisture content. Both these event occur at 0 

1 cm. At 400 s

(Figure 11) much of the batting material is essentially dry. The vapor pressure curve shows a peak at 0 

22

cm, and the temperature in the batting is beginning to increase at a rapid rate. At t 500 s (Figure 12), we

observe that the temperature has reached its steady state value everywhere in the thermal liner. The vapor

pressure is equal to the ambient pressure and the moisture content is zero at each point in the fabric. The

fabric is now completely dry. The density distribution curve indicates that the fabric density is equal to that

of the dry fabric.

At t 750 s, the external radiation source is cut off, and as a result, we observe a rapid drop in temperatures due to convective losses at the boundaries. Because of higher heat capacity of the face cloth (higher

density), the temperature of the batting is less than that of the face cloth. We also observe that since the

19
Time = 200.0 seconds

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Figure 9: Simulation results at time t 200 s for a wet thermal liner subjected to an external incident flux 2 5

kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content (bottom

left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of distance

measured from the front face of the thermal liner.

vapor pressure is less than the ambient vapor pressure small quantities of water is absorbed at the fabric

boundaries due to convective mass transfer.

7.3 Boundary Fluxes

Figure 14 shows the convective heat flux at the front surface and the back surface as a function of time.

This term is a measure of how rapidly energy is removed from the fabric layers at the outer boundaries. At

the front surface, a negative value indicates that the energy flux is in the x direction implying that energy

is being removed from the front face. Similarly at the back face, a positive value indicates that the energy

flux is in the 

x direction which implies that energy is being removed from the fabric layers. The profile

looks very similar to the temperature profiles at the front and back face as shown in Figure 4. In the case of

front surface, the profile is inverted or reflected about the x axis. The convective heat flux increases as the

temperature of the fabric increases.

The radiative flux on the front and back surfaces have been shown in figure 15. The radiative flux

incident on the front surface is 2 5 kW/m2. As the front surface becomes heated it also radiates some

20
Time = 300.0 seconds

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Figure 10: Simulation results at time t 300 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

distance measured from the front face of the thermal liner.

energy to the surroundings. The net flux, which is the difference between the incident flux and the reradiated amount is shown. For the back face, the radiative flux term is primarily because of heating of the

back face, and as a result, it exhibits a pattern similar to the temperature profile at the back face (Figure 4).

Convective mass transfer at the outer boundaries is shown in Figure 16. A negative value of mass flux

at the front face, indicates flux in the x direction and signifies removal of water vapor at the front face.

A positive value of mass flux at the back face, indicates flux in the 

x direction and removal of vapor at

the back face. At the front face, the mass flux initially increases rapidly with time as the water on the front

face starts evaporating. It then stabilizes at an absolute value of 4 0 105 g/cm2 s until the front face is

completely dry (t 200 s). Beyond 200 s, the convective mass flux at the front face decreases and then

stabilizes at 0 0 when the fabric is completely dry. After t 750 s, when the external radiation is cut off,

the convective mass flux at the front face becomes positive, indicating absorption of moisture at the front

face. At the back face, convective mass flux increases rapidly within 30  40 s and then stabilizes at a value

of 8 0 105 g/cm2 s. Note that the absolute value of mass flux at the back face is larger than that at the

front face. As the face cloth dries up around t 400 s, there is a sharp jump in convective flux at the back

face. Once the material is completely dry the flux settles down to zero until t 750 s. At this point the

21
Time = 400.0 seconds

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Figure 11: Simulation results at time t 400 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

distance measured from the front face of the thermal liner.

convective mass flux values at the back face becomes negative indicating absorption of moisture from the

ambient atmosphere.

7.4 Wet Turnout Coat Simulation

A series of simulations were next conducted to study the performance of a typical turnout coat used by fire

fighters. The turnout coat consists of three fabric layers, the shell (outermost layer, farthest from skin), the

moisture barrier and the thermal liner. The shell material used in these calculations is Nomex III-Defender,

the moisture barrier is Neo-Guard and the thermal liner is Aralite. Figure 17 shows the three fabric layers

separated by an air gap of 1 

0 mm. Unlike the earlier calculations, the thermal liner was not separated

into the batting and the face cloth, but instead treated as one material. Many fire fighter coats are made

using these materials. To perform a simulation, the thickness, density, conductivity, specific heat and the

optical properties of transmissivity and reflectivity were needed. These properties have been measured and

tabulated by Lawson et al [23] and were directly used in our calculations.

For the turnout coat simulations, the left face of the outer shell is subjected to an external incident flux

22
Time = 500.0 seconds

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Figure 12: Simulation results at time t 500 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

distance measured from the front face of the thermal liner.

of 2 5 kW/m2starting at t 0 s and lasting for approximately 750 s. The simulation carries on until 850 s

to allow for the fabrics to cool down. Wet turnout coat simulations were performed by assuming that only

the thermal liner is initially wet and has a moisture content value of 1 

0. Even though the outer shell and

the moisture barrier are initially completely dry, water vapor can diffuse and convect to and condense on

these fabric layers. Convective heat and mass transfer from the turnout coat occur at the front and back face,

which are open to the atmosphere. It is assumed that the air-gap which is approximately 1 mm thick does not

allow for a fully developed boundary layer. Therefore, the dominant mechanisms of heat and mass transfer

at the fabric air-gap interface are through conduction and mass diffusion, respectively.

Figure 18 shows temperature time curves for the front and back faces of the turnout coat ensemble.

The comparison in this case is for a thermal liner that is initially completely dry and a wet thermal liner.

At the front face, the differences between dry turnout coat and wet turnout coat are not very significant.

However, the back face shows large differences in temperature between dry and wet turnout coat ensemble.

This is because for the wet turnout coat simulation, water is present only in the thermal liner, while the outer

shell is completely dry initially. This moisture distribution affects the temperature at the back face much

more significantly than that at the front face. The clothing ensemble clearly provides protection against the

23
Time = 800.0 seconds

Distance (cm)

Density Distribution (gm/cm3

)

0 0.1 0.2 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6 Fabric Density

Dry Density

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3

0

0.5

1

1.5

2

2.5

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3

0

10

20

30

40

50

60

70

80

90

100

110

120

Distance (cm)

Vapor Pressure (dynes/cm2

)

0 0.1 0.2 0.3

0

20000

40000

60000

80000

100000

120000

140000

Figure 13: Simulation results at time t 800 s for a wet thermal liner subjected to an external incident

flux 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

distance measured from the front face of the thermal liner.

incident radiative flux. From the outside of the shell to the back of the thermal liner the temperature fell

nearly 70 oC for the wet thermal liner case, and 40 oC for the dry thermal liner case.

Figures 19 and 20 show time dependent simulation results for a wet turnout coat ensemble, subjected to

an external incident flux. These figures are similar to Figures 7-13 and the reader is directed to the discussion

of Figure 7 for the significance of these plots. Dotted lines have been drawn on Figure 19 and 20 indicating

the location of the interfaces. The various fabric layers have also been marked for clarity. Initially, at t 0

s, only the thermal liner is wet, with a moisture content value of 1 

0. When the turnout coat is subjected

to radiative heating, temperatures in the outer shell and moisture barrier increase significantly. At t 100

s (Figure 19), the temperature in the thermal liner is relatively small and is almost constant through out its

thickness. We observe that the front of the thermal liner has started drying. The vapor pressure curve peaks

in this area, and shows a relatively lower value on either side. This indicates diffusion of water vapor from

the thermal liner to the shell material and the moisture barrier. At t 600 s, (Figure 20) we observe higher

temperatures in the thermal liner. The front part of the thermal liner is completely dry at this stage. We also

observe convective mass loss at the back end of the liner. The wet fabric density is also shown to approach

the dry density as moisture evaporates from the turnout coat ensemble.

24
TIME(s)

C

o

n

v

e

ctiv

e

h

e

at flu

x (k

W/

m

2

)

0 200 400 600 800

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4 Front Surface

Back Surface

Figure 14: Numerical predictions of convective heat flux at the boundaries (front and back faces) as a

function of time.

8 Concluding Remarks

Governing equations for transient heat and mass (moisture) transfer through fire fighter protective clothing

when subjected to a radiative heat flux are derived from first principles. These equations account for the

conductive, convective and radiative heat transfer through multi-layered fabric, as well as solve for convection, diffusion, evaporation, condensation, adsorption and desorption of moisture through the porous cloth.

The effect of moisture on thermodynamic and transport properties is also accounted for in the governing

equations. A simplified approximation for the governing equations are solved using an explicit, second

order Runge-Kutta time stepping technique, subjected to appropriate boundary and interface conditions.

Numerical simulations are performed to obtain a detailed understanding of heat and mass transport

through wet thermal liners and turnout coat ensemble. Results are compared with experimental data when

available and are found to be in good agreement. Peak temperatures are predicted to within 10 % accuracy.

Moisture in the cloth evaporates when heated and part of it diffuses and recondenses on different parts of the

fabric depending on local temperature. Moisture content and distribution along the thickness of the fabric is

found to have a profound effect on the computed and measured temperature. We also conclude that moisture

can have a significant effect on observed temperature and heat flux at the skin surface and can enhance or

reduce burn injury (under different conditions) to the fire fighter.

25
TIME(s)

R

a

diativ

e

Flu

x (k

W/

m

2

)

0 200 400 600 800

-0.5

0

0.5

1

1.5

2

Front Surface

Back Surface

Figure 15: Numerical predictions of radiative heat flux at the boundaries (front and back faces) as a function

of time.

9 Directions for Future Research Activities

Many more studies (similar to the one described in this report) need to be completed, to better understand the

thermal performance of fire fighters’ protective clothing, to design safe and effective protective garments, to

predict burn injury and to develop tools for training and assisting the fire fighters subjected to different fire

scenarios. The following is a list of research activities that we are planning for the next few years and which

will be reported in subsequent publications.

1. A detailed sensitivity study on the effect of various parameters such as thermal conductivity, diffusion

coefficient and heat capacity on the final result should be conducted. The influence of the convective

heat and mass transfer correlations on the predicted results should be investigated further. Effect of

geometric parameters such as thickness of the fabric layers and air gap on the final result should be

studied carefully.

2. Effect of moisture on the optical properties of the fabric should be investigated. Note that in the current

simulations, the optical properties of dry fabric layers have been used. Water has strong absorbtion

bands in the near infrared regime, which should be included in the analysis. The sensitivity of optical

properties on computed results should be studied carefully. Use of highly reflective and opaque fabrics

26
TIME(s)

C

o

n

v

e

ctiv

e

M

a

s

s

Flu

x (g

m

/

c

m

2

/

s)

0 200 400 600 800

-4E-05

-2E-05

0

2E-05

4E-05

6E-05

8E-05

0.0001

Front Face

Back Face

Figure 16: Numerical predictions of moisture mass flux at the boundaries (front and back faces) as a function

of time.

in designing protective clothing can reduce fire fighter burn injury.

3. Adsorption isotherms measurements have been limited to three fabrics (Aralite, Neo-Guard and Nom

ex III-Defender) that were directly relevant to this study. Measurement of adsorption isotherm for

other fire fighter protective clothing should be completed, to make the model as general as possible.

These measurements should cover a wide range of temperature.

4. More experiments with mass loss measurements, temperature measurements and heat flux measurements should be performed and compared with the numerical results to fully evaluate the model

approximations.

5. A skin model should be coupled with the heat and mass transfer model to predict burn injury to the

fire fighter. This model should account for energy removal by the flow of blood and sweat formation

at the skin surface for which correlations should be developed [12]. Such a coupled model would be

very useful in predicting time to onset of pain and 1

st

and 2

nd degree burns from thermal radiation

[24], [25], [26], [27].

6. Scald injuries and steam burns (when moisture condenses on the skin surface) should be investigated

using model discussed in item 5.

27
Firefighter protective clothing ensemble

Air

G

a

p

External

Incident

Flux

X

Convective Heat

and Mass Transfer

Convective Heat

and Mass Transfer

Air

G

a

p

O

u

t

e

r

S

h

ell

M

ois

t

u

r

e

B

a

r

rie

r

T

h

e

r

m

al Lin

e

r

Figure 17: Schematic of a typical three layered turnout coat used as firefighter protective clothing, subjected

to an incident radiative flux.

7. The heat and mass transfer model for porous clothing assemblies should be coupled with an engineering model of the human body to perform a detailed thermal analysis of human body clothing

environment systems.

8. The thermal model of the human body - clothing system should obtain input data (heat flux, ambient

temperature and humidity) from an FDS simulation [28] of a typical fire in an office building, town

house, wildland fire or any other fire scenario in which a fire fighter will be present.

10 Acknowledgments

Appreciation is extended to Robert T. McCarthy of the United States Fire Administration for assistance

provided during discussions related to fire fighter burn injuries and protective clothing performance. The

authors would like to thank TAKASHI KASHIWAGI for his encouragement in studying the subject of transport processes in porous media and numerical modeling of condensed phases. Appreciation is extended to

HOWARD BAUM for very helpful discussions on radiative heat transfer modeling. TINH NGUYEN and ERIC

BYRD have assisted in obtaining the equilibrium sorption isotherms measurements for typical fire fighter

protective clothing. We appreciate SIMON KAPLAN for providing measurements on thermo-optical proper28
TIME(s)

T

e

m

p

e

r

atu

r

e (

o

C)

T

otal w

eig

ht of w

ate

r (g)

0 200 400 600 800

20

30

40

50

60

70

80

90

100

110

120

2

4

6

8

10

12

14

16

18

Wet Protective Clothing

Front Surface

Back Surface

Total weight of water

0 200 400 600 800

20

30

40

50

60

70

80

90

100

110

120

Front Surface

Back Surface

Dry Protective Clothing

Figure 18: Comparison of numerically predicted temperature histories for the dry and wet turnout coat. For

each case, numerical results have been shown for the front and back faces. The mass loss curve during

evaporation of water from the turnout coat has also been shown on the Y2 axis.

ties of the fabrics and for informative discussions. Finally, we thank ANTHONY HAMINS, DAVE EVANS,

NELSON BRYNER and DAN MADRYZKOWSKI for their overall support and guidance.

References

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[4] E.R.G. Eckert and M. Faghri. A general analysis of moisture migration caused by temperature differences in an unsaturated porous medium. Int. J. Heat Mass Transfer, 23:1613–1623, 1980.

29
Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

90

100

110

Thermal Liner

Moisture Barrier

Outer Shell

Air Gap

Air Gap

Distance (cm)

Vapor Pressure dynes/cm2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10000

20000

30000

40000

50000

60000

70000

80000

Distance (cm)

Weight Distribution gm/cm3

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0

0.1

0.2

0.3

0.4

0.5

0.6

Wet Fabric

Dry Fabric

Time = 100.0 seconds

Figure 19: Simulation results at time t 100 s for a wet turnout coat subjected to an external incident flux

of 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

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30
Time = 600.0 seconds

Distance (cm)

Moisture Content gm/gm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Distance (cm)

Weight Distribution gm/cm3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

Wet Fabric

Dry Fabric

Distance (cm)

Temperature 0

C

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

90

100

110

Thermal Liner

Moisture Barrier

Outer Shell

Air Gap

Air Gap

Distance (cm)

Vapor Pressure dynes/cm2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10000

20000

30000

40000

50000

60000

70000

80000

Figure 20: Simulation results at time t 600 s for a wet turnout coat subjected to an external incident flux

of 2 5 kW/m2. Temperature (top left sub-figure), vapor pressure (top right sub-figure), moisture content

(bottom left sub-figure) and dry / wet density (bottom right sub-figure) has been shown as a function of

distance measured from the front face of the turnout coat.

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Fire Dynamics Simulator (Version 2) - Technical Reference Guide. Technical Report NISTIR 6783,

National Institute of Standards and Technology, Gaithersburg, Maryland, November 2001.

32