NIST IR 7461 

Heat and Mass Transfer Through 

Gypsum Partitions Subjected to Fire 

Exposures 

S Kukuck 

 

 

NISTIR 7461

Heat and Mass Transfer Through 

Gypsum Partitions Subjected to Fire 

Exposures

Scott Kukuck 

Building and Fire Research Laboratory 

August 2009

U.S. Department of Commerce

Gary Locke, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Deputy Director
ii 
iii 

ABSTRACT 

A model is presented that describes the heat transfer through a gypsum wallboard partition 

assembly incorporating the mass transport effects of water in liquid and vapor form. Sources of 

water include surface bound (adsorbed) water and hydrated water that is chemically bound with 

the crystal matrix of gypsum. Liberated water is allowed to migrate through the porous structure 

through molecular diffusion and pressure driven flow. Evaporation or condensation occurs when 

the partial pressure of water vapor with the pore space is less than or greater than the saturation 

pressure, respectively. Results obtained from the model are compared to measurements taken 

during a standard fire resistance test. It is found that the surface temperatures are typically underpredicted, although qualitatively similar behavior is observed. The analysis implies that the 

liberation and transport of water in both its liquid and vapor form plays a significant role in the 

thermal response of gypsum wallboard subjected to fire exposures, perhaps even beyond the 

extent to which the current model has been developed. The model can be used, under the 

assumptions through which it was developed, to conduct sensitivity studies of the physical 

parameters and evaluate the effect upon the fire resistance of the system. 
iv 

ACKNOWLEDGEMENTS

 

The author wishes to acknowledge Samuel Manzello, Richard Gann, Kuldeep Prasad and Walter 

Jones of the Fire Research Division for their assistance during the formulation of the model and 

discussions about the physical response of gypsum board subjected to fire exposures. 

DISCLAIMER 

Certain companies and commercial products are identified in this paper in order to specify 

adequately the source of information or of equipment used. Such identification does not imply 

endorsement or recommendation by the National Institute of Standards and Technology, nor 

does it imply that this source or equipment is the best available for the purpose. 

POLICY OF NIST REGARDING THE INTERNATIONAL SYSTEM OF UNITS 

The policy of NIST is to use the International System of Units (metric units) in all publications. 

In this document, however, units are presented in metric units or the inch-pound system, 

whichever is prevalent to the discipline. 
v 

TABLE OF CONTENTS 

page

ABSTRACT .......................................................................................... iii 

ACKNOWLEDGEMENTS ........................................................................ iv 

DISCLAIMER ................................................................................. iv 

POLICY OF NIST REGARDING THE INTERNATIONAL SYSTEM OF UNITS iv 

INTRODUCTION ................................................................................. 1 

MODEL DEVELOPMENT ........................................................................ 4 

 GYPSUM WALLBOARD 4 

 GAS LAYERS 7 

 BOUNDARY CONDITIONS 9 

 SOLUTION TECHNIQUE 10 

MODEL PARAMETERS ........................................................................ 11 

 DENSITY 11 

 SPECIFIC HEAT 11 

 THERMAL CONDUCTIVITY 11 

 POROSITY 12 

 DIFFUSIVITY 12 

 PERMEABILITY 13 

 ADSORPTION 13 

 REACTIONS 13 

 GAS PROPERTIES 14 

 WATER PROPERTIES 14 

RESULTS .......................................................................................... 14 

CONCLUSIONS & FUTURE WORK ...................................................... 18 

REFERENCES ................................................................................. 21 
vi 
1

Heat and Mass Transfer Through Gypsum Partitions Subjected to Fire 

Exposures 

INTRODUCTION 

Traditional fire resistance testing in the United States has been based upon ASTM standard E119, 

“Standard Test Methods for Fire Tests of Building Construction and Materials” [1]. In this test, 

building components are subjected to a furnace exposure intended to represent a standard fire. 

The components are then rated, with units of time, on their ability to withstand the exposure up 

to some defined criteria. The results of the test have been typically placed in prescriptive 

building codes that mandate specific ratings for construction assemblies. Issues with this 

approach revolve around the inability to predict the response of the construction to fires that 

almost certainly will not match the standard fire simulated in the furnace. Thus while 

construction A may achieve a rating twice as long as construction B in the furnace exposure, it is 

not possible to predict how long these constructions will survive, either absolutely or relatively, 

under a real exposure from simply the test measurements. Furthermore, prescribed ratings for all 

components of a building design may result in excessive protection of portions of the 

construction that may never see exposures matching the standard fire or perhaps, more 

dangerously, insufficient protection of critical components that may see exposures exceeding that 

of the standard fire. 

With these issues in mind, some authorizing bodies have begun to implement the use of 

performance-based criteria in their building codes. Under this approach, designs are assessed on 

how they would perform during actual exposures. The caveat to this approach is that it is not 

feasible, neither practically nor economically, to test in the full scale all possible exposures a 

building design may be subjected to. What is needed for this approach are models capable of 

accurately predicting the response of construction assemblies to a wide range of various 

conditions. These models could draw upon a small subset of full and reduced scale tests to yield 

the predicted response. 

In the following work we focus on modeling one of the most common means of reducing fire 

growth and spread, i.e. compartmentation. Specifically, we deal with the response of gypsum 

partitions subjected to fire exposures. While models do currently exist [2-4], most utilize a single 

energy conservation equation. To approximate the effects of mass transport through and 

chemical dehydration of the materials that comprise the core of the gypsum wallboard, the 

thermal properties of the core material are typically modified in some manner. These models 

have shown success in predicting results from standard exposures. It is unclear, however, how 

the property modifications of these models respond to non-standard exposures. Mixed success 

has been observed in cases where comparisons of model results have been made with 

measurements from nonstandard fires. 

The core material of gypsum wallboard is a porous solid composed primarily of calcium sulfate 

dihydrate (CaSO4.2H2O), a naturally occurring mineral in which two water molecules are 

chemically bound for every one calcium sulfate molecule within the crystal matrix. The presence 
2

of the water molecules is a key feature in establishing the fire resistance properties of gypsum. 

When heated, crystalline gypsum dehydrates and water is liberated, typically in two separate 

reversible chemical reactions [5], 

H O

2

3 H O

2

1 CaSO .2H O CaSO . 4 2  Q  4 2  2 (1) 

H O

2

1 H O CaSO

2

1 CaSO . 4 2  Q  4  2 (2) 

Both of these dehydration reactions are endothermic, i.e. they absorb energy, and therefore retard 

the flow of heat and enhance the fire resistance. These reactions generally occur at temperatures 

of between 125 °C and 225 °C. 

A third reaction occurs at even higher temperature when the molecular structure of the soluble 

crystal reorganizes itself into a lower insoluble energy state, 

CaSO4 (sol)  CaSO4 (insol)  Q (3) 

In contrast to the dehydration, this reaction is exothermic, i.e. releases energy. While the amount 

of energy released is not a significantly large amount, the molecular restructuring may eventually 

play an important role in establishing conditions for cracking of the gypsum board. This reaction 

occurs at temperature of around 400 °C, a temperature which also corresponds to a significant 

contraction of gypsum boards [6]. 

To demonstrate the importance of these reactions, the results of a Differential Scanning 

Calorimeter (DSC) scan is presented in figure 1 for the material comprising the core of a Type-X 

gypsum board [7]. In the figure, the specific heat with respect to the initial specimen mass is 

plotted as a function of temperature. Clearly visible on the graph are the two peaks from the 

dehydration reactions as well as the molecular restructuring reaction. The large contribution to 

the apparent specific heat from the dehydrations demonstrates the need to incorporate reaction 

effects into any heat transfer model for gypsum wallboard. 

Including simply the thermal effects does not complete the story, however. A simple mass 

balance shows that CaSO4.2H2O is composed of approximately 21 % by mass water. A gypsum 

core containing 85 % by mass CaSO4.2H2O and having a density of 

650 kg / m3

 therefore has a potential water density of 116 kg/m3. It is easy to show that if this 

water remains completely in situ that it would necessarily exist in the saturated state. This would 

result in the internal pore pressure of the board being at the saturation pressure. At 250 °C this is 

4.0 MPa (39 atm. Or 580 psi) and by 350 °C the pore pressures would be 16.5 MPa (163 atm. Or 

2400 psi). The porous nature of gypsum board necessitates that these pressures result in at least 

some migration of the water vapor. This migration is not trivial, however, and may present its 

own unique challenge. If liberated water vapor migrates to a cooler region it may condense, 

releasing energy and increasing the local temperature. As heat continues to be transported across 

the material this water will eventually evaporate again, continuing the cycle through the width of 

the board. While in its liquid state, the relatively large thermal conductivity of water will 

increase the flux of heat conducted through the region. 

An additional source of water that exists for gypsum board is due to adsorption effects. 

Adsorption is a weak bonding of liquid water to the pore surfaces. The amount of water adsorbed 

is a weak function of temperature, and a strong function of the relative humidity [8]. Although 
3

the overall amount of adsorbed water is typically small, approximately 

3 %, energy is required to liberate it, further retarding the flow of heat. As in case of the hydrated 

water, once liberated the de-adsorbed water vapor will also migrate and potentially condense 

further along during the exposure. 

We present a model that incorporates not only the heat transfer across partitions, but also 

includes the effects of mass transport through the materials comprising the partition. State and 

constitutive relations are included that simulate the dehydration, adsorption and condensation / 

evaporation of water. Bulk mass transport arises from pressure driven flow through a porous 

substance utilizing Darcy’s Law. Molecular diffusion is also included in the model. Results 

obtained using the model are checked against test data from a standard fire resistance test [4,9]. 

Still in the development stage, current model results show qualitatively similar behavior to test 

measurements, however the model under predicts the temperature response of the partition. 

Analysis implies that the transport of moisture does in fact play a significant role in the thermal 

response of gypsum partitions subjected to fire exposure and that transport may well go beyond 

simply pressure driven flow. Although the prediction of temperatures is not yet accurate, useful 

information can still be obtained from the model. These results will be discussed as will future 

avenues of research intended to improve and expand the model. 

0

5000

10000

15000

20000

25000

30000

0 100 200 300 400 500 600

Temperature ( C )

Cp* ( J / K (initial kg) )

Figure 1: Apparent specific heat of 0.0159 m thick Type-X gypsum wallboard [7]. 
4

Model Development 

The basic construction being considered in this work is displayed schematically in figure 2. Here, 

layers of gypsum wallboard are attached on either side of a series of wall studs currently 

considered to be of arbitrary composition. Although the model will be derived in general for any 

given number of dimension, in this initial phase of model development we have restricted 

attention to the thermal response of the gypsum wallboard and therefore will consider a onedimensional model as outlined in the figure. The following sections outline the derivation of the 

model equations for: a) the gypsum wallboard, b) the gas layer between the wallboards arising 

from the studs and c) the boundary conditions. Following the derivations, a brief section 

describing the techniques utilizing in solving the series of derived equations is presented. 

(1) Gypsum Wallboard 

The governing equations utilized to model the transport of heat and mass across gypsum boards 

are obtained from conservation equations adapted for use in a porous substance. Darcy’s law for 

bulk average flow through a porous material therefore supplants the momentum equation. As we 

are interested in heat and mass transfer, it is necessary to express conservation equations for each 

of the possible gas species as well as for any liquid phase water that may arise. 

The gas conservation equations are expressed in molar form as, 

   



 



     





C

C f C f C f CD

t g g g g

1 0 1 1V (4) 

Fire (furnace) 

exposure

One-dimensional 

region of interest

Stud

Gypsum Wallboard

A

B

C

D

Figure 2: A schematic representation of the gypsum partition considered in the model 
5

     S W A

C M t

C f C f C f CD

t g g g g W  



  



 



     





2

2

0 2 2

1

 V (5) 

where in the above expressions: fg is the pore fraction available for the gas, C1 is the molar 

density of air in the pore space, C2 is the molar density of water vapor in the pore space, C is the 

total gas molar density in the pore space and Vg is the bulk average velocity of the gas. Source 

terms in these equations arise from the liberation of hydrated water SW, the evaporation / 

condensation of free water W, and the adsorption / desorption of surface bound water A. 

Parameters and constants in these expressions are the unsaturated porosity of the material , the 

unsaturated diffusivity of water vapor D and the molecular weight of water M2. 

In a similar fashion we can write the conservation of liquid water in mass form as 

   t

W f f

t 



   



0    V (6) 

where fl is the pore fraction containing liquid water, l is the density of water and Vl is the bulk 

average velocity of the liquid. 

As stated above, the bulk average velocities for both the liquid and gases are obtained utilizing 

Darcy’s law, 

p

   

V (7) 

where  is the permeability,  is the viscosity and p is the pressure. 

The final conservation equation governs the transport of energy across the system. If we neglect 

energy transport in the gas phase due to convective effects and assume that the internal energy 

and enthalpy of the solid and gas phases are approximately equal, then we obtain, 

  



 









 





 



     

 

















t

A h

t

W h

t

S k T h

f h

t

h A

t

h W

t

h S

c S W A

S A

   

  V

 (8) 

where S is the density of the underlying porous solid, hS is the enthalpy of the porous solid, hl is 

the enthalpy of the free liquid water and hA is the enthalpy of the adsorbed water. The terms hS, 

hW and hA correspond to the energy required for the changes in state / phase associated with 

the dehydration of water from the gypsum, the condensation of free liquid water and the 

adsorption of surface bound water, respectively. The remaining parameter on the right hand side 

of the equation is the composite thermal conductivity kc, which includes not only the 

conductivity of the solid material but also includes a contribution from the presence of any liquid 

phase water and is approximated by the expression, 

  k k f k c  S 0 (9) 

with ks the thermal conductivity of the solid and kl the thermal conductivity of liquid water. We 

now introduce the concept of specific heat to obtain the final form of the energy equation, 
6

 

  



 









 





 



     

 





 

t

A h

t

W h

t

S k T h

f C T

t

T SC WC AC

c S W A

S  A   V

 (10) 

with CS, Cl and CA the specific heats of the porous solid, free liquid water and adsorbed water 

respectively and T the temperature. 

The conservation equations are supplemented with appropriate equations to fully define the state 

of the gas and liquid. Each gas phase component is considered to be an ideal gas, 

p1  C1R0T (11) 

p2  C2R0T (12) 

1 2 p  p  p (13) 

where pi is the partial pressure of the i

 th gas component, p is the total pressure and R0 is the 

universal gas constant. Condensation / evaporation is governed by partial pressure of the water 

vapor, p2, and the saturation pressure which is a function of temperature only, 

psat  psat  T . (14) 

With the conservation and state equations so defined, we turn now to the evaluation of specific 

terms. For the absorption term, we recognize that although the amount of adsorbed moisture 

depends upon the temperature, this dependence is typically weak. We chose therefore to neglect 

the temperature dependence and allow the amount of absorbed moisture to depend upon the local 

relative humidity only. The main purpose of including the effect of adsorption is to incorporate 

the initial presence of the surface bound water. We therefore will also introduce the 

approximation that adsorption is only important for the core material in its initial, and not 

dehydrated state. The equation that will govern the amount of adsorbed moisture then is, 

A  A   (15) 

where  is the local relative humidity. This isotherm can be measured and then a functional 

correlation introduced that allows us to define the amount of adsorbed moisture present for a 

pore space at a given local relative humidity. 

For the chemical reaction terms, we recognize from figure 1 that there may exist for the core 

material the possibility of four unique states, each with its own thermal properties. We chose 

therefore to define a constitutive variable for each state, i, that ranges from zero to one. If i is 

identically zero, then there does not exist any solid in state i at that location. When i is equal to 

one, then the entire solid is composed of only the i

 th state. Transitions from one state to the next 

are considered to be reactions of an Arrhenius form that we write as, 

n B T A e

t

 /  



 (16) 

where A is a pre-exponential term (necessarily negative for the above form), B is similar to the 

activation energy of gas phase kinetics, and n is the reaction order. The dehydration reactions for 

gypsum are complex, and in actuality depend upon not only the amount of the initial state 

present () but also on the partial pressure of water vapor surrounding the substance (p2) [5]. The 

level of detail required to completely define the reaction including this fact does not exist in the 

literature, however, and so we chose the above form as the model for the reactions. The presence 
7

of any material in a lower state (e.g. state 2) will depend first upon there being a reaction of the 

next higher state (e.g. state 1). The complete system of equations for the possible states of the 

core material is expressed therefore as, 

n B T A e

t

/

1 1

1 1  1  



 (17) 

n B T n B T A e A e

t

/

1 1

/

2 2

2 2  2 1  1    



 (18) 

n B T n B T A e A e

t

/

2 2

/

3 3

3 3  3 2  2    



 (19) 

n B T A e

t

/

3 3

4 3  3   



 . (20) 

The introduction of the constitutive variables for each state, i, further allows us to define the 

thermal properties of the solid material as a sum of the properties for each of the individual states, 

S  1 S1  2 S 2  3 S 3  4 S 4 (21) 

SCS  1 S1CS1  2 S 2CS 2  3 S 3CS 3  4 S 4CS 4 (22) 

S 1 S1 2 S 2 3 S 3 4 S 4 k   k   k   k   k (23) 

where Si is the density, CSi is the specific heat and kSi is the thermal conductivity of the 

i

 th state. 

(2) Gas Layers 

We treat the gas layers created by the studs as a lumped control volume at a uniform state, and 

therefore assume a well-mixed gas volume. We also assume that although the wallboards are 

securely fastened to the underlying structural framework that there exists sufficient leak points so 

as to maintain a constant pressure with the gas layer. A simplified schematic for this volume is 

presented in figure 3. 

Conservation of species applied to the control volume yields the following equations, 

   



A

C dA VC e t

C V 1

''

1

1  (24) 

   



A

VC e C dA

t

C V 2

''

2

2  (25) 

and conservation of energy the following 

     e e e e

A

C u C u C h C h q dA V C h C h

t

V 1 1 2 2

''

2

''

1 2

''

1 1 2 2 1        



  . (26) 

In the above equations V is the volume of the gas layer, A the associated area of the boundaries 

of the gas layer, C1 the molar density of air molecules, C2 the molar density of water vapor 

molecules and ui the molar specific internal energy of the i

th gas species. The flux terms '' C1 and 

'' C2 correspond to the mass flux that enters the control volume through the wallboard boundaries 

with corresponding molar specific enthalpy hi. The terms C1e  and C2e  as h1e and h2e are the 

molar densities and molar specific enthalpies associated with the flow of gas that must exit (or 

enter) the control volume so as to satisfy the constant pressure constraint. We assume that the gas 
8

comprising the control volume is transparent to radiation and therefore the heat flux '' q is simply 

due to convection effects from the wallboard boundaries to the gas. 

The mass flux terms included in the above equations may arise from multiple sources. The first 

and most obvious is the flow of gas from the porous solid to the gas layer. The second source 

that may arise is from the evaporation / condensation of liquid water from the boundary of the 

wallboard. We assume that this layer (if it exists) is small and does not intrude upon the control 

volume. Furthermore, any heat gain or loss associated with the liquid change of state is applied 

to the solid and not to the gas. Lastly, if the associated flux is positive, i.e. mass is entering the 

control volume, then the enthalpy hi is evaluated at the boundary temperature. If the flux is 

negative, i.e. mass is leaving the control volume, then the enthalpy hi is evaluated at the control 

volume temperature. 

These equations are again supplemented by the appropriate state equations for a multicomponent ideal gas, 

p1  C1R0T (27) 

p2  C2R0T (28) 

1 2 p  p  p . (29) 

We will also introduce specific heats for the gases to express both the internal energy and the 

enthalpy through, 

  h  h0  Cp T T0 (30) 

  u  u0  Cv T T0 (31) 

Tb1 Tb2

Heat Flux

Mass Flux

Mass flow to maintain 

pressure constraint

T

p

p2

Figure 3: A simplified schematic of the control volume representation for the gas layer 
9

where Cp is the specific heat of the gas at constant pressure and Cv is the specific heat of the gas 

at constant volume. The subscript 0 in the above expressions denote a suitable reference state. 

(3) Boundary Conditions 

We now discuss appropriate boundary conditions for use in the model. Because the model 

incorporates not only heat but also mass transfer, the number of applied conditions increases as it 

is necessary to supply information regarding the state and composition of the gases on either side 

of the porous wallboard. We distinguish between external (absolute) boundary conditions 

representing the fire exposure and ambient, and internal boundary conditions at gas layer / 

wallboard interfaces. 

External Boundaries 

As in the air layers we assume that the gas surrounding the wallboard is well mixed. Thus for the 

mass conservation conditions on the external boundaries, we apply pressure (partial and total) 

conditions at the interface with the values equal to those of the gas. We further assume that the 

total pressure in both the fire and in the ambient is maintained at a constant value, 

0 p p boundary  (30) 

p p  t 2 boundary  2 (31) 

For the thermal boundary conditions, heat flux is applied to the wallboard through both 

convective and radiative mechanisms. For the convective condition we introduce an expression 

appropriate for natural convection on a vertical surface, 

  qconvective  h T0 Tb

'' (32) 

with the heat transfer coefficient evaluated according to the appropriate correlation, c.f. [10]. In 

the above expression, h is the effective heat transfer coefficient, T0 is the gas temperature and Tb

is the boundary surface temperature. We recognize that while the well-mixed assumption of the 

gas layer implies a sufficient velocity distribution to stir the gas, this may negate the assumption 

of natural convection. Unfortunately, there is typically insufficient information provided to 

evaluate a forced convection correlation. Furthermore, while there are convective influences, 

especially early in the exposure and at the ambient boundary, the dominant mechanism for heat 

transfer throughout the majority of the exposure will be due primarily to radiation and will 

quickly overshadow the convection. 

For the radiative flux contribution, we note that there may be both an applied flux independent of 

the gas condition, e.g. for radiant panel exposures during testing or perhaps walls on the opposite 

side of the compartment that are at a different temperature, as well as contribution from the 

surrounding gas in fire exposures. We choose therefore to include separate terms for each of 

these possible radiant sources, 

    4 4

0

'' ''

radiative ext eff T Tb q  q t    (33) 

where eff is the effective emissivity that incorporates the emissivities of the surrounding gas and 

that of the porous solid. 
10

By applying an infinitesimally thin control volume at the boundary interface, the thermal 

boundary condition is derived from the conservation of energy at the boundary and can be 

expressed as, 

    ''

0

4 4 n 0 ˆ comp T boundary eff T Tb h T Tb qext  k          . (34) 

Internal Boundaries 

The application of boundary conditions for the internal gas layers is similar to that presented 

above for the external boundaries. We assume, however, that the gas layer is transparent to 

radiation, and therefore the heat flux at the two opposing surfaces is dependent upon the 

temperature of each surface. In a similar manner to that presented above for the external 

boundary conditions, the equations expressing conditions at the internal boundaries are given to 

be, 

p boundary 1  p boundary 2  pg (35) 

boundary boundary g p p p 2 1  2 2  2 (36) 

    comp T boundary eff Tb Tb h Tb Tg  k      1 1  4

2

4 n

1 1 ˆ   (37) 

    2 2

4

2

4

1 2

nˆ eff b b g b boundary  kcompT     T T  h T T (38) 

where the terms pg, p2g and Tg represent the pressure, partial pressure of water vapor and 

temperature of the gas layer, respectively. The effective emissivity in the above expressions now 

depends upon the emissivities of each of the two surfaces, and is evaluated from the expression, 

1

1 2

1 1 1 















     

 eff . (39) 

The convective heat transfer coefficients, h1 and h2, are evaluated utilizing the same natural 

convection correlations as for the external boundaries. 

(4) Solution Technique 

The complex and nonlinear nature of the presented equations for modeling the heat and mass 

transfer through gypsum partitions necessitates the use of numerical methods in obtaining 

solutions. We implement a marker and cell (MAC) approach with the solid material divided into 

a finite number of cells. Vector quantities are evaluated at cell boundaries while scalar terms are 

evaluated at cell centers. Diffusive terms are calculated using a second-order central difference 

scheme while convective terms utilize an upwind biased approach. 

To reduce as much as possible issues of stability, we adopt a backward Euler approach for the 

temporal derivatives. While this method is unconditionally stable for linear equations, the 

nonlinear nature of the equations as well as the discontinuities arising from liquid / gas phase 

changes require the use of a stability criteria similar to the CFL condition observed for explicit 

schemes, 

Vmax

x

t

   (40) 

where Vmax is the maximum convective velocity of the gas or liquid. The condition manifests 

itself most noticeable when calculations are performed during the dehydration stages of the 

wallboard heating. Once the dehydration of the boards is complete and any liquid water has 
11

evaporated, the mass transport equations become almost trivial and unconditional stability is 

recovered. We use a variable time step where, at the completion of a calculation, the results are 

checked to assess whether the condition expressed in (40) is violated. If it is, the time step is 

reduced and the solution recalculated. If the condition in (40) is not violated, a new time step is 

determined and the solution proceeds. 

Model Parameters 

Of as much importance as the equations are the thermal properties of the gypsum board utilized 

in the model. The parameters utilized are presented below with a discussion of the source from 

which quantities were obtained. 

(1) Density 

The density of the Type-X gypsum board utilized in the simulation was obtained from the 

measurements of Mehaffey et al [9]. This value was chosen as this was the source for the furnace 

test that the model presented will be used to simulate. The measurements further showed that the 

core of the 0.0159 m board lost approximately 17.5 % of its mass during heating. From this value, 

the density of the core material for each state of the CaSO4 

n-hydrite was calculated by assuming that mass loss only occurred through dehydration of the 

gypsum. The calculations predict that the cores were initially composed of approximately 84 % 

CaSO4.2H2O. With these values, the density of the gypsum wallboard for each state of calcium 

sulfate is 

 State # Density ( kg / m3 )

 1 648. 

 2 570. 

 3 534. 

 4 534. 

(2) Specific Heat 

A study is currently underway to measure the specific heat of core material utilized in gypsum 

wallboard as well as describe the dehydration mechanism [7], but is at present still incomplete. 

For the development of the model, therefore, specific heat values were obtained from handbook 

results [11] by assuming that the entire core was composed of initially CaSO4.2H2O. 

 State # Specific Heat ( J / kg K )

 1 1080. 

 2 803. 

 3 703. 

 4 703. 

(3) Thermal Conductivity 

The thermal conductivity utilized was obtained from data presented in [5], and shown in figure 4. 

While conclusions may be reached concerning the state of the calcium sulfate for the measured 

values, incomplete information exists for describing the thermal conductivity across the entire 

temperature range for all states of the calcium sulfate. We therefore chose to assume the 
12

temperature dependent thermal conductivity presented as the solid line in figure 6 for all states of 

the core. 

(4) Porosity 

The porosity of the gypsum board was estimated from mercury injection measurements 

presented in [12]. In this study two different gypsum board samples, one obtained from France 

and one from Denmark, were tested. The similarity of the results provides at least some 

confidence as to the porosity of the boards utilized in the experiment. The porosity value 

assumed for the gypsum board was  0 = 0.3. 

(5) Diffusivity 

The diffusivity of water vapor across a gypsum board has been found to depend upon the amount 

of free or absorbed moisture present in the board as well as on the temperature of the board [13]. 

We chose to model the diffusivity by using the 0 % moisture content diffusivity presented for 

measurements at 6.7 °C (44 °F). The presented governing equations then implement their own 

model for the dependence of the diffusivity on the amount of free condensed water present in the 

board by including the pore fraction available for the gas fg. Temperature and pressure 

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000

Temperature ( C )

k ( W / m K )

measured

model

Figure 4: Measured [6] and as modeled thermal conductivity of gypsum wallboard. 
13

dependence is modeled by assuming ideal gas behavior and estimating the diffusion coefficient 

from the relation [8], 

p

p

T

T

D

D 0

3 2

0 0















  (41) 

where the subscript 0 terms represents the reference state. Both the temperature and pressure 

values used in this expression are absolute. The reference value of the water vapor diffusivity 

was D0 = 9.03E-09 m2

 / s. 

(6) Permeability 

The permeability of gypsum board was calculated from the air flow resistance measurements of 

Bassett [14] for gypsum plasterboard. From these results the permeability is estimated from the 

relation, 

R

l   (42) 

where  is the viscosity, l is the thickness of the board and R is the air flow resistance measured 

at a given pressure differential. The calculated permeability for gypsum board was taken to be 

2.0E-14 m2

. 

(7) Adsorption 

The adsorption of water to the pore surfaces was estimated from the isotherms presented in [8]. 

As discussed previously, no temperature dependence was incorporated on the adsorption 

mechanism. The functional form of the correlation used to express the isotherm is, 

    



   1 1

A S (43) 

with the utilized parameters:  = 0.00336,  = 0 and  = 0.9010. 

(8) Reactions 

The parameters used in the reaction expressions are estimated from early analytical results that 

will be presented in a future publication [7]. The values were obtained by decomposing apparent 

specific heat curves similar to that presented in figure 1. From these values and the Arrhenius 

model, an estimate of the parameters can be made. For the current model, reactions were 

assumed to be only of order 1. The values for A and B from equation (16) used in the 

calculations presented here are, 

 Reaction # A B ( K )

 1 -3.56E30 31 700 

 2 -1.93E21 25 100 

 3 -8.51E23 41 630 

Heats of reaction were calculated from handbook enthalpies of formation [11]. While it was 

possible from the apparent specific heat curves to estimate the heat absorbed or released during 

the chemical reactions, these values required imposing temperature dependent specific heat 

values. This level of detail was not desired in the initial formulation of the model. The heats of 

reaction used in the presented calculations are, 

 Reaction # h ( J / kg of state i )
14

 1 -490 000 

 2 -209 000 

 3 78 000 

(9) Gas Properties 

When constitutive properties are required for the gas mixture, it is assumed that the entire 

mixture is simply air. Thus, for example, in the implementation of Darcy’s Law for the flow of 

gas through the porous material, the viscosity utilized is that for air. Temperature dependence of 

the properties was obtained from the appendix tables of [10]. 

(10) Water Properties 

Viscosity, specific heat and thermal conductivity values for liquid water were obtained from the 

appendix tables of [10]. Enthalpies of evaporation were obtained from the steam tables of [15]. 

Due to the nearly incompressible nature of liquid water, the density of liquid water was assumed 

to be independent of pressure but dependent on temperature with the density values taken from 

the saturated steam tables of [15]. 

Results 

We choose to simulate the results of a fire resistance test originally presented in [4]. The test 

simulated, test #6, is a full scale test of 0.0159 m thick Type-X gypsum board on either side of 

0.089 m wood studs spaced 0.4 m on center. The furnace exposure of the test matches the time / 

temperature curve of ASTM standard E119. Surface temperature results are presented in figure 5 

for the experimental measurements and model predictions along with the ASTM furnace 

temperature curve. 

As can be seen from the figure, the results of the model under-predict the surface temperature as 

compared to the experiment with a few exceptions. The qualitative response however is 

promising as we see that many of the features of the experimental measurements are recovered in 

the model calculations. The model results show that the internal surface of the exposed board 

heats up and then levels off for a brief amount of time. This portion of the curve corresponds to 

the presence of condensed liquid water present within the board between the fire and the internal 

surface. The presence of the liquid water acts as a temperature regulator for the unexposed 

surface. Once the water fully evaporates from the board, the temperature then begins to rise 

again. Similar behavior is also observed on the ambient side of the unexposed board, with the 

additional feature of a slight cooling of the board as the water evaporates. Again, once the water 

fully evaporates from the board, the temperature again begins to rise. While the results of the 

simulation have only been presented for 60 minutes, the simulations were actually allowed to 

proceed for a 75-minute exposure. At the completion of the simulation, conditions had still not 

yet been reached that would represent an insulation failure for the partition, that is 139 °C over 

the initial temperature. While the experiment considered above failed structurally at 50 minutes, 

we can compare the simulation results with a similar test conducted for Type-X gypsum 

wallboard on steel studs with a time to insulation failure was 52 minutes [16]. This comparison 

illustrates the models under-prediction of the rise in temperature. 
15

Quantitatively it appears that insufficient heat is being transported across the boards especially 

during those times when the temperatures are low. During the experiment, the temperature on the 

interior surface of the exposed wallboard was already approximately 60 °C two minutes into the 

test. By five minutes, the temperature on the interior surface was approximately 80 °C. This 

rapid rise cannot be explained through simply conductive effects and therefore points to an 

additional heat transfer mechanism. It was, in fact, this behavior that drove the initial derivation 

of the current model, although it appears that the mass transport in its current form is unable to 

produce the initial heating. It should be noted that the rapid early rise in temperature has been 

observed in the presentation of results from other similar fire resistance test of gypsum partitions 

as well, c.f. [2-4,9]. 

Even though the model does not accurately predict the response of the gypsum board, results of 

the calculations do provide some insight as to how the partition responds to the applied heat flux. 

In figure 6, the total amount of condensed (free) liquid water present in the boards in plotted as a 

function of time. Initially, there is not any liquid water present, however shortly into the test, less 

than 5 minutes, a condensation layer begins to form in the exposed board. The amount of liquid 

water then increases as heat continues to be transferred across the board until approximately 11 

minutes into the test at which point the amount of water rapidly diminishes. The thermal 

conductivity of liquid water at 100 °C is 0.68 W / m K and is approximately four times the 

0

200

400

600

800

1000

0 10 20 30 40 50 60

Time ( min )

Temperature ( C )

ASTM E119

B (exp)

C (exp)

D (exp)

B (mod)

C (mod)

D (mod)

Figure 5: Surface temperature comparison between experimental measurements [4] and 

model predictions. Points B, C and D correspond to labels in figure 2. 
16

thermal conductivity of the underlying solid material. Therefore, when liquid water exists within 

the pore spaces, a greater amount of thermal energy can be conducted through these spaces. The 

rapid heating of the exposed board along with the presence of the liquid water implies that a 

significant amount of water, more than that currently predicted, is condensing out of the gas into 

the pore space. A similar, albeit less severe, result is observed in the unexposed board as well. 

For this board, the slower rate of temperature rise resulted in there being liquid water present 

over a longer time, that is the condensation front moved at a slower rate, although the maximum 

total amount of liquid water present was consistent with that of the exposed board. 

The condensation front that arose in the model remained thin for a majority of its existence. For 

the exposed board, the front initially began in a single computational cell at approximately 250 

seconds into the simulation. The front then grew only very slowly as it progressed through the 

board. At the point at which it reached the unexposed face, approximately 700 seconds into the 

simulation, the thickness was approximately 1 mm, or 6 % of the total board thickness. While the 

heat transfer through the cells that experienced condensation was significantly greater than those 

in which there was not any liquid water present, the small thickness of the condensation layer 

does not allow for sufficient energy transport to match the experimental measurements. This can 

be observed more clearly if we compare the results of the above simulation with a similar 

calculation where we neglect mass transport effects. In figure 7, the surface temperatures are 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60

Time ( min )

Liquid Water Mass ( kg / m 2 )

Exposed Board

Unexposed Board

Figure 6: Total liquid (condensed) water mass per unit area in gypsum boards during 

furnace exposure. 
17

plotted versus time for simulations including mass transport effects and simulations neglecting 

mass transport effects but with all other properties kept equivalent. The figure shows that while 

there is some differences between the two simulations, most noticeably over the time ranges 

where the condensation front is at or near the corresponding surface, generally speaking the 

results are very similar due to the thinness of the condensation front. 

In figure 8, the mole fraction of liquid water present in the air space is plotted as a function of 

time. Initially, a very small portion of the gas contained between the boards is water vapor. As 

the boards heat up, and the dehydrated water migrates, the gas eventually consists almost entirely 

of water vapor. This may play a role in describing the transfer of heat across the gas layer. As 

water vapor absorbs a considerable amount of radiative energy, the assumption that the gas layer 

between the boards is transparent to radiation should be revisited, especially at later times of the 

exposure. Furthermore, that the gas layer is composed of almost entirely water vapor means that 

although the paper backing of the gypsum wallboard will still pyrolyze as the temperature 

increases, there is a lack of any oxygen to support combustion of the products of the pyrolosis. 

Clearly, this fact will only remain consistent until a crack or other entry path opens through the 

wallboard from the inner gas layer to either the fire exposure or to the ambient. 

0.00

100.00

200.00

300.00

400.00

500.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00

Time ( min )

Temperature ( C )

B (mass)

B (no mass)

C (mass)

C (no mass)

D (mass)

D (no mass)

Figure 7: Surface temperature comparison of simulation including mass transport with 

simulation neglecting mass transport. 
18

Conclusions and Future Work 

A model has been presented for describing the heat and mass transfer through gypsum partitions 

subjected to fire exposures. The model, while still in the development stage, under-predicts the 

heat transfer across a partition assembly, but exhibits qualitatively similar behavior to that 

observed during experiments. The model is further able to yield information not only regarding 

the temperature of the gypsum board, but also information regarding the molecular form of the 

CaSO4 present in the board core. This information may be useful in determining conditions for 

crack formation as the board undergoes both heating and cooling during a fire exposure. An 

analysis of the results yields further information as to the importance of incorporating the effects 

of the mass transfer brought about by the dehydration of the gypsum boards especially at early 

stages of the exposure when heat is rapidly transferred across the board as evidenced by the rapid 

rise in temperature on the inner face of the exposed board. 

While the model does not yet accurately predict the thermal response of gypsum boards to fire 

exposures, the results obtained so far point to improvements and enhancements for the model. 

First and foremost in this list is the mass transport model. As stated above, the rapid rise in 

temperature of the internal face of the exposed board implies that an additional heat transfer 

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60

Time ( min )

Mole Fraction ( X 2 )

Figure 8: Water vapor mole fraction in gas layer between gypsum wallboards. 
19

mechanism, not included in the present model, must be present. While mass transfer has been 

included from pressure or expansion driven effects, other mechanisms may still exist that drive 

flows through the gypsum board. The most likely mechanism not included is the potential for 

capillary flow through the pore spaces of the board. This is currently being looked at for possible 

inclusion. 

Another issue that needs to be considered relates to the transfer of heat across the gas layer. The 

current model assumes that any gas present within the layer is transparent to radiation emitted 

from the wallboards. As the wallboards dehydrate, however, the gas layer becomes almost 

entirely composed of water vapor. The absorption spectrum of water vapor may make the 

transparent gas approximation no longer valid. This will depend of course of the optical depth of 

the gas. 

As much as was possible, the values chosen for the physical parameters present with the model 

were selected to represent, from the literature, those most likely to describe the material. Small 

changes in these values could, however, affect the thermal response of the wall construction, 

especially under long duration exposures. A sensitivity study should be conducted, with the 

current model, to assess the relative importance of the physical parameters. This may provide 

additional guidance regarding the capabilities and the gaps present with the model. 

Lastly, the current model treats the wallboard’s structure as remaining fixed throughout the 

exposure and predicts only the thermal response of gypsum. Other effects must also be 

incorporated if the model is to describe all of the possible failure mechanisms that may arise 

when gypsum partitions are exposed to fire. Some effects that could be included are cracking, 

crazing, shrinkage and ablation of the wallboard material. 
20
21

References: 

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Construction and Materials, ASTM Standard E119-00a, West Conshohocken, PA (2003). 

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Materials 26, pp. 37-45 (2002). 

[3] Collier P C R and Buchanan A H, “Fire Resistance of Lightweight Timber Framed Walls,” 

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[13] Fanney A H, Thomas W C, Burch D M and Mathena L R, “Measurements of Moisture 

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[14] Bassett M, “Air Flow Resistances in Timber Frame Walls,” Proceedings of the New 

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