Postgraduate Research Conference 2009
The Prize Winners
PRESENTATION: A Numerical Method for Extracting Temperature-Dependent Thermal Conductivity of Gypsum Boards
student: Ima Rahmanian
supervisor: Dr Yong Wang
Abstract
Gypsum board based systems are now widely used in buildings, as walls or ceilings, to provide
passive fire protection. Their fire resistance is obtained through the low thermal conductivity
and evaporation of water content of gypsum, which delays the temperature rise through the
system.
Introduction
Thermal properties of gypsum are temperature-dependent and among them, thermal
conductivity has a critical influence, yet there is a wide difference in reported values in literature
(Fig. 1). Given the effects of porosity, non-homogeneity and moisture in gypsum, direct
experimental measurement of thermal conductivity of gypsum at high temperatures is not an
easy task. As an alternative, proposed here is a hybrid numerical and experimental method to
extract thermal conductivity of gypsum, as summarised in the chart below.
Thermal conductivity-temperature relationship
Being a porous material, heat transfer through gypsum is a combination of conduction through
the solid and convection and radiation through the pores. The effective thermal conductivity of
gypsum may be calculated using the following equation[1]:
Hence, the proposal is to define the effective thermal conductivity-temperature relationship in three parts as demonstrated in Fig. 2:
- Constant thermal conductivity up to 95°C before water evaporation, equal to that at ambient temperature reported by the manufacturer;
- Linear reduction of conductivity up to 155°C due to evaporation of water;
- Non-linear increase in thermal conductivity based on equations [1] and [2].
 Fig. 1. Thermal conductivity of gypsum as reported by various researchers[2] |
 Fig. 2. Effective thermal conductivity of gypsum as used in this study |
Small-scale high temperature tests
400x400mm specimens of gypsum board panels were placed horizontally on top of an electric
kiln so that one side of the panel was subjected to elevated kiln temperature and the other side
faced up to room temperature. Figs. 3 and 4 demonstrate some of the test results, where the
temperature histories measured from the tests and calculated by the program using pore size of
0.15mm are compared. Also plotted in these figures are the numerical results utilizing thermal
conductivity of gypsum as used by Mehaffey et al [4] .
 Fig. 3. Temperature history for 12.5mm Fireline gypsum panel |
 Fig. 4. Temperature history for 25mm Fireline gypsum panel |
Conclusions
This paper has presented a hybrid method to determine the effective thermal conductivity of
gypsum at high temperatures, based on using small-scale experimental results and a thermal
conductivity model which includes the effects of radiation in voids. Despite the simplicity of the
method, the results are in good agreement with test measurements and show great improvement
when compared to those produced using thermal conductivity values reported in literature.
References
[1] Yuan. J. Intumescent Coating Performance on Steel Structures under realistic Fire
Conditions.
PhD Thesis. University of Manchester, 2009.
[2] Thomas. G. Fire and Materials, 26:37-45, 2002.
[3] Mehaffey. J.R. et al. Fire and Materials, 18:297-305, 1994.