A combined experimental and numerical method for extracting temperature-dependent thermal conductivity of gypsum boards

Abstract

This paper proposes a hybrid numerical–experimental method for extracting thermal conductivity of various gypsum board products at elevated temperatures. Gypsum board is ubiquitously used in fire resistant construction, yet there is wide variability in reported values of thermal conductivity of gypsum at high temperatures. Given the effects of porosity, moisture and non-linear temperature distribution in gypsum under heating, direct measurement of thermal conductivity, e.g. by using the hot plate method, is not an easy task. This paper proposes a thermal conductivity model for gypsum at high temperatures, treating gypsum as a porous material consisting of solid and pores and takes into consideration the effects of radiation at high temperatures. This enables the gypsum thermal conductivity–temperature relationship to be described as a function of two variables: reduction in thermal conductivity from its value at ambient temperature to that of dried gypsum, and effective spherical void size. To enable these two parameters to be quantified, a hybrid experimental–numerical method is proposed. This hybrid model uses a validated one-dimensional Finite Difference heat conduction program and high temperature test results on small samples of gypsum boards. Through a clearly defined trial and error procedure, the water evaporation induced drop in the thermal conductivity, and the void size that gives the best agreement between numerical prediction and high temperature tests are obtained to quantify the gypsum thermal conductivity–temperature relationship.