Mathematical modelling of heat transfer problem for two layered gypsum board products exposed to fire

Abstract

In this paper we study the problem of the heat transfer through the two layered material of gypsum (with different densities) board products exposed to fire. This paper proposes a thermal conductivity model in two gypsum product layers for foam gypsum plate and gypsum board with different density and at high temperatures. For transfer of heat the system of 2 non-stationary partial differential equations (PDEs) is derived expressing the rate of the change of temperature T in every layer. The approximation of the corresponding initial boundary value problem of this system is based on the conservative averaging method (CAM) by using special splines with hyperbolic functions. This procedure allows reducing the 2-D heat transfer initial-boundary problem described by a system of 2 PDEs to the initial value problem for a system of 2 ordinary differential equations (ODEs) of the first order. The results of calculations are obtained by MATLAB.