No abstract

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.Keywords: gypsum, heat, averaging method, splines, numerical solution. IntroductionThe standards in building construction increase and it leads to the development of new materials. Fire protection becomes a prime requirement of building regulations in many countries in the construction industry. New composite materials with good properties as thermal insulators at elevated temperatures are developed. Commercial gypsum boards are widely used in the building industry as facing materials for walls and ceilings due to their very good mechanical and thermal properties. Thermal response of gypsum materials has been experimentally and numerically studied during the past years [1][2][3][4][5]. Gypsum based materials are known for excellent properties in fire protection and are used as general materials to protect building structures against fire. Most of the gypsum based materials are made as low or high density boards, but it is not common to make composite materials combining low and high density layers. Boards made with different layer density can achieve better results in fire safety, thermal insulation and acoustics [6; 7]. The endothermic dehydration process that takes place at high temperatures is capable of slowing down the fire spread through gypsum board based systems. A very important role here is played by the heat transfer processes in the same material. Experimentally it is very difficult to determine, therefore, it uses the heat transfer process of mathematical modeling. There are several computation models made to predict the thermal behaviour of gypsum boards under fire conditions. They revealed the significance of using appropriate physical properties for simulating the temperature evolution inside a gypsum board when exposed to fire conditions [8][9][10][11][12]. As noted "no significant influence of vapour transport on temperature is observed when the phase change is omitted" [12].The objective of the present study is to develop a mathematical model of heat transfer thought the two layered material of gypsum (foam gypsum and gypsum board) with different densiti...

Sandwich type panels are popular building materials with low weight and high strength. Sandwichtype panels nowadays are mostly used in high thickness as elements for external walls or roofs. But in most cases modern building panels contain lots of combustible additives, which can produce toxic fumes and expedite fire in buildings. In this paper, sandwich-type panels are discussed with structural, acoustic, fire and heat insulation properties made of foamed gypsum core with an open and close cellular structure and higher strength lining on both sides made of regular plasterboard. Gypsum is used as a fire protection and acoustical material with excellent fire protection, because it dehydrates at a temperature around 100 ºC absorbing energy and acting as a heat barrier. This research shows that combining desirable properties of gypsum as a high density composition and low density composition can improve the overall material properties and variety of application. It was found that a thinner and lighter composite sandwich panel made of gypsum can resist fire for longer time than rigid gypsum boards with complex structure.

Abstract. The problem of heat transfer through layered material of gypsum board products exposed to fire is studied in the paper. This paper proposes a thermal nonlinear conductivity model in different gypsum product layers for foam gypsum plate (density 300kg·m -3 ) and gypsum board (density 1000 kg·m -3 )with high temperatures. The specific heat and thermal conductivity coefficients depend on temperature. These types of connection are obtained using approximation by cubic splines. The 1-D nonlinearparabolic type partial differential equation (PDE), expressing the rate of the change of temperature in every layer, is derived for heat transfer. The approximation and calculation of corresponding initial boundary value problem is based on the Matlab solver "pdepe". The results of calculations are presented for one, two and three layered environment. The results of calculations are compared with the experiments at the Faculty of Environment and Civil Engineering of the Latvia University of Life Sciences and Technologies.