On mathematical modelling of heat and moisture distribution in the drying process for porous two layered gypsum board products

Abstract

Abstract. In this paper we study the problem of the heat and diffusion of one substance through the pores of two layered material of gypsum board products, which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. This paper proposes a thermal conductivity model for gypsum plate and gypsum carton at high temperatures, treating gypsum as a porous material consisting of solid and pores. We shall further assume linear dependence on both the temperature T and the moisture content in every layer M=const+aC-bT, where C is the concentration of water vapour in the air spaces, M is the amount of moisture absorbed by unit mass of fibre, a and b are positive constants. For two processes, the transfer of heat and moisture, we derive the system of 4 non-stationary partial differential equations (PDEs), 2 expressing the rate of the change of concentration of water vapour C in the air spaces and the other 2 the rate of the change of temperature T in every layer. The approximation of the corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM) by using special splines with hyperbolic functions. This procedure allows reducing the 2-D heat and mass transfer initial-boundary problem described by a system of 4 PDEs to initial value problem for a system of 4 ordinary differential equations (ODEs) of the first order. The results of calculations are obtained by MATLAB.Keywords: gypsum board products, heat and diffusion distribution, conservative averaging method, special splines, analytic and numerical solution. The mathematical modelThe study of heat and mass transfer through a porous media becomes much more interesting due to its vast applications. Many mathematical models are developed for the analysis of such processes, for example, mathematical models of moisture movement in wood, when the wood is considered as porous media.The study of hydrodynamic flow and heat transfer through a porous media becomes much more interesting due to its vast applications, such as drying in porous solids and soils, drying of wood and paper, soil mechanics, porous heat pipes, paper machines, liquid composite moulding. Many mathematical models are developed for the analysis of such processes, for example mathematical models of moisture movement in wood, when the wood is considered as porous media [1; 2]. This paper proposes a thermal conductivity model for gypsum at high temperatures, treating gypsum as a porous material consisting of solid and pores. We study the heat and moisture transfer processes in the two porous layers of gypsum material. We consider the gypsum board material with two layered plates: gypsum plate (0.0525 m) with density 300 kg·m -3 and gypsum carton plate (0.0125 m) with density 1000 kg·m -3 . The gypsum plate on one border is heated with temperature 20 + 345lg(8t +1) ºC, where t is the time in minutes. In one layer the heat and mass transfer process are analysed and described in [1; 2; 5; 6].The article [4] has viewed ...

Conservative averaging method for solving some nonlinear heat transfer problems related to combustion

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Thermal conductivity of construction materials based on gypsum

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