On mathematical modelling of heat and moisture distribution in the drying process for porous two layered gypsum board products
2017
Aboltins, A., Latvia Univ. of Agriculture, Jelgava (Latvia) | Kalis, H., University of Latvia, Riga (Latvia). Inst. of Mathematics and Computer Science | Kangro, I., Rezekne Academy of Technologies (Latvia)
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.
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