Mathematical modeling of the unsteady moisture condition of enclosures with application of the discrete-continuous approach

Abstract

Introduction. The paper considers mathematical models developed by K.F. Fokin, A.V. Lykov, V.I. Lukyanov, V.N. Bogoslovskiy, and H.M. Künzel and shows the advantages of using the moisture potential as compared with separate consideration of the transfer potentials. An analytical expression for the moisture potential F developed by V.G. Gagarin and V.V. Kozlov is given. Materials and methods. The article formulated a differential moisture transfer equation with time-constant coefficients and and described boundary conditions. An analytical expression determining the moisture potential using the discrete-continuous approach was obtained. Results. The article compares some calculation methods on the theory of moisture potential F for the single-layer aerated concrete enclosure, the two-layer brick wall, as well as two composite facade heat-insulation systems with external plaster layers with heat-insulation of mineral wool and foamed polystyrene. The solution of the unsteady equation of moisture transfer by the finite difference method using an explicit difference scheme and by the discrete-continuous method, the solution of the stationary equation of moisture transfer are considered. Conclusions. The moisture distribution obtained using the discrete-continuous approach, both quantitatively and qualitatively, coincides with the moisture distribution by the finite difference method. However, this distribution is obtained by the final formula without using the numerical method, which simplifies the calculation. The scientific novelty of the research consists in the development of a mathematical model based on the moisture potential F as well as in solving the equation of the unsteady moisture transfer through the discrete-continuous approach. The possibility of obtaining moisture distribution over the thickness of the enclosure according to the obtained formula is the practical relevance of the research.