A numerical analysis of moisture behavior in a porous wall by quasilinearized equations

Abstract

In order to predict the performance and to estimate the durability of building materials, an understanding of the behavior of heat and moisture in them, especially the maximum value of the moisture state of each material, is required. The governing equations are the system of heat- and moisture-transfer equations. These equations are nonlinear, because their coefficients are strongly dependent on dependent variables such as moisture content. If the system can be approximated by quasilinearized equations with adequate accuracy, a solution can be obtained simply by applying the superposition principle. In this paper, quasilinearized time-variant equations are derived, and the allowable range of approximation of the linearized equations is discussed. The system of quasilinearized equations is obtained by expanding the original nonlinear equations around the reference solutions. After the nonlinear equations have been solved under reference boundary conditions, the quasilinearized equations are solved under the variation of the boundary value. The sum of the two solutions (the reference solution and the solution of the linearized equation) is the approximate solution. To determine the allowable range of approximation, two cases of variation of the boundary value, which are a step function and a sinusoidal function with a period of one year, are calculated. The structure of the building wall treated here is an internally insulated autoclaved lightweight concrete (ALC) wall, and the outdoor climate is that of Osaka, Japan. In the case of step function variation, the allowable range of application is ± 1°C and ±10 4 J/kg (the chemical potential of water). In the case of sinusoidal function variations, the linear approximate solutions show fair agreement with exact solutions within 1 K of amplitude and 10 4 J/kg. It has been shown that quasilinearization produces acceptable approximate solutions and is effective in the prediction of moisture variation in a building structure.