A Fickian model for temperature-dependent sorption hysteresis in hygrothermal modeling of wood materials

The sorption isotherm is one of the most important hygric properties for modeling moisture transport in hygroscopic materials. For wood and wood based materials, the equilibrium moisture content within hygroscopic range is a function of temperature and relative humidity as well as its sorption history. The constitutive equations of the existing models in literature, which attempted to take into account temperature dependent sorption hysteresis, are either incomplete or have too many model parameters needed to be experimentally determined. As a result they are not suitable for practical applications in building physics. Therefore, a coupled heat and moisture transport model is formulated based on the classical local thermodynamic equilibrium assumption. Frandsen's hysteresis model is adopted and implemented in this Fickian model to determine the moisture capacity and thermal moisture capacity, since it avoids the needs to store the entire moisture history. The formulated hygrothermal model is numerically resolved in Modelica by virtue of a combination of storage model and flow model. For hygroscopic material with sorption hysteresis, its water vapor resistance factor has also been recalculated as a univalued function of moisture content instead of relative humidity. With different considerations for the moisture sorption isotherms, the new model provides the possibility of numerical study under different levels depending on the way to consider moisture sorption property. A simple example case is carried out to show the performance of the new model.