Non-isothermal Moisture Balance Equation in Porous Media: A Review of Mathematical Formulations in Building Physics

Understanding heat and mass transfers in porous materials is crucial in many areas of scientific research. Mathematical models have constantly evolved, their differences lying mainly in the choice of the driving potentials used to describe moisture flows, as well as in the complexity of characterizing the physical phenomena involved. Models developed in the field of Building Physics (HAM models) are used to describe the behavior of envelope parts and assess their impact on user comfort and energy performance. The water balance equation can be described in many ways; it is a function of the boundary conditions considered and the fact they induce high or low water content in the porous materials used. This paper gives an overview of various formulations for this equation that are found in the Building Physics literature. It focuses first on the physically based formulation of moisture balance, drawing on the Representative Elementary Volume (REV) concept, coupled with thermodynamic flow rates description. This is then reformulated in line with various main moisture state variables offering a wide variety of expressions that are compared with available models. This approach provides access to all secondary transport coefficients associated with the process of mathematical transformation. Particular emphasis is placed on the moisture storage function choice and its impact on the final mathematical formulations.