Convective and conductive thermal homogenization for non-saturated porous building materials: Application on the thermal conductivity tensor

Abstract

Porous materials possess a complex structure on a microscopic scale and present strong heterogeneities, which makes their precise study extremely complex. In fact, the macroscopic behavior of these materials is strongly dependent on mechanisms that act to the scale of their components. The present work focus on the development of a macroscopic conductive and convective fluid heat transfer model, with a heat source in the unsaturated porous materials. This model is established by periodic homogenization of energy conservation equations written on a microscopic scale in each phase (solid, liquid and gas). The resulting input parameters formulations of the submodel were explicitly identified. Numerical calculations of the homogenized thermal conductivity tensor are performed on a representative 3-D elementary cell of the porous medium. Finally, a sensitivity study of this tensor depending of the variation of the water content and porosity of the concerned elementary cell has been performed. This sensitivity is required to be considered in simulations to better understand the behavior of building materials and improve the prediction of energy performance.