Numerical modeling of heat exchange and unsaturated–saturated flow in porous media

Abstract

We discuss the numerical modeling of heat and mass transport in unsaturated–saturated porous media. The heat is transported by infiltrated water underlying capillary and gravitation driven forces. Heat energy is governed by molecular diffusion, convection, dispersion and exchange between the infiltrated water and porous media matrix. An unsaturated–saturated flow is considered with boundary conditions reflecting the external driven forces. The presented mathematical model is motivated by analysis of hygrothermal isolation properties of facades. The main contribution is focused on the determination of model parameters including soil parameters, dispersion coefficients, thermal transmission coefficient, thermal conductivity of porous media matrix and external transmission coefficients. The used mathematical model does not include the vapor transport and its phase exchange with water due to vaporization and condensation. It will be the next step of our research. Thus, practical applications of our model are limited. The developed numerical method is a good candidate for solving corresponding inverse problems. Numerical experiments support our method.