Strong non-linear behavior of the effective thermal conductivity during heating of a wet porous medium
Résumé
We consider the great heating of the soil surface leading to the water phase change within a wet porous medium. Experimental temperature curves show that there is always a long plateau (up to one hour) at 100 degrees which is difficult to reproduce by numerical simulations, when using an ordinary continuous model for the heat transfer in the soil. Suitable models for this effective conductivity must be used. In this work, we propose a simple approach to derive some effective conductivity laws via a 2D granular model of circular solid cylinders, packed in some regular ways, with the presence of a variable quantity of liquid water, which forms identical menisci in the gap around each contact point of the cylinders. The doubly periodic pattern is then reduced to a minimal computational domain using the symmetries of the system. The steady heat equation is numerically solved in this small domain, containing three different media (solid, liquid and air) using a Mixed Finite Element scheme. Numerical results show that the effective conductivity has a non-linear behavior versus the liquid fraction of the water. Even if the 2D geometry is not directly applicable to the 3D real granular medium, we think that he can give some ideas to extend the results to our wet porous medium. The application of our work takes place in archæology, for the study of prehistoric fires.