Physics Modelling from microscale to macroscale: Homogenisation Technique, 1999 International Paper Physics Conference Proceedings

Bloch, J.-F., Auriault, J.-L.

This article is devoted to the presentation of the theoretical modelling of heat transfer in paper by a mathematical technique based on asymptotic expansions. It allows carrying out a scale change: an equivalent medium is deduced at the macroscale (sample size) from the physical description at the microscale (pore size). The main characteristics of the method are briefly described in the first part. Then the main results obtained from this method are presented. The macroscopic equivalent medium is obtained from the classical description of the energy balance at the pore level. The determination of both the macroscopic behaviour laws and the corresponding effective parameters are described. Furthermore the knowledge of the validity domain of the macroscopic description is also of great importance. In the last part, a technological example is presented by way of illustration. It deals with heat transfer occurring during hot pressing of paper. Both theoretical calculations and numerical illustrations are presented. More generally, the correct macroscopic model has to be selected from a model catalogue using only the specific physical data dedicated to the studied conditions, without any macroscopic prerequisites. These results may be extrapolated to any porous medium in accordance to the different presented hypotheses.