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Contribution to certain Physical and Numerical Aspects of the Study of the Heat Transfer in a Granular Medium

In this work, we are interested in studying heat and mass transfer in water saturated and unsaturated porous medium with a strong heating at the surface. Applications concerned are archaeology, agriculture and geothermal engineering.

The first part of this work concerns the improvement of the AHC (Apparent Heat Capacity) method used in the numerical resolution of phase change problem in a homogeneous medium: the phase change temperature interval, over which the heat capacity varies, appears as a key parameter which must be chosen proportional to the mesh size.
Accurate and smooth results are obtained thanks to a local refinement of the mesh near the phase change interface.

The second part is about the estimation of the thermophysical properties of the soil by inverse problem using both synthetic and experimental data. The Damped Gauss-Newton and the Levenberg-Marquardt algorithms are used to solve the problem. In relation with the AHC method, the choice of the phase change temperature interval caused convergence problems which have been fixed by chaining many inverse problems.

The obtained results show good convergence to the desired solution.
The third part presents a simple model to calculate the effective thermal conductivity of a granular medium which contains a small quantity of liquid water. The exact shape of the liquid menisci between the grains is calculated at equilibrium. The effective thermal conductivity experiences a hysteresis behavior with respect to the liquid volume. A future work that concerns a new unsaturated model, restricted to the pendular regime and detailed at the end of this thesis, should be able to use this result.

Tuesday, 8. December 2015 - 10:30
IRISA RENNES, Campus de Beaulieu, 263 Av du Général leclerc, entrée Bât 12 F, Salle MÉTIVIER
Defense Type: 
Composition of jury: 

Amel BEN ABDA, Professeur à l’ENIT, Tunis, rapporteuse
Denis MAILLET, Professeur à l’Université de Lorraine, rapporteur
Sean MCNAMARA, Maître de conférence à l’Université de Rennes 1, examinateur
Édouard CANOT, Chargé de recherche CNRS, IRISA Rennes, directeur de thèse