Non-Fourier heat conduction: The cattaneo equation

Details

Supervisors

Moës, Nicolas

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enThis document introduces the subject of non-Fourier heat conduction. In particular, infinite speed of heat propagation associated with Fourier’s law is explained. The Cattaneo law is introduced to correct this paradox. An analysis of this new heat equation is proposed to build a good understanding of its properties: discontinuities, modal analysis, variational formulation and numerical methods are discussed. The new heat model is then applied to a thermokeratoplasty operation and solution profiles are explained. Finally, a step toward other laws and applications is given with the introduction to fractional derivative heat conduction models.