The use of fractional calculus in heat diffusion modeling

Prof. Jean-Luc Battaglia

Full Professor, University of Bordeaux

Mechanical, Engineering and Aeronautics Department 


Data: 01/09/2010, 4ª feira.

HORÁRIO: 13:00 horas.

LOCAL: Sala G-205, Centro de Tecnologia - UFRJ.

The fractional  calculus is a funny mathematical tool. It was mainly a mathematical curiosity at the time of its discovery by Liuouville in 1832 and its rigorous presentation. In fact, Fourier was maybe the first to write (in his “traité analytique de la chaleur”) that a non derative order derivative could have existence and sense. But it was necessary to wait until the work of Sturm and Liouville to have a clear formulation. In the 70’s Oldham and Spanier wrote a book where there show the link between the diffusion equation and the fractional calculus (which is a comparable expression for non integer order derivation). This will be the subject of this talk.


Jean-Luc Battaglia obtained his PhD in Mechanics and Engineering from the University of Bordeaux (France) in 1995. He joined the University of Bordeaux as a Lecture in 1997. He directs the team of research “Thermal Characterization” of the TREFLE Laboratory (UMR CNRS 8508) at the Ecole Nationale Supérieures d’Arts et Métiers since 2002. Mains topics of interest in research are: thermal characterization of material, inverse heat conduction, thermal systemidenification and thermal model reduction. In the last years, he developed new approaches for the thermal characterization of thin films by modulated photothermal radiometry and time domain thermoreflectance. He obtained a chair of Professor at the University of Bordeaux in June 2006 and became Full Professor in 2010. His teaching activity mainly concerns heat transfer and fluid mechanics. He joined the MDM as a visiting scientist in 2006 within the framework of the Intra-European Fellowship Marie Curie Project TCAMMD (August 2006-July 2007). During this project he was mainly interested by the thermal characterization of phase change material used for the non-volatile memory operating mode. He wrote 4 books and has currently 51 publications in peer-reviewed journals.