Non entire representation of the heat transfer by broadcasting. Usefulness for characterization and the thermal non destructive check

The non integer differentiation operator is used in order to express the model of heat diffusion in homogeneous materials. This continuous representation, according to the time variable, is exact with respect to the transfer function expressed in the Laplace variable domain. A significant reduction can be performed on the non integer model and the asymptotic behaviours of the system are exactly described whatever the reduction order. This reduced noninteger model is used as an identified system in the framework of front face thermal characterization experiments. These experiments consist in measuring the temperature at the surface of the material where a random heat flux is applied. This approach leads to rebuild the impulse response of the concerned system from a weak number of parameters. On the other hand, the confidence domain of the impulse response remains good on the entire time domain concerned by the experiment.