Estimation of thermal parameters using fractional modelling

Heat transfer problems in homogeneous medium obey to diffusion phenomenon. In this paper, we study heat conduction through a sphere which can be modelled with the help of fractional systems. We use models based on an original fractional integrator whose order 12 acts only over a limited spectral band. Simulations of front face thermal characterization consisting in measuring the inner surface temperature of the sphere where a random heat flux is applied are carried out. These simulations allow to validate the ability of the proposed estimation algorithms not only to rebuild the inner surface temperature but also to identify with a good accuracy the heat conductivity and diffusivity. Monte-Carlo simulations are also performed in order to provide statistical properties of the thermo-physical parameter estimates.