Fractional modelling applied to heat conductivity and diffusivity estimation

Abstract

Heat transfer in a homogeneous medium obeys diffusion phenomena, which can be modelled with the help of fractional systems. In this paper, we use fractional models based on an original fractional integrator whose order 1/2 acts only over a limited spectral band. These models, not linear in thermal parameters but linear in structural parameters, allow us to provide accurate simulations for transients with which it is possible to apply an output error technique to estimate the thermophysical parameters. Simulations of front face thermal characterization consisting of measuring the temperature at the surface of a material where a random heat flux is applied are carried out. These simulations allow us to validate the ability of the proposed estimation algorithms not only to rebuild the 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 thermal parameter estimates.