Parameters estimation for a new anomalous thermal diffusion model in layered media

In this paper, we study an inverse problem of parameters estimation for a new time-fractional heat conduction model in multilayered medium. In the anomalous thermal diffusion model, we consider the fractional derivative boundary conditions and the conduction obeys modified Fourier law with Riemann-Liouville fractional operator of different order in each layer. For the direct problem, we construct an effective finite difference scheme by using the balance method to deal with the discontinuity interface. For the inverse problem, we apply the nonlinear conjugate gradient (NCG) method with different conjugated coefficients to simultaneously identify the fractional exponent in each layer. Finally, we use experimental data to verify the effectiveness of the proposed technique, in which the Jacobian matrix is achieved by a derivative-free approach. We analyze the sensitivity coefficients and the convergence behaviors of the NCG algorithm. The simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate fitting than the classical counterpart and the NCG method is a feasible and effective technique for the inverse problem of parameters estimation in fractional model.