An inverse problem of parameter estimation for time-fractional heat conduction in a composite medium using carbon–carbon experimental data

In this paper, a time-fractional heat conduction problem is mathematically proposed for an experimental heat conduction process in a 3-layer composite medium. A numerical solution to the direct problem is obtained with finite difference method. In regard to the inverse problem, the optimal order of Caputo fractional derivative is estimated with Levenberg–Marquardt method. Comparing with the carbon–carbon experimental data, the results show that the time-fractional heat conduction model provides an effective and accurate simulation of the experimental data. The rationality of the proposed time-fractional model and validity of Levenberg–Marquardt method in solving the time-fractional inverse heat conduction problem are also manifested according to the results. By conducting the sensitivity analysis, the feasibility of the parameter estimation is further discussed.