Temperature prediction by a fractional heat conduction model for the bi-layered spherical tissue in the hyperthermia experiment

Abstract

In this paper, a novel time-fractional heat conduction model is presented for the bi-layered spherical tissue in the hyperthermia experiment, and an efficient numerical technique to estimate the unknown fractional parameter in the proposed time-fractional heat conduction model is investigated. Firstly, for the solution of the proposed time-fractional heat conduction model, the technique of variable transformation and the implicit finite difference method are employed. Secondly, based on the measured experimental data, an efficient numerical technique to estimate the unknown order of the fractional derivative is investigated. The fractional sensitivity equation is first obtained by means of the digamma function, and the conjugate gradient method based on the fractional derivative is constructed to obtain the optimal estimation of the unknown order of the fractional derivative in the proposed time-fractional heat conduction model. Lastly, compared with the hyperthermia experimental data, it is observed that the calculated temperature increase values agree well with the measured temperature increase values in the experiment, which implies that the proposed time-fractional heat conduction model is effective in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical technique to estimate the unknown fractional parameter is efficient.