Article ID Journal Published Year Pages File Type
6419926 Applied Mathematics and Computation 2016 13 Pages PDF
Abstract
In this paper, we formulate a fractional thermal wave model for a bi-layered spherical tissue. Implicit finite difference method is employed to obtain the solution of the direct problem. The inverse analysis for simultaneously estimating the Caputo fractional derivative and the relaxation time parameters is implemented by means of the Levenberg-Marquardt method. Compared with the experimental data, we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment. We have also discussed the effect of the fractional derivative, the relaxation time parameters, the initial guess as well as the sensitivity problem. All the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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