Numerical simulation of time-fractional bioheat transfer model during cryosurgical treatment of skin cancer

Abstract

In this study, a time-fractional dual-phase lag bioheat transfer model for the treatment of skin cancer using cryosurgery has been developed. The cryoprobe is placed just near the tumor tissue. The generalized boundary conditions are im-posed on the outer surface (dermis layer) of the skin. The mathematical model of this problem is a time-fractional moving-boundary bioheat transfer problem. We applied the Legendre wavelet Galerkin method to find the solution of our problem. We have used this method to find the temperature distribution for different fractional order derivatives of all the layers of skin. The error bound and stability analysis of the approximate method is analyzed. In a specific case, the results obtained are compared with the exact solution and are in strong agreement. A variation is observed from the graphs of temperature distribution and moving layers thickness with respect to different values of fractional order α for different layer of skin. We see that when the value of α decreases, the temperature profile decreases and the moving layer thickness increases accordingly. © 2021 by Begell House, Inc.