An analytical study on the fractional transient heating within the skin tissue during the thermal therapy

In the present paper, the bioheat equation under fractional derivatives is used to study the thermal damage within the skin tissue during the thermal therapy. Basically, the analytical solutions in the Laplace domain are easily obtainable. The influences of the fractional derivative and moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The outcomes show that the fractional bioheat model are reduced to the hyperbolic and parabolic bioheat models when the fractional order parameter is equal to one and the relaxation time is close to zero respectively. The thermal injuries to the tissue are assessed by the denatured protein range using the formulation of Arrhenius. The numerical outcomes of thermal injuries and temperatures are graphically introduced. In conclusion, a parametric analysis is devoted to the identification of an appropriate procedure for selecting important design variables to reach effective heating in hyperthermia treatment.