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In the present analysis, the bio-heat equation has been studied in the context of memory responses which is defined in the form of convolution having kernels as power functions. The heat transport equation for this problem involving the memory-dependent derivative on a slipping interval in the context of Dual-phase (DP) lag model, which is used to study the thermal damage within the graded spherical skin tissue during the thermal therapy, whose outer surface is thermally insulated. Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and time-dependent moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The thermal injuries to the tissue are assessed by the denatured protein range using the current formulation in which the numerical inversion of the Laplace transform is carried out using Zakian method. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different kernel functions to reach effective heating in hyperthermia treatment. The significant effect of the thermal therapy is reported due to the effect of nonhomogeneity and delay time also.

A graded spherical tissue under thermal therapy : the treatment of cancer cells