Prediction of accurate temperature profile and control of temperature are two important factors to treat the cancerous cells effectively in the living tissue during thermal therapy. To deal with this, we have generated a space-fractional mathematical model of bioheat transfer within the living skin tissue by using threephase-lag constitutive relation. The present model with Dirichlet's boundary condition is investigated in the companionship of the metabolic and external heat source during the thermal therapy. Exponentially decaying (with position) laser heat source is used as an external heating source term. To find out the solution, the model is converted to an initial value problem by using a fractional backward finite difference scheme and then Runge-Kutta (4,5) scheme is applied for determining the temperature profile within the living biological skin tissue. The effect on the dimensionless temperature profile during thermal therapy due to variations in the value of parameters like an order of space-fractional derivative, relaxation times, blood perfusion coefficient, rate of thermal conductivity, and the external laser heat source incorporated in the current bioheat transfer model is discussed graphically. Results obtained from the study are beneficial in the field of medicine, especially for oncologists.

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Various heat transmits models exhibit a thermal response in the tissue during thermal therapies. In the present work, we proposed a three‐phase‐lag (TPL) bio‐heat‐transmitting model including an external laser heating term amidst thermal treatment for the generalized coordinate system. The TPL model is based on the law of heat conduction containing heat flux, temperature gradient, and thermal displacement gradient terms. The solution is determined by implementing a discretization scheme of finite difference in the company of the Runge–Kutta (4,5) technique to examine the temperature repercussion throughout the thermal treatment of the tumor. In addition to this, the impact of various parameters such as phase lag in heat flux, temperature gradient, thermal displacement gradient, the heat generated because of blood perfusion, metabolism, and external heat source term is studied. A comparison has been shown graphically during the thermal treatment. The temperature profile is studied for different coordinate systems, and results are discussed. Moreover, validation has been made of the TPL model used in this paper with the experimental results. Thus the outcomes achieved from this study are purposeful in the therapeutical field, especially for oncologists.

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