A numerical study of space‐fractional three‐phase‐lag bioheat transfer model during thermal therapy

Abstract

AbstractPrediction 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 three‐phase‐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.