Variable thermal conductivity approach for bioheat transfer during thermal ablation

Abstract

The aim of the article is to present a mathematical model that predicts tissue temperature during thermal therapy (thermal ablation). The mathematical formulation of variable thermal conductivity of thermal wave bioheat transfer model for a generalized coordinate system due to external heat source during thermal ablation has been given. The governing bioheat transfer equation is simplified by Kirchhoff's transformation. The numerical solution of the problem has been achieved using a finite difference scheme to discretize in space coordinate; the reduced system of second order ordinary differential equation is solved by the finite element Legendre wavelet Galerkin method (FELWGM). The obtained result from FELWGM is compared with exact analytical solution and shows good agreement. Parametric study is performed to evaluate the effect of variable thermal conductivity on tissue temperature distribution for different physical parameters and illustrated graphically. Particular cases are also deduced from present investigation. The effect of variability of thermal conductivity parameter, variability of time, generalized coordinate system, lagging time and external heat source coefficient on tissue temperature is discussed in detail. Thus, the consideration of the variable thermal conductivity is extremely beneficial for the clinical therapeutic application in the treatment of cancerous cells.

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

“…To formulate energy equation, variable thermal conductivity, which depends on temperature, is presumed. References [36,[41][42][43][44][45][46][47] comprise some current studies related to variable thermal conductivity. Not many works are available concerning the effect of temperaturedependent variable thermal conductivity and viscous dissipation on mixed convective heat transfer, especially past a stretched cylinder.…”