Numerical solution of generalized DPL model using wavelet method during thermal therapy applications

Abstract

In this paper, generalized dual-phase-lag (DPL) model has been studied for the numerical analysis of spatial variation of temperature within living biological tissues during thermal therapy applications. A new hybrid numerical scheme based on finite difference scheme and Chebyshev wavelet Galerkin method are used to solve the generalized DPL model with constant heat flux boundary condition. Multi-resolution and multi-scale computational property of Chebyshev wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. Our study demonstrates that due to presence of coupling factor (convection–perfusion), generalized DPL model predicts lower temperature than classical DPL and Pennes model at the tumor position. Higher values of phase lag times results in lower temperature at the tumor position. But, in case of variation of phase lag time due to temperature gradient, the nature of temperature profile also depends on the spatial coordinate. The effect of the blood temperature, porosity and interfacial convective heat transfer on temperature distribution has been investigated. It is found that larger values of porosity and interfacial convective heat transfer results in lower temperature at the tumor position. Also, both porosity and interfacial convective heat transfer are pronounced more at higher values. The whole analysis is presented in dimensionless form.