Mathematical modelling and simulation of three phase lag bio-heat transfer model during cancer treatment

Abstract

We have developed a two-dimensional mathematical model that described the study of bio-heat transfer. Our model is an initial boundary value problem of partial differential equation. The solution consists of the three step procedure- (i) transformation of problem in dimensionless form (ii) by using finite differences, the problem converted into ordinary matrix differential equation (iii) applying Legendre wavelet Galerkin method, the problem is transferred into the generalised system of Sylvester equations which are solved by applying Bartels-Stewart Algorithm of generalised inverse. We have used this method to determine the temperature profile in three different boundary conditions. The consequence of boundary conditions on temperature profile are discussed in detail. The effect of phase lag due to heat flux, phase lag due to temperature gradient and phase lag due to thermal displacement have been observed. And, we have seen that temperature profile increases when the phase lags decreases. We have also observed the effect of blood perfusion rate and metabolic heat generation in specific. Results are validated with exact results in particular case.