An axisymmetric bioheat transfer analysis through a unified model

A unified model is developed for the analysis of heat transfer (radiation and non-Fourier conduction) in an axisymmetric participating medium. The proposed model includes three different variants of hyperbolic-parabolic heat conduction models, that is, the single phase lag model, dual phase lag model, and the Fourier (no phase lag) model. The radiating-conducting medium is radiatively absorbing, emitting, and isotropically scattering. Significance of all the above mentioned models on the heat transfer characteristics is investigated in a two-dimensional axisymmetric geometry. The equation of transfer and the coupled non-Fourier conduction-radiation equation are solved via finite volume method. A fully implicit scheme is used to resolve the transient terms in the energy equation. For spatial resolution of radiation information, the STEP scheme is applied. Tri-diagonal-matrix-algorithm is used to solve the resulting set of linear discrete equations. Effects of two important influencing parameters: the scattering albedo and the radiation- conduction parameter are studied on the temporal evolution of temperature field in the radiatively participating medium. The non-Fourier effect of heat transport captured well with the proposed unified model. A good agreement can be found between the proposed model predictions and those available in the literature. It is also found that when the phase lag of the temperature gradient and the heat flux are the same, it reduces to conventional Fourier conduction-radiation and the wave behavior diminishes. However, the reduction to this Fourier model fails in the presence of constant blood perfusion and metabolic heat generation.