Analytical study on the transient heating of a two-dimensional skin tissue using parabolic and hyperbolic bioheat transfer equations

In this study, exact analytical analysis of two-dimensional Fourier and non-Fourier bioheat transfer equations in skin tissue exposed to an instantaneous heating condition is presented. The effects of blood perfusion and metabolic heat generation on the tissue thermal behavior are considered. Corresponding analytical approach is developed through Laplace transform (LT) technique in conjunction with the separation of variables method and inversion theorem. The dual-phase-lag (DPL), thermal wave (TW) and Pennes models of bioheat transfer equation are studied by utilizing a generalized model. The reliability of the presented results has been evidenced through enforcing appropriate circumstances on the DPL model and comparing the outcome results with that of predicted by the Pennes and TW models. It is proved that the DPL bioheat transfer equation with the effects of blood perfusion and metabolic heat generation can be reduced to the Pennes bioheat transfer equation when τq=τT. The effects of local non-equilibrium on the tissue thermal behavior are examined and discussed by comparing the gradient precedence (GP) and flux precedence (FP) heat flow regimes of the DPL model. The first- and second-degree burn times of a 2D skin tissue for different bioheat models are introduced and compared with the 1D case.