Nonlinear behavior of thermal lagging in concentric living tissues with Gaussian distribution source

The high-order effects of thermal lagging were instated in describing non-equilibrium heating in tissues. This work theoretically studies the temperature rise behavior in living tissues during magnetic tumor hyperthermia treatment within the non-linear form of the dual-phase-lag model. It was experimentally discovered that the concentration of magnetic particles is in Gaussian distribution along the radial direction as magnetic fluid is injected into the tissue structure. Therefore, the non-linear high order partial differential equation in concentric spherical domain, which would introduce the complexity and cause some mathematical difficulties, is numerically solved. The comparison between the linear and non-linear effects of phase lag times on bio-heat transfer has been done. The results show that the effect of τq2 strengthens the behavior of thermal wave as well as the effect of τT2 affects the behavior of diffusion. The effect of τq2 on the behavior of non-Fourier bio-heat transfer would fade away for τT > τq.