An axisymmetric dual-phase-lag bioheat model for laser heating of living tissues

Unphysical effects of the dual-phase-lag model of heat conduction

In this work, an analytical solution for thermoelastic waves in a metal induced by an ultrafast laser pulse was formulated in the form of a Fourier series. The two-step heat transfer model was applied to account for the thermal nonequilibrium between electrons and the lattice during ultrafast pulsed laser heating. The coupling between the strain rate and the temperature field was also considered. Calculations were carried out to study generation, propagation, and attenuation of thermoelastic waves induced by a pico- and a femtosecond laser pulse. Results were compared with those obtained without considering the two-step heat transfer effect.

http://web.me.iastate.edu/wang/2002_J.%20Thermal%20Stress.pdf

Thermoelastic wave in metal induced by ultrafast laser pulses

Dual-phase-lag model of bioheat transfer equation is utilized in treating the transient heat transfer problems in skin tissue considering prevalent heating conditions in thermal therapy applications, namely, pulse train and periodic heat flux. Comparisons between the presented analytical results for limiting cases and previous studies display an excellent agreement. The effects of temperature gradient relaxation time on the tissue temperature, damage, and also on the blood perfusion in skin tissue are studied.

Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue

Relativistic heat conduction

For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This scheme uses the characteristic properties of a hyperbolic equation and has no oscillation. By solving a model problem, we show that the conventional hyperbolic heat conduction equation can give physically wrong solutions (temperature less than absolute zero) under some conditions. The modified equation does not display these erroneous results. However, the difference between results of these two models is negligible except under extreme conditions.

On Hyperbolic Heat Conduction and the Second Law of Thermodynamics

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On Hyperbolic Heat Conduction and the Second Law of Thermodynamics