Chinese Journal of Lasers, Vol. 47, Issue 12, 1207003 (2020)
Effect of Non-Fourier Heat-Flux Boundary Conditions on Heat Conduction Behavior of Laser-Irradiated Biological Tissues
Xu Guangying, Xue Dawen*, and Wang Jinbao
- School of Naval Architecture and Maritime Affair, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China
The dual phase lagging (DPL) non-Fourier heat transfer model can reflect the transient interaction process between pulsed laser and biological tissues. However, in many literatures where the DPL model is used to study the heat conduction mechanism of biological tissues, there exist both Fourier and non-Fourier boundary conditions and thus many induced conclusions are contradictory. In this paper, the control equation based on the DPL non-Fourier model is adopted and the Fourier and non-Fourier boundary conditions are derived. Meanwhile, the analytical solutions under the above conditions are obtained by integral transformation and Laplace transformation. The biological tissues are taken as an example and the calculation results show that as for the non-Fourier control equation, the predicted temperature distribution in tissues based on the non-Fourier boundary condition is in accordance with the energy conservation law, while the result based on the Fourier boundary condition is not. The conclusions on the temperature rising amplitude and temperature rising rate are opposite for the two kinds of boundary conditions. Moreover, the thermal damage predicted under the Fourier boundary conditions is overly conservative and obviously lower than that under the non-Fourier boundary conditions. Finally, from the point view of energy conservation, the DPL non-Fourier boundary condition is just the DPL energy conservation equation of boundary, while the Fourier boundary condition is the energy conservation equation of the Fourier model. The Fourier control equation of bio-heat conduction should be matched with the Fourier boundary conditions, while the non-Fourier control equation of bio-heat conduction should be matched with the non-Fourier boundary conditions.
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