Introduction
To consider the effect of micro-structural interactions in the fast transient process of heat transport, Tzou [Ref.1] introduced a phase lag for temperature gradient absent in the thermal wave model. The corresponding model is called the dual-phase-lag (DPL) model [Ref.2].
to solve the paradox of instantaneous responses of thermal disturbance that occurred in the Pennes bio-heat transfer equation, the non-Fourier models of bio-heat transfer were proposed for the investigation of physical mechanisms and the behaviors in thermal propagation in living tissues [Ref.2]. The basic formula of dual-phase lag heat transfer is:
![\left(1+\tau_{T}\frac{\partial}{\partial t}\right) k\nabla^2 T= \left(1+\tau_{q}\frac{\partial}{\partial t}\right)\left[\rho c\frac{\partial T}{\partial t} -w_{b}\rho_{b} c_{b} \left(T_{b} -T\right) -q_{m}-q_{r} \right]](https://simlab.center/wp-content/ql-cache/quicklatex.com-5fc054ca59dec3405f5e183183bf3b0a_l3.png "Rendered by QuickLaTeX.com")
Fig.1: Compare of present simulation and Ref.2 results.
Notes about the COMSOL implementation
1. The “weak form pde” in the mathematics module of the COMSOL Multiphysics simulation software is used.
2. Pennes bioheat transfer equation is predefined physics in COMSOL Multiphysics software, but the DPL model has been missed.
References for dual-phase lag heat transfer
[Ref.1] Tzou, Da Yu. Macro-to microscale heat transfer: the lagging behavior. John Wiley & Sons, 2014.
[Ref.2] Liu, Kuo-Chi, and Jung-Chang Wang. “Analysis of thermal damage to laser irradiated tissue based on the dual-phase-lag model.” International Journal of Heat and Mass Transfer 70 (2014): 621-628.
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