用内变量和GENERIC求解非傅立叶热传导问题
A case study of non-Fourier heat conduction using Internal Variables and GENERIC
摘要：
同时应用含内变量的非平衡热力学方法（NET-IV）和非平衡可逆-不可逆耦合通用方程（GENERIC）框架，我们证明了在热传导理论中，熵流乘数可以被解释为松弛状态变量。傅立叶定律及其各种扩展-Maxwell-Cattaneo-Vernotte，Guyer-Krumhansl，Jeffreys型，Ginzburg-Landau（Allen-Cahn）型和弹道扩散-热传导方程在这两种配方中推导出来。沿着这些路线，NET-IV和GENERIC的比较也进行。我们的研究结果可能会铺平道路的微观/多尺度的理解超越傅立叶热传导，并开辟新的途径，热传导问题的数值模拟。
英文摘要：
Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law and its various extensions -- the Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type and ballistic-diffusive -- heat conduction equations are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction, and open new ways for numerical simulations of heat-conduction problems.
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