普适热传导--某些弱非局部理论的热力学
Universal heat conduction -- the thermodynamics of some weakly nonlocal theories
摘要：
介绍了刚性导体热传导的线性不可逆热力学框架。偏离局部平衡的特征在于一个单一的内部变量和电流强度因子。通过引入热力学力与通量之间的线性关系，导出了内能电流密度的一般本构演化方程。作为特例，得到了Fourier型、Maxwell-Cattaneo-Vernotte型、Guyer-Krumhansl型、Jeffreys型和Green-Naghdi型热传导方程。两个例子证明了这种方法的普遍性。给出了具有跳跃边界条件的方程的解的性质。
英文摘要：
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive evolution equation of the current density of the internal energy is derived by introducing linear relationship between the thermodynamic forces and fluxes. The Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type and Green-Naghdi type equations of heat conduction are obtained as special cases. The universal character of the approach is demonstrated by two examples. Solutions illustrating the properties of the equation with jump boundary conditions are given.
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