A non-isothermal phase-field approach to the second-sound transition in solids

摘要

Stationary and non-stationary models of heat conduction in solids are associated with two different phases of the solid. The passage between the two regimes is then viewed as a phase transition of the second kind. The order parameter of the transition is modelled as a phase field which changes smoothly in space. A thermodynamic approach is developed by regarding the phase field as a scalar internal variable and the kinetic or evolution equation is regarded as a constitutive equation. Also, the heat flux is described through a vector internal variable. Along with the other constitutive equations, the unknown evolution equations are required to satisfy the second law of thermodynamics. Necessary and sufficient restrictions placed by thermodynamics are derived for the constitutive equations. This provides a unified scheme of heat conduction which simplifies in the pertinent models for the two single phases. The generality of the scheme allows previous models to be recovered as particular cases.