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Keywords:

  • Heat conduction;
  • weakly nonlocal thermodynamics.

Abstract

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 multiplier. A general constitutive evolution equation of the current density of the internal energy is derived by introducing a linear relationship between the thermodynamic forces and fluxes. The well-known 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.