Nonlocal effects and second sound in a nonequilibrium steady state

Abstract

The influence of weakly nonlocal effects on the speed of second sound along or against the direction of a nonvanishing average heat flow is explored in a formalism based on a dynamical nonequilibrium temperature. The restrictions from the second law of thermodynamics on the nonlocal evolution equation of this temperature are studied from a gradient extension of classical Liu procedure, and the corresponding form of the entropy is derived. Stability requirements obtained from the second differential of the entropy are seen to restrict a nonlinear dependence of the thermal conductivity on the temperature gradient

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

“…(14) while the evolution of the heat flux is ruled by an equation of the type (16), then the use of a dynamical nonequilibrium temperature β [4,20,21,45], allows to obtain a nonlinear generalization of the classical Maxwell-Cattaneo-vernotte and Guyer-Krumhansl equations [5][6][7]. For instance, Eq.…”

“…Three such approaches are the phonon hydrodynamics [5][6][7], the thermomass theory [12][13][14], and the dualphase-lag model [15,16]. All these models consider the heat carriers as a fluid, whose hydrodynamic-like equations of motion describe the heat transport.…”

“…(1) to the nonlinear regime may be obtained in the framework of Extended Irreversible Thermodynamics (EIT) [6,7,21,27,28], a theory which upgrades the dissipative fluxes to the rank of independent thermodynamic variables [10,22,[29][30][31], while nonlinear generalizations of Eq. (2) have been obtained either in EIT [5], or in the framework of the thermomass theory [12][13][14], which also pays a special attention to nonlinear terms in the heat transport equation.…”

“…One of them is the meaning of temperature and its relation with heat transport [3][4][5][6][7]. In fact, different degrees of freedom, far from equilibrium, may be associated with different "temperatures".…”

Theories and heat pulse experiments of non-Fourier heat conduction

“…Non-Fourier effects are in principle enhanced by reducing the size of the samples and the speed of the phenomena [36][37][38]. GuyerKrumhansl equation is extensively analyzed in this respect [39,40].…”