Nonlinear evolution and stability of the heat flow in nanosystems: Beyond linear phonon hydrodynamics

Abstract

A heat-transport equation incorporating nonlocal and nonlinear contributions of the heat flux is derived in\ud the framework of weakly nonlocal nonequilibrium thermodynamics. The motivation for these terms arises from\ud applications to nanosystems, where strong gradients are found, due to the small distance over which changes\ud in temperature and heat flux take place. This equation generalizes to the nonlinear domain previous equations\ud used in the context of phonon hydrodynamics. Compatibility with second law of thermodynamics is investigated\ud and a comparison with the thermomass model of heat transport is carried out. The analogy between the\ud equations describing the heat flow problem and the hydrodynamic equations is shown and the stability of the\ud heat flow is analyzed in a special case

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.…”

“…Extensions of Eq. (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

“…Guyer [66]. With suitable constitutive assumptions several nonlinear equations fit in this general framework like the thermomass transport equation [67], the nonlinear Maxwell-Cattaneo-Vernotte equation derived in [39] and also the nonlinear Guyer-Krumhansl equation derived in [68].…”