The thermodynamic theory of anisotropic rigid heat conductors with gradient constitutive equations is revisited in the framework of both extended irreversible thermodynamics and rational thermodynamics. The Second Law is exploited through a generalized Coleman–Noll procedure. Some interesting physical properties of the entropy flux and the entropy production are pointed out.
We present an overview of the modern approaches to continuum nonequilibrium thermodynamics from the perspective of their connection with the problem of heat conduction with finite speed. The celebrated Cattaneo and Guyer–Krumhansl equations for the evolution of the heat flux are reinspected in the framework of the different thermodynamic theories which, in such a way, are reviewed and compared.
We provide an overview on the problem of modeling heat transport at nanoscale and in far-from-equilibrium processes. A survey of recent results is summarized, and a conceptual discussion of them in the framework of Extended Irreversible Thermodynamics is developed.
In a recent paper the authors proved that the dispersion relation of heat waves along nanowires could allow one to illustrate the difference between different definitions of non-equilibrium temperature. It turns out that, from the practical perspective, one is led to the same conclusions by using both the absolute non-equilibrium temperature and a dynamical non-equilibrium temperature. Starting from these results, in the present paper the propagation of heat waves in core-shell nanowires is analyzed by using the concept of absolute non-equilibrium temperature. It is shown how the wave speed depends on the properties of both media and on their mutual interaction. Some useful information about the system is presented.
A generalized Coleman–Noll procedure for the exploitation of the entropy principle is presented. It is shown that it is able to dismantle some physical properties of nonlocal materials, which do not emerge if one uses the classical procedure. As an application, Korteweg fluids with a scalar internal variable are studied.
In this paper we determine the physical conditions ensuring that the efficiency of a thermoelectric nanowire with two temperatures is optimal. We consider the case in which the entropy for unitary volume depends on the equilibrium variables only, and the case in which such a quantity depends on the dissipative fluxes, too. We prove that in these two different situations the conditions of optimal efficiency are different.
We propose a description of heat conduction in rigid solids in which the classical state space of extended thermodynamics is substituted with another one, spanned by a dynamical semi-empirical temperature and a renormalized flux variable, given by the thermodynamic conjugate of the heat flux and proportional to the heat relaxation time and the dynamical temperature gradient. Propagation of heat pulses in dielectric crystals at low temperatures is analyzed, and the results are compared with those obtained by Lebon et al. (J. Phys.: Condens. Matter, 20 (2008), 025223). We propose a possible experiment in order to check what is the most well-suited definition of temperature in non-equilibrium situations.
We develop a mesoscopic model of thermoelectric coupling in nanosystems, allowing for different phonon and electron temperatures, and mutual energy exchange. Its compatibility with the second law of thermodynamics is proved. By comparisons with other theoretical proposals, the different coefficients involved in the model are identified. We consider two illustrations: (a) for systems where the electron mean-free path is considerably shorter than the phonon mean-free path, the non-equilibrium phonon temperature may be different with respect to the local-equilibrium temperature of electrons; (b) for systems with large electron mean-free path, one may have the so-called “hot electrons,” namely, electrons having a higher temperature than that of the phonons.