Second law of thermodynamics and phonon-boundary conditions in nanowires

Abstract

The restrictions placed by the second law of thermodynamics on the boundary conditions have a special interest in nanosystems, where the Knudsen boundary layer, whose width is of the order of the mean-free path of heat carriers, becomes comparable to the size of the whole system. Here we explore second-order boundary conditions and show that the constraints of the classical irreversible thermodynamics are too restrictive, and that other formalisms going beyond local-equilibrium approach yield more realistic constraints for hydrodynamic phonon flow along nanowires. Furthermore, our analysis suggests a transition to zero thermal conductivity for very thin nanowires due to phonon backscattering. © 2010 American Institute of Physics

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

“…Then, the nonlocal term in Eq. (5) may be more important than the heat flux itself [32][33][34][35], and that equation reduces to…”

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

“…Therefore, the extended entropy has the functional dependence s eit = s eit (e; q; Q). If the relaxation time of Q is sufficiently smaller than that of q, then the flux of heat flux reduces to Q = 2 Vq (Jou et al 1999;Sellitto et al 2010a), and the extended entropy becomes s eit = s eit (e; q; Vq), exhibiting, in a more explicit way, the influence of non-local terms. In this formalism, the entropy production is given by Jou et al (1999) and Sellitto et al (2010a),…”

“…Let us remark that in Sellitto et al (2010a), we already pointed out the need of considering equation (4.3) in the thermodynamic description of phonon backscattering in rough-walled nanowires. Indeed, in that situation, there was a very thin layer, near the wall of the system, the characteristic size of which was of the order of the roughness size, wherein the heat flux pointed in the same direction as the temperature gradient, instead of pointing in the opposite direction, as required by the Fourier law.…”

Thermomass Theory: A Mechanical Pathway to Analyze Anomalous Heat Conduction in Nanomaterials

“…The phonon hydrodynamics [26][27][28][29][30][31] is another pathway to model the nanoscale heat conduction. It originates from the solving of linearized Boltzmann equation.…”