Abstract
A nonlocal model for heat transfer with phonons and electrons is applied to infer the steady-state radial temperature profile in a circular layer surrounding an inner hot component. Such a profile, following by the numerical solution of the heat equation, predicts that the temperature behaves in an anomalous way, since for radial distances from the heat source smaller than the mean-free path of phonons and electrons, it increases for increasing distances. The compatibility of this temperature behavior with the second law of thermodynamics is investigated by calculating numerically the local entropy production as a function of the radial distance. It turns out that such a production is positive and strictly decreasing with the radial distance.
Highlights
Nanotechnology has changed our vision, expectations and abilities to control all of the material world
In order to investigate the influence of nonlocal effects on the radial heat transfer in a practical situation, here, we assume that the circular surrounding layer in Figure 1 is made of a p-doped sample of Bi2 Te3 at the average temperature of 300 K
We have applied the nonlocal model Equations (2) to describe heat transport in quasicrystalline materials [25], namely, in materials that should be properly located at the border line between metals and semiconductors [26]
Summary
Nanotechnology has changed our vision, expectations and abilities to control all of the material world. It offers a huge amount of potential applications and solutions that in the recent past were only possible in the realm of scientific fiction. Its usefulness has been known for many years, especially. From the theoretical point of view, the use of nanotechnologies requires revising some well-known theories, as for example the classical Fourier law. Several theories have been developed to describe heat transport in nanostructured materials [8,9,10,11,12,13,14,15]
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