Heat reduction by thermal wave crystals

Abstract

Non-Fourier heat conduction models assume wave-like behavior does exist in the heat conduction process. Based on this wave-like behavior, thermal conduction controlled in a one-dimensional periodical structure, named thermal wave crystal, has been demonstrated through both theoretical analysis and numerical simulation based on the Cattaneo-Vernotte (CV) heat-conduction model. The transfer matrix method and Bloch analysis have been applied to calculate the band structure of thermal wave propagating in thermal wave crystals. And the temperature responses are obtained by using the FDTD method, which is also used to verify the correctness of the band structure. The results show that band gaps do exist due to the Bragg scattering. Then, a calculation method to predict the mid-gap frequency of band gaps for the thermal wave crystal has been introduced in this Letter. And key parameters determining the band gaps have been discussed. This study shows the potential applications of this novel mechanism, such as thermal imagining, thermal diodes and thermal waveguides.

Thermal Bragg Shields for Thermal Waves.

“…For example, a Table 1. Thermal properties of the materials used in the numerical example of a layered system taken from 16,24 .…”

“…In this section we derive the transfer matrix and the reflectance coefficients for a layered media or thermal crystals 24 .…”

“…Optical Bragg mirrors are made of alternate layers of high and low dielectric function materials. To extend the definition to thermal waves we consider three specific materials: Aluminum 32 (Al) and two materials with thermal properties of biological tissue 16,24,33 . From the experimental point of view, materials with biological-like responses can be design with specific thermal properties using gel-phantoms 34 .…”

“…Several authors have discussed the differences and misconceptions of heat waves [20][21][22][23] . The wave-like behavior can be used to control the heat flux with systems that are similar to those used in optics or acoustics, for example designing thermal crystals 24 and metamaterials where concepts such as thermal cloaking have been proposed 25 .…”

Bragg Mirrors for Thermal Waves

“…We want to compare the reflectivity r of the finite and infinite superlattice. For the infinite case we use Bloch's theorem [18,19], which establishes the dispersion relation of the Bloch wavenumber Q as cos(pQ) = 1 2 Tr(M), where p = d 1 + d 2 is the period of the superlattice, and M = M 2 M 1 is the transfer matrix of the unit cell. In the infinite case the reflectivity r will be given by Eq.…”