Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity.

Federico Vázquez,Róbert Kovács,Péter Ván

doi:10.3390/e22020167

Abstract

There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.

Highlights

This work was motivated by the increasing interest in heat transport in superlattices due to their potential applications in a variety of devices, e.g., for the thermoelectric generation of energy, the design of intelligent coatings for temperature conditioning of enclosures, the construction of devices for processing information, the storage of thermal energy, and design of biomedical devices among others [1]
We propose to use irreversible thermodynamics with two vectorial dissipative fluxes to incorporate features of the wave-like behavior of the heat carriers and to describe transient processes associated with the results reported by the experiments above mentioned on superlattices
The wave-like behavior ofwave the heat carriersofisheat represented by theexplain non-dimensional coefficients in contains the essence of the properties carriers which their transport properties

Summary

Introduction

This work was motivated by the increasing interest in heat transport in superlattices due to their potential applications in a variety of devices, e.g., for the thermoelectric generation of energy, the design of intelligent coatings for temperature conditioning of enclosures, the construction of devices for processing information, the storage of thermal energy, and design of biomedical devices among others [1]. When the thickness of a heat conducting layer approaches the nanoscale, other non-Fourier types of transport appear, such as ballistic and wave-like [8,9,10]. The second is a result of the coherent coupling of heat carriers. It arises when there are no dispersive processes that eliminate their phase information

Methods

Results

Discussion

Conclusion