Reduction of the effective thermal conductivity by circulation of the quasi-ballistic heat-flux

TL;DR

This paper demonstrates how to reduce the effective thermal conductivity in materials at the nanoscale by leveraging the circulatory component of heat flux in the quasi-ballistic phonon transport regime, challenging classical Fourier law assumptions.

Contribution

It introduces a method to lower thermal conductivity by exploiting the solenoidal heat-flux term in the quasi-ballistic regime, based on Boltzmann transport equation analysis.

Findings

Effective thermal conductivity can be reduced via circulatory heat-flux.

The approach applies to materials with dimensions comparable to phonon mean-free path.

The method offers new ways to control heat transfer at the nanoscale.

Abstract

For a thermal conductivity that is spatially uniform and independent of temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In the quasi-ballistic phonon transport regime, where the Fourier law breaks down, it has been proven starting from the Boltzmann transport equation that the constitutive relation for the heat-flux contains a solenoidal (circulatory) term with zero divergence and non-zero curl. In this paper we show how to reduce the effective thermal conductivity of a material with dimensions on the same scale as the phonon mean-free path, by exploiting the solenoidal term in the constitutive relation.