Nondiffusive thermal transport from micro/nanoscale sources producing nonthermal phonon populations exceeds Fourier heat conduction

TL;DR

This paper investigates nondiffusive phonon-mediated thermal transport at micro/nanoscale sources, revealing conditions where heat transfer exceeds or falls below Fourier law predictions due to phonon distribution effects.

Contribution

It provides analytical and numerical solutions to the Boltzmann transport equation for specific source geometries, highlighting the impact of phonon populations on thermal transport beyond Fourier's law.

Findings

Hotter-than-expected temperature for sources emitting thermal phonons.

Potential for significantly cooler temperatures with low-frequency phonon sources.

Enhanced heat transport observed when phonon distributions deviate from thermal equilibrium.

Abstract

We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three- dimensional Gaussian hot spot, and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than predicted by the heat equation, yielding an enhanced heat transport.