Heat dissipation in the quasiballistic regime studied using Boltzmann equation in the spatial frequency domain

TL;DR

This paper investigates how heater geometry and spectral distribution influence thermal resistance in quasiballistic heat conduction, revealing that spatial frequency and spectral factors can cause resistance to align with Fourier's law predictions.

Contribution

It provides analytical solutions linking heater geometry and spectral distribution to thermal resistance in the quasiballistic regime, challenging previous assumptions.

Findings

Thermal resistance depends on spatial frequency of heater pattern.

In many geometries, quasiballistic resistance matches Fourier's law.

Spectral distribution significantly affects heat transport.

Abstract

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law, however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistance rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We also demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.