A generalized enhanced Fourier law and underlying connections to major frameworks for quasi-ballistic phonon transport

TL;DR

This paper derives a generalized enhanced Fourier law from the Boltzmann transport equation, connecting various phonon transport models and accounting for quasi-ballistic effects in a physically observable framework.

Contribution

It introduces a generalized EFL applicable to arbitrary phonon populations, unifying different models of quasi-ballistic phonon transport.

Findings

Derived a generalized EFL from the Boltzmann equation

Connected the EFL to other phonon transport models

Revealed the unity among various models in literature

Abstract

An enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables, is derived from the Boltzmann transport equation, assuming a gray population of quasi-ballistic phonon modes. This equation is generalized to an arbitrary phonon population. Other phonon transport models are analyzed in the context of the generalized EFL and connections are made between the generalized EFL and other models, revealing the essential unity of seemingly disparate models reported in the literature.