Space-time dependent thermal conductivity in nonlocal thermal transport

TL;DR

This paper introduces a novel eigendecomposition method to solve the space-time dependent Peierls-Boltzmann equation, revealing a generalized Fourier relation with a space-time dependent thermal conductivity that explains oscillatory temperature responses in high thermal conductivity materials.

Contribution

It presents a direct eigendecomposition solution to the space-time dependent PBE and demonstrates the physical implications of a generalized Fourier law with variable thermal conductivity.

Findings

Thermal conductivity depends on both space and time.

Oscillatory temperature responses occur in transient grating experiments.

Method extends computational capabilities for nonlocal thermal transport.

Abstract

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. This capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.