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Title: A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.
Authors:
;  [1]
  1. Network for Computational Nanotechnology, School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States)
Publication Date:
OSTI Identifier:
22399402
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 117; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOLTZMANN EQUATION; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; ELECTRONS; ENERGY DEPENDENCE; MEAN FREE PATH; PHONONS; TEMPERATURE DEPENDENCE; TEMPERATURE GRADIENTS; THERMAL CONDUCTION; TRANSIENTS