2017/11/20 by Vazrik Chiloyan, Samuel Huberman, Chiloyan, Vazrik +11 · 3 citations
Engineering · Materials Science · Mathematics · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Numerical methods in inverse problems #Thermal Radiation and Cooling Technologies #Thermal properties of materials
paper · pdf · doi:10.48550/arxiv.1711.07151
openalex publication_date 2017/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The phonon Boltzmann transport equation (BTE) has been widely utilized to study thermal transport in solids. While for a number of materials the exact solution to the BTE has been obtained for a uniform heat flow, problems arising in micro/nanoscale heat transport have been analyzed within the relaxation time approximation (RTA). Since the RTA breaks down at temperatures low compared to the Debye temperature, this approximation prevents the study of an important class of high Debye temperature materials such as diamond, graphite, graphene and some other 2D materials. We present a full scattering matrix formalism that goes beyond the RTA approximation and obtain a Green's function solution for the linearized BTE, which leads to an explicit expression for the phonon distribution and temperature field produced by an arbitrary spatio-temporal distribution of heat sources in an unbounded medium. The presented formalism is capable of describing a wide range of phenomena, from heat dissipation by nanoscale hot spots to the propagation of second sound waves. We provide numerical results for graphene for a spatially sinusoidal heating profile and discuss the importance of using the full scattering matrix compared to the RTA.