TY - JOUR
T1 - Modified ballistic–diffusive equations for obtaining phonon mean free path spectrum from ballistic thermal resistance
T2 - I. Introduction and validation of the equations
AU - Kwon, Ohmyoung
AU - Wehmeyer, Geoff
AU - Dames, Chris
N1 - Funding Information:
This research was supported by the Nano-material Technology Development Program (No.2011–0030146) and Basic Science Research Program (NRF-2018R1A2B2002837) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology.
Funding Information:
This work was supported by the Basic Science Research Program (NRF-2018R1A2B2002837) [National Research Foundation of Korea (NRF) funded]; National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [Nano-material Technology Development Program (No.2)].
Publisher Copyright:
© 2019, © 2019 Taylor & Francis.
PY - 2019/7/3
Y1 - 2019/7/3
N2 - Phonon mean free path (MFP) spectra are essential for the accurate prediction and utilization of the classical size effect. Rebuilding an MFP spectrum from experimental data remains challenging. It requires solving the thermal transport phenomenon of a heat source of a given shape across the entire size range. Herein, to do this for a heat source embedded in an infinite medium, we derive a new set of modified ballistic–diffusive equations by analyzing the cause of the erroneous results observed in a steady-state solution of the original ballistic-diffusive equations. We demonstrate their ease and accuracy by obtaining the effective thermal conductivity for a spherical nanoparticle embedded in an infinite medium in an explicit closed-form and comparing it with that obtained by the Boltzmann transport equation (differences estimated as <3%).
AB - Phonon mean free path (MFP) spectra are essential for the accurate prediction and utilization of the classical size effect. Rebuilding an MFP spectrum from experimental data remains challenging. It requires solving the thermal transport phenomenon of a heat source of a given shape across the entire size range. Herein, to do this for a heat source embedded in an infinite medium, we derive a new set of modified ballistic–diffusive equations by analyzing the cause of the erroneous results observed in a steady-state solution of the original ballistic-diffusive equations. We demonstrate their ease and accuracy by obtaining the effective thermal conductivity for a spherical nanoparticle embedded in an infinite medium in an explicit closed-form and comparing it with that obtained by the Boltzmann transport equation (differences estimated as <3%).
KW - Phonon mean free path
KW - ballistic thermal resistance
KW - ballistic–diffusive equations
KW - effective thermal conductivity
KW - phonon mean free path spectrum
UR - http://www.scopus.com/inward/record.url?scp=85066617085&partnerID=8YFLogxK
U2 - 10.1080/15567265.2019.1619885
DO - 10.1080/15567265.2019.1619885
M3 - Article
AN - SCOPUS:85066617085
SN - 1556-7265
VL - 23
SP - 259
EP - 273
JO - Nanoscale and Microscale Thermophysical Engineering
JF - Nanoscale and Microscale Thermophysical Engineering
IS - 3
ER -