Modified ballistic–diffusive equations for obtaining phonon mean free path spectrum from ballistic thermal resistance: I. Introduction and validation of the equations

Ohmyoung Kwon, Geoff Wehmeyer, Chris Dames

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    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%).

    Original languageEnglish
    Pages (from-to)259-273
    Number of pages15
    JournalNanoscale and Microscale Thermophysical Engineering
    Volume23
    Issue number3
    DOIs
    Publication statusPublished - 2019 Jul 3

    Bibliographical note

    Publisher Copyright:
    © 2019, © 2019 Taylor & Francis.

    Keywords

    • Phonon mean free path
    • ballistic thermal resistance
    • ballistic–diffusive equations
    • effective thermal conductivity
    • phonon mean free path spectrum

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics
    • General Materials Science
    • Condensed Matter Physics
    • Mechanics of Materials

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