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Licensed Unlicensed Requires Authentication Published by De Gruyter August 19, 2020

Three-Dimensional Ballistic-Diffusive Heat Transport in Silicon: Transient Response and Thermal Conductivity

  • Saad Bin Mansoor EMAIL logo and Bekir S. Yilbas ORCID logo

Abstract

Phonons are the main contributors to thermal energy transfer in thin films. The size dependence of the thermal transport characteristics alters the film properties such as thermal conductivity. Hence, in the present study, three-dimensional, transient phonon transport in dielectric material is studied through the Equation of Phonon Radiative Transport (EPRT) to assess the size dependence of thermal conductivity. The numerical scheme is introduced solving the EPRT in three dimensions and the governing algorithm is described in detail. A parametric study is carried out examining the effect of the Kn number on the thermal energy transport characteristics in three-dimensional thermally excited film. The formulation and estimation of the effective thermal conductivity tensor is presented and discussed, thereby extending, to some extent, the one-dimensional results obtained earlier. We demonstrate that thermal conductivity changes in all directions, depending on the size effect. In addition, the directions of the temperature gradient and heat flux vectors differ as the Kn number approaches unity.

Award Identifier / Grant number: RG181003

Funding statement: The authors acknowledge the support of the Deanship of Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for the funded project RG181003.

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Received: 2020-04-04
Revised: 2020-07-14
Accepted: 2020-07-31
Published Online: 2020-08-19
Published in Print: 2020-10-25

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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