A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method

Yan Su; Jane H. Davidson

doi:10.1016/j.ijheatmasstransfer.2018.06.148

A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method

Yan Su, Jane H. Davidson

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A new three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method (NDLBM) is developed to be applicable in the sub-continuum regime for diffusive and ballistic phonon transport. Two Knudsen numbers based on the base frequency and variable frequency, Kn_ω₀ and Kn_ω, are defined in order to isolate the effects of material size and phonon transfer frequency. Both the relaxation time and boundary conditions of the phonon Boltzmann transport equation are modeled in dimensionless form. The physical meaning of each component in the relaxation time and discontinuous boundary models is interpreted. By introducing the Boltzmann constant and Planck's constant, all other coefficients can be simplified into order of one. The transient dimensionless phonon probability distribution functions are solved by the Parallel NDLBM with D3Q27 grids. The dimensionless temperature distributions, i.e. the dimensionless phonon energy density distributions, compare favorably with previous experimental and numerical results for various Kn_ω₀. The effects of material size, temperature, and phonon transfer frequency are investigated.

Original language	English (US)
Pages (from-to)	303-318
Number of pages	16
Journal	International Journal of Heat and Mass Transfer
Volume	127
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.148
State	Published - Dec 2018

Bibliographical note

Funding Information:
Yan Su’s study was supported by Solar Energy Laboratory of University of Macau with project from the Research Committee of the University of Macau No. MYRG2017-00003-FST and MYRG2018-00018-FST. Also thanks the High Performance Computing Cluster of Information and Communication Technology Office of the University of Macau.

Publisher Copyright:
© 2018 Elsevier Ltd

Keywords

Knudsen numbers
Lattice Boltzmann method
Phonon transport
Size effect

Access

10.1016/j.ijheatmasstransfer.2018.06.148

OpenUrl availability

Full text

Cite this

@article{9231b90e96534195a253ea1960b2421e,

title = "A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method",

abstract = "A new three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method (NDLBM) is developed to be applicable in the sub-continuum regime for diffusive and ballistic phonon transport. Two Knudsen numbers based on the base frequency and variable frequency, Knω0 and Knω, are defined in order to isolate the effects of material size and phonon transfer frequency. Both the relaxation time and boundary conditions of the phonon Boltzmann transport equation are modeled in dimensionless form. The physical meaning of each component in the relaxation time and discontinuous boundary models is interpreted. By introducing the Boltzmann constant and Planck's constant, all other coefficients can be simplified into order of one. The transient dimensionless phonon probability distribution functions are solved by the Parallel NDLBM with D3Q27 grids. The dimensionless temperature distributions, i.e. the dimensionless phonon energy density distributions, compare favorably with previous experimental and numerical results for various Knω0 . The effects of material size, temperature, and phonon transfer frequency are investigated.",

keywords = "Knudsen numbers, Lattice Boltzmann method, Phonon transport, Size effect",

author = "Yan Su and Davidson, {Jane H.}",

note = "Funding Information: Yan Su{\textquoteright}s study was supported by Solar Energy Laboratory of University of Macau with project from the Research Committee of the University of Macau No. MYRG2017-00003-FST and MYRG2018-00018-FST. Also thanks the High Performance Computing Cluster of Information and Communication Technology Office of the University of Macau. Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2018",

month = dec,

doi = "10.1016/j.ijheatmasstransfer.2018.06.148",

language = "English (US)",

volume = "127",

pages = "303--318",

journal = "International Journal of Heat and Mass Transfer",

issn = "0017-9310",

publisher = "Elsevier Limited",

}

TY - JOUR

T1 - A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method

AU - Su, Yan

AU - Davidson, Jane H.

N1 - Funding Information: Yan Su’s study was supported by Solar Energy Laboratory of University of Macau with project from the Research Committee of the University of Macau No. MYRG2017-00003-FST and MYRG2018-00018-FST. Also thanks the High Performance Computing Cluster of Information and Communication Technology Office of the University of Macau. Publisher Copyright: © 2018 Elsevier Ltd

PY - 2018/12

Y1 - 2018/12

N2 - A new three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method (NDLBM) is developed to be applicable in the sub-continuum regime for diffusive and ballistic phonon transport. Two Knudsen numbers based on the base frequency and variable frequency, Knω0 and Knω, are defined in order to isolate the effects of material size and phonon transfer frequency. Both the relaxation time and boundary conditions of the phonon Boltzmann transport equation are modeled in dimensionless form. The physical meaning of each component in the relaxation time and discontinuous boundary models is interpreted. By introducing the Boltzmann constant and Planck's constant, all other coefficients can be simplified into order of one. The transient dimensionless phonon probability distribution functions are solved by the Parallel NDLBM with D3Q27 grids. The dimensionless temperature distributions, i.e. the dimensionless phonon energy density distributions, compare favorably with previous experimental and numerical results for various Knω0 . The effects of material size, temperature, and phonon transfer frequency are investigated.

AB - A new three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method (NDLBM) is developed to be applicable in the sub-continuum regime for diffusive and ballistic phonon transport. Two Knudsen numbers based on the base frequency and variable frequency, Knω0 and Knω, are defined in order to isolate the effects of material size and phonon transfer frequency. Both the relaxation time and boundary conditions of the phonon Boltzmann transport equation are modeled in dimensionless form. The physical meaning of each component in the relaxation time and discontinuous boundary models is interpreted. By introducing the Boltzmann constant and Planck's constant, all other coefficients can be simplified into order of one. The transient dimensionless phonon probability distribution functions are solved by the Parallel NDLBM with D3Q27 grids. The dimensionless temperature distributions, i.e. the dimensionless phonon energy density distributions, compare favorably with previous experimental and numerical results for various Knω0 . The effects of material size, temperature, and phonon transfer frequency are investigated.

KW - Knudsen numbers

KW - Lattice Boltzmann method

KW - Phonon transport

KW - Size effect

UR - http://www.scopus.com/inward/record.url?scp=85049746923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049746923&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2018.06.148

DO - 10.1016/j.ijheatmasstransfer.2018.06.148

M3 - Article

AN - SCOPUS:85049746923

SN - 0017-9310

VL - 127

SP - 303

EP - 318

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

ER -

A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this