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A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method
Su Y.2; Davidson J.H.1
2018-12-01
Source PublicationInternational Journal of Heat and Mass Transfer
ISSN00179310
Volume127Pages:303-318
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 and Kn, 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. The effects of material size, temperature, and phonon transfer frequency are investigated.

KeywordKnudsen Numbers Lattice Boltzmann Method Phonon Transport Size Effect
DOI10.1016/j.ijheatmasstransfer.2018.06.148
URLView the original
Indexed BySCI
WOS Research AreaThermodynamics ; Engineering ; Mechanics
WOS SubjectThermodynamics ; Engineering, Mechanical ; Mechanics
WOS IDWOS:000445994000032
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Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF ELECTROMECHANICAL ENGINEERING
Affiliation1.University of Minnesota Twin Cities
2.Universidade de Macau
Recommended Citation
GB/T 7714
Su Y.,Davidson J.H.. A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method[J]. International Journal of Heat and Mass Transfer,2018,127:303-318.
APA Su Y.,&Davidson J.H..(2018).A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method.International Journal of Heat and Mass Transfer,127,303-318.
MLA Su Y.,et al."A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method".International Journal of Heat and Mass Transfer 127(2018):303-318.
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