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.
|Original language||English (US)|
|Number of pages||16|
|Journal||International Journal of Heat and Mass Transfer|
|State||Published - Dec 2018|
Bibliographical noteFunding 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.
- Knudsen numbers
- Lattice Boltzmann method
- Phonon transport
- Size effect