Ali Nouri - School of Mech. Eng., Sharif University of Technology
Navid Sarikhani - School of Mech. Eng. (Computational Mechanics Lab), Sharif University of Technology

This study has further developed the lattice Boltzmann method for modeling the heat conduction in thin solid films. Heat conduction is modeled as a gas of Bose- Einstein particles (phonons), which carry quanta of heat. The bulk value of thermal conductivity in connection with Fourier’s law cannot be used to predict heat transport phenomena if the characteristic length or time decreases to the order of heat carriers mean free pathabout 100 nm and relaxation time about 10 ps. The Debye assumption is employed to connect phonon wave length and frequency via a single group velocity. The group velocity is defined based on the average transverse and longitudinal sound velocity in the medium to account for the phonon polarization. A new nondimensionalization scheme is applied to transform phonon distribution function to energy distribution function. Also the distribution dynamic is adjusted so that the collision does take place just after phonons surpass the mean free path. Effective Knudsen number for correlating cross plane thermal conductivity is introduced and discussed, too. Sub-continuum effects such as temperature slip at the boundaries and transition from diffusive to ballistic are investigated. The results are compared with the Fourier’s law continuum based model as well as with the available experimental and numerical data in literature.

thermal conductivity, thin solid films, lattice Boltzmann method, sub-continuum heat transfer