Sub-continuum thermal transport modeling using diffusion in the Lattice Boltzmann Transport Equation

The Boltzmann Transport Equation is employed to model one-dimensional heat conduction problems at sub-continuum scales. A semi-gray Lattice Boltzmann (LB) model is presented and validated against a diffusive model of steady state thin film heat conduction with temperature boundary conditions. The size-dependent effective thermal conductivity curves of a gray LB model and a semi-gray LB model for Silicon are generated. In addition, a new semi-gray LB model with diffusion term is applied to determine the effective thermal conductivity. The transient features and dimension concerns of the new semi-gray LB model are also investigated. Results demonstrate that the semi-gray LB model with a diffusion term successfully recovers the size-dependent data of effective thermal conductivity and matches well with the diffusive solution valid at large scales. This approach can be applied to improve the accuracy of thermal modeling on micro-scale electronic systems.