A novel alternate approach for multiscale thermal transport using diffusion in the Boltzmann Transport Equation

The Boltzmann Transport Equation (BTE) with the single Relaxation Time Approximation (RTA) can be employed to simulate energy transport in the sub-continuum regime, as long as the particle assumption for the heat carriers is valid. Here, analytical and numerical solutions of the BTE in one space dimension are obtained for two different sets of boundary conditions. For the steady case, numerical solutions obtained are found to be identical (to within purely numerical error) to the analytical solutions. Transient solutions are obtained using the Lattice Boltzmann Method (LBM). Additionally, the impact of introducing a diffusive term in the BTE is investigated. When the diffusive model is solved, an increasing gradient (but no jump) in the temperature at the boundaries is observed as the Knudsen number (Kn) increases. The results for the transient case are compared to those obtained from the Fourier solution for small values of Kn. It is observed that the BTE with an added diffusion term is applicable for all Kn.