Lattice Boltzmann method for rarefied channel flows with heat transfer

A thermal lattice Boltzmann method (TLBM) is presented for the analysis of fluid flow and heat transfer in two-dimensional channels with non-continuum effects. The relaxation times (τf,τgτf,τg) are linked to the Knudsen number which accounts for the rarefaction that can be present at micro geometries or at low density conditions. The TLBM used here employs inlet/outlet boundary conditions to generate a forced convection problem where the calculation of equilibrium distributions at the wall surfaces are modified to incorporate the velocity slip and temperature jump conditions. Numerical simulations are obtained for thermal micro-Couette and thermal micro-Poiseuille channel flows and the effect of the Knudsen number on the velocity and temperature profile is investigated.