Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: Evidence of temperature jump and slip velocity in microchannels

We discuss the implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model for which the upwind finite difference scheme is used to solve the set of evolution equations recovered after discretization of the velocity space. Simulation of heat transport between two parallel walls at rest shows evidence of temperature jumps at the walls that increase with Knudsen number. When the walls move in opposite directions with speeds +/- u(W), fluid velocity slip is observed at the walls, together with temperature jumps.