Temperature jump and velocity slip in the moment method

The moment method of the kinetic theory requires boundary conditions for the moments. It is not possible to derive these in an easy manner from the boundary conditions for the phase density. The conservation laws of mass, momentum and energy give only five relations between the moments and the properties of the wall. Additional boundary conditions may be determined from the minimax principle for the entropy production which was recently proposed by Struchtrup & Weiss [1]. These ideas are outlined for the case of 13 and 14 moments and Maxwell’s boundary conditions for the phase density which lead to temperature jumps and velocity slip at walls. In particular, one-dimensional stationary heat transfer between two walls at rest is considered. The temperature jumps at the walls are shown to depend on the values of all moments in front of the wall. The results obtained by the minimax principle are compared with results obtained for the same problem by a minimum principle for the global entropy production and by the so-called kinetic schemes [2].