Non-equilibrium thermodynamics of the gas kinetic boundary value problem

The gas is described by the linearized Boltzmann equation, the wall by hydrodynamics. The rate of interfacial entropy production and an interfacial reciprocity postulate are formulated. Both are rewritten in terms of an interfacial thermodynamical force-flux pair, essentially the sum and the difference of the distribution function and its motion-reversed counterpart, for particles approaching the wall. The boundary condition constitutes a linear relation within this pair. Combination with the Green's relation stemming from the Boltzmann equation, leads to an integral formulation of the boundary value problem. Certain biothonormalized half-range eigenfunctions are introduced. They serve to expand the interfacial force-flux pair and formally to treat Couette flow and heat transfer between parallel plates, for any pressure. Upper and lower bounds for mechanical velocity slip and temperature jump ensue. The Knudsen case as a limit and complete accomodation as a numerical example are considered.