Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates II: effect of nonuniform surface properties in the longitudinal direction

Poiseuille flow and thermal transpiration of a rarefied gas between two parallel plates are studied for the situation that one of the walls is a Maxwell-type boundary with a periodic distribution of the accommodation coefficient in the longitudinal direction. The flow behavior is studied numerically based on the Bhatnager-Gross-Krook-Welander model of the Boltzmann equation. The solution is sought in a superposition of a linear and a periodic functions in the longitudinal coordinate. The numerical solution is provided over a wide range of the mean free path and the parameters characterizing the distribution of the accommodation coefficient. Due to the nonuniform surface properties in the longitudinal direction, the flow is nonparallel, and a deviation in the pressure and the temperature of the gas from those of the conventional parallel flow is observed. An energy transfer between the gas and the walls arises. The mass flow rate of the gas is approximated by a formula consisting of the data of one-dimensional flows; however, a non-negligible disagreement is observed in Poiseuille flow when the amplitude of the variation of the accommodation coefficient is sufficiently large. The validity of the present approach is confirmed by a direct numerical analysis of a flow through a long channel.