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Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform suiface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundaty on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar-Gross-Krook-Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (ID) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate. [ABSTRACT FROM AUTHOR]

Plane thermal transpiration o f a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas. [ABSTRACT FROM AUTHOR]