Abstract
Flows of a rarefied gas between coaxial circular cylinders with nonuniform surface properties are studied on the basis of kinetic theory. It is assumed that the outer cylinder is a diffuse reflection boundary and the inner cylinder is a Maxwell-type boundary whose accommodation coefficient varies in the circumferential direction. Three fundamental flows are studied: 1) a flow caused by the rotation of the outer cylinder (Couette flow), 2) a flow induced between the cylinders at rest kept at different temperatures (heat transfer problem), and 3) a flow induced by the circumferential temperature distribution along the cylindrical surfaces (thermal creep flow). The linearized ES-BGK model of the Boltzmann equation is numerically analyzed using a finite difference method. The time-independent behavior of the gas is studied over a wide range of the gas rarefaction degree, the radii ratio, and a parameter characterizing the distribution of the accommodation coefficient. Due to an effect of nonuniform surface properties, a local heat transfer occurs between the gas and the cylindrical surfaces in Couette flow; a local tangential stress arises in the heat transfer problem. However, the total heat transfer between the two cylinders in Couette flow and the total torque acting on the inner cylinder in the heat transfer problem vanish irrespective of the flow parameters. Two nondegenerate reciprocity relations arise due to the effect of nonuniform surface properties. The reciprocity relations among the above-mentioned three flows are numerically confirmed over a wide range of the flow parameters. The force on the inner cylinder, which also arises due to the effect of nonuniform surface properties in Couette flow and the heat transfer problems, is studied.
Highlights
Internal flows of a rarefied gas have wide applications, e.g., in vacuum science and micro engineering, and have been studied extensively on the basis of kinetic theory
Due to an effect of nonuniform surface properties, a local heat transfer occurs between the gas and the cylindrical surfaces in Couette flow; a local tangential stress arises in the heat transfer problem
The total heat transfer between the two cylinders in Couette flow and the total torque acting on the inner cylinder in the heat transfer problem vanish irrespective of the flow parameters
Summary
Internal flows of a rarefied gas have wide applications, e.g., in vacuum science and micro engineering, and have been studied extensively on the basis of kinetic theory (see Refs. [1]-[7] and the references therein). The following four flows are studied: a flow induced by a temperature distribution along the wall surfaces (thermal creep flow), a flow induced between the walls at rest kept at different temperatures (heat transfer problem), and the above-mentioned Poiseuille and Couette flows. In this setting, the flow is no longer parallel, and a heat transfer between the gas and the wall surfaces occurs due to the combined effects of gas rarefaction and nonuniform surface properties. A question arises whether this vanishing property is a special characteristic limited to the plane channel flow or it has a universality over a wider class of flow prob-
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