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Flows of a Rarefied Gas between Coaxial Circular Cylinders with Nonuniform Surface Properties

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Document pages: 27 pages

Abstract: Flows of a rarefied gas between coaxial circular cylinders with nonuniformsurface properties are studied on the basis of kinetic theory. It is assumed thatthe outer cylinder is a diffuse reflection boundary and the inner cylinder is aMaxwell-type boundary whose accommodation coefficient varies in the circumferentialdirection. Three fundamental flows are studied: 1) a flow causedby the rotation of the outer cylinder (Couette flow), 2) a flow induced betweenthe cylinders at rest kept at different temperatures (heat transfer problem),and 3) a flow induced by the circumferential temperature distributionalong the cylindrical surfaces (thermal creep flow). The linearized ES-BGKmodel of the Boltzmann equation is numerically analyzed using a finite differencemethod. The time-independent behavior of the gas is studied over awide range of the gas rarefaction degree, the radii ratio, and a parameter characterizingthe distribution of the accommodation coefficient. Due to an effectof nonuniform surface properties, a local heat transfer occurs betweenthe gas and the cylindrical surfaces in Couette flow; a local tangential stressarises in the heat transfer problem. However, the total heat transfer betweenthe two cylinders in Couette flow and the total torque acting on the inner cylinderin the heat transfer problem vanish irrespective of the flow parameters.Two nondegenerate reciprocity relations arise due to the effect of nonuniformsurface properties. The reciprocity relations among the above-mentioned threeflows 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 nonuniformsurface properties in Couette flow and the heat transfer problems, isstudied.

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