Thermally driven flow in a gas centrifuge with an insulated side wall

Abstract

A thermally driven steady axisymmetric flow of gas of small diffusivity in a vertical circular cylinder rotating rapidly about its axis of symmetry is studied. The side wall is a thermal insulator and the horizontal end plates are perfect conductors. The temperature of the top end plate is kept slightly higher than that of the bottom one.The boundary-layer method is applied to solve the linearized basic equations and the following results are obtained.The axial velocity in the inner core is fully controlled by the Ekman suction on the horizontal plates and is the same as that in the case of a perfectly conducting side wall.The closed circulation in the side-wall Stewartson E½ layer is strongly suppressed compared with the case of a perfectly conducting side wall.This situation is reflected in the inner temperature field, which deviates from that in the case of a perfectly conducting side wall. The critical parameter governing the solution is found to be (γ − 1) PrG0E−1/3/4γ, where Pr is the Prandtl number, γ the ratio of specific heats, E the Ekman number and G0 the square of the Mach number based on the peripheral speed of the cylinder.