Flow induced by a vibrating heated sphere

Abstract

Mean flows induced by a heated or cold sphere vibrating in a liquid are studied. The cases of a sphere immersed in an unbounded liquid and a liquid layer of finite thickness, bounded by two rigid coaxial spheres, are considered. An analytical solution is obtained in the creeping flow approximation for small values of the governing parameters. The vibrating flow structure is shown to depend to a considerable extent on the clearance and to be fairly complex for small clearances. For a fixed clearance, the creeping flow structure is determined by a single parameter, the ratio of the vibrating Grashof number to the pulsating Reynolds number (Schlichting parameter). For large values of the parameters, the vibrating flow structure is determined by the vibrating Grashof number and the Schlichting parameter separately. The changes in the flow structure with increase in the values of the governing parameters are studied numerically by a finite difference method.