Abstract
Time-averaged flows induced by oscillations of a heated (or cooled) solid sphere immersed in a liquid are investigated. The cases of an infinite surrounding liquid and the liquid placed into the spherical rigid envelope are considered. The gravity is absent. The interaction of thermovibrational flows and vibrational Schlichting flows is studied. New generalized equations are used for the description of thermovibrational convection. Analytical solutions have been obtained for small values of the governing parameters, under restriction of creeping flows, both in the case of infinite surrounding liquid and liquid placed into the rigid envelope. It has been found that the vibrational flow essentially depends on the layer thickness and can be rather complicated in the case of small thicknesses. At a fixed layer thickness, the creeping flow structure is defined by only one parameter, which is the ratio of vibrational Grashof number and Schlichting parameter. In the case of arbitrary values of the parameters, vibrational flows have been studied by a finite-difference method. The evolution of the finite-amplitude vibrational flow structure with the increase of the vibrational Grashof number has been investigated.
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