Abstract
Free-convective flow in the neighbourhood of the upper pole of a heated sphere at high Grashof number is considered. Direct buoyancy effects have been studied previously, and it is known that the unsteady boundary-layer solution may terminate in singular behaviour. For a spatially varying surface temperature, a self-induced pressure gradient is present. The effects of this are examined in detail, and it is shown that a singular behaviour may again terminate the solution. The competing effects of buoyancy and induced pressure gradient are examined to delineate those cases in which a steady-state flow is achieved.
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