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I think the answer is, it depends. There are two opposing effects here. Suppose you have a liquid-filled pot over a burner. If a layer of hot liquid forms against the bottom of the pot, that will reduce the rate of heat transfer from the burner. Stirring might keep cooler liquid in contact with the bottom of the pot, and therefore increase the efficiency ...


You're on the right track here. For convection between plates to 'stop' (it won't really stop, just get wicked slow) you want viscosity to be very high relative to buoyancy, so you want low Grashof. Also, in the case of very narrow plates, you'd want to use the gap width as your characteristic length $L$. $10^8$ is the transition point at which the flow ...

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