The key difference is that buoyancy force is normal to the plate. Flow and heat transfer depend on whether the plate is hot or cold.
The only thing causing circulation is the heat of the plate in these cases. The Nusselt number correlations to be used in this case:
L is the length scale. This is required so that the correlation can account for different shapes of plate. The other two cases to be considered are when free convection causes movement past a plate.
The Nusselt number correlation is different in this instance.
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