Upright Heat sinks for f5

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From looking at various datasheets (Fischer) I would say that´s a very rough estimate at best.
The problem is "isothermal".
If the backplate had infinitely low thermal resistance then the sqrt rule would be accurate.

When doubling or quadrupling the height using a standard sink geometry, the backplate thickness to width/height ratio changes and this obscures the sqrt law.

If you download the software linked above you can experiment with different heights and widths and see/model the effects for yourself.

Hint:
when you quadruple the height you can try quadrupling the number of devices spread evenly around the backplate and each device dissipating half the power of the ref shape. This way you approach isothermal and have doubled the power dissipation.
 
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As mentioned, one of the factors for dissipation of heat depends upon the rate of heat transfer, modified by the distance traveled.

maybe re-stating the obvious,

Another factor (more significant) for vertical orientation is the conditioning of upper portions of the sink by the heat that has already been radiated. The Delta T is not as great for the parts of the sink surrounded by air warmed by the heat leaving the sink itself. This contributes to the lower efficiency.
 
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