A stirring fan doesnt do anything. If properly installed according to the manual a vFD will circulate the air around it. Everything else is natural convection...hot air rises, cold air sinks, just like an oil filled transformer. The big limit, and Hoffmann as mentioned has formulas for this, is it's hard to radiate much off a panel. VFD heat load is easy. Multiply the maximum input in watts or if not given maximum continuous input rating x volts x 1.732 by the losses which is 100% minus the efficiency which will be in the specs too. Don't forget to add in all the other heat sources like any and all transformers and reactors/filters which you figure the same way.
This is conservative...worst case. If you won't be running the VFD wide open and you know the efficiency at points other than peak power (you won't) you can design for other conditions but in those cases you're basically guessing or taking measurements and hoping the process never changes.
Usually the calculation tells you that you will need external fans or thermal electric or air conditioning coolers.
Another approach is using flange mount VFDs. The heat sink and fans on the VFD are mounted on a plate on the back of the VFD. You cut a big hole in the enclosure and mount the VFD so that the heat sink is on the back or side. The only thing left in the enclosure is the control board and wiring.
Along the same concept and this is strictly in space limited situations large (1000+ HP) VFDs can be water or oil cooled so the radiators go outside. The cost is much higher than air cooled so this is only done when space is a premium. I used this on a set of 5 VFDs running 2000+ HP motors on a 4 axis servo system, 5 motors per axis in parallel, with roughly 12-15 MW peak power. It was an excavator so space is a premium. Running air ducts that big would not be practical compared to a couple large fan coooed radiators.
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