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A fan creates kinda long "channel" in front of it and behind it, where the air is moving rather fast (at the speed that the fan creates). Imagine the narrow beam of light from a flashlight. You want that channel to go right through the window to have a good amount of air flowing.
I don't know that you need to keep a distance from the window. I think 1-2m is just more practical than having the fan right inside the window frame.
do you happen to know whether this is significantly different for a blower-style fan that has its air intake on one side? for example
https://lasko.com/collections/air-movers-blowers/products/lasko-12-pivoting-pro-high-velocity-utility-blower-fan-with-3-speeds-u12104-gray
I don't know the type, so I am judging it from that picture.
It shows a rather small area where the air comes out. I imagine that it creates high speed, but the "channel" would have the exact same size and shape as that small area where the air comes out. So I'd consider it as less effective.
A fan with a large diameter could probably move more air.
No, it should be roughly the same.
The thing you're trying to take advantage of when placing a fan a meter or two from a window is that when you have a moving mass of air and it passes by static air, it "drags" the static air with it. As a result you move more air mass that what was blown by the fan directly out of the fan blades.
A blower fan still blows air in a direction, and can likely take an even bigger advantage than a traditional box fan since a blower fan's output direction will be more orderly aka closer to a laminar flow than a box fan. But the real advantage of the blower style fan is that its enclosure allows you to direct both the intake and exhaust portions of the air being moved.