To make a jet pump, which is the intended scope of using the fan blast to push additional air out through the window, I would recommend:
1 fan diameter 1/3 to 1/2 of the window opening.
2 Fan distance 3 to 6 times the fan diameter.
3 Fan speed max.
Note 1: For lower speeds, reduce fan distance.
Super important note 2: you can push air out only as much as fresh air can replace it. You need a big air entrance somewhere else, roughly 2 times bigger than the fan window.
If the window is the only opening, use the fan placed at the window, zero to two diameter distance. The fan must be placed on a side, pointing out at an angle so the flow of ejected air doesn’t impede or mix with inward flow.
Source: I have a shit fan and I make best use of it. Force hot air out in summer and shoot my wood burner heat around the house in winter. And yea there’s better ways but I work in aviation so this game is fun to me. I don’t want a better fan, I’m having fun.
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