I have my office and rack in the basement where I work out of during the week. In the early spring and late fall when there isn't much cooling it would get rather warm to be comfortable (80F-82F).
A few weeks ago I realized that I have a cold air return duct in the ceiling so I cut an 8"x10" hole in it and left the furnace fan on 24/7 hoping that would help...it didn't really.
Last week I decided to hang an ~8" fan 3" below the hole I cut into the cold air return to see what would happen if I forced air into the duct...it didn't do much.
Last Thursday I remembered something from my volunteer firefighter days about how to set up a fan to ventilate a room through a window/door and how it was important to have the wind cover the entire opening. This led me to put a 12" fan in place of the 8" fan at 9PM.
Fast forward about an hour and my office was now 76F. The next morning it was 72F and it has stayed at 72F-73F ever since then.
The side benefit is that I'm able to provide a bunch of supplemental heat to the upstairs meaning that rather than my heat pump running 16hr+ per day with the electric strips kicking on periodically overnight during the <15F weather we've been having the heat pump has been running for 8hrs per day and the electric backup strips haven't needed to kick on at all.
I'm curious how it works for cooling next summer when I won't be able to run the furnace fan 24/7 since that'd just dump humidity back into the house so we'll see how that goes.
I'm still pretty happy with the results at the moment.
Energy spent in spinning also ends up turning into heat, due to friction.
In case of a fan, the friction is very low. Otherwise you would have a very inefficient fan. Most energy is used to move air.
So if a server pulls 200w, 50w is spent moving air. Not generating heat.
Pc case fans are rated at 1.5-2W, most of it is converted into heat because of the motor coil resistance. The rest (a few mW) is used to move air. The air will stop moving, because of friction too (with the rest of the air, the furniture of the room, ...) converting those last mW into heat too.
100% is converted into heat.
Read the link to r/askscience in another answer.
First, we're talking servers here, those are beefy fans easily pulling 10W each (https://store.supermicro.com/us_en/80mm-fan-0206l4.html) 3A at 12v is 3x12= 36 watts at full blast!
Secondly, moving air is putting the energy in to moving something, that will heat up the air a tiny bit because of the friction of the blades with the air, but this is marginal. There is indeed more heat coming from the coil.
The air you are moving is not magically heating it up. The wind on earth is also not warming up the globe. Just a diff in pressure. Same goes for fans, they create low pressure in front, causing the air to move to the other direction.
Ok, more powerful fans, but the proportion scales.
When you use energy to move the air, that energy is transformed from electric (in the case of fans) to kinetic. The air keeps that energy in kinetic form while it's moving.
But if you move away a couple of meter from the servers, you won't feel the air moving anymore. Why? Because it stopped moving. Why? It lost its kinetic energy. How? Friction! With the case, with the walls, with the still air. Where did that energy go? Heat, just a few 0,01°C because the energy was very low to begin with, and spread in a large volume. So very marginal heating.
That was my whole point, never said the heat is generating in the fans, but the energy transferred to the air is dissipated as heat in other parts of the room.
"The wind on earth is also not warming the globe". Of course not, it's the other way round. The warming of the air is what causes it to move. It's a different way to generate wind, cannot compare it with fans.