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If a fan that is using 50 watts is moving 1 m³/min of air. Lets say the walls are the same temperature as the air so there’s no heat dissipation there. How do I know if the fan is putting in more energy in to the room than its dissipating?

If the walls are 10 deg cooler than the air will this be sufficient for the molecules to dissipate the heat in to them. Where’s the point of balance.

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Too many variables for a useful answer; it depends entirely on the airflow generated by the fan, which is likely to be very complex. You'll have to make assumptions about the rate at which air is being circulated over the walls. – Will Vousden Jun 22 '11 at 7:57
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You have some basic misunderstandings about heat. If the walls are at the same temperature as the air, then no net transfer of heat will occur. You need a small temperature gradient. The fan simply improves the kinetics, i.e. makes the transfer happen faster. The exact answer will therefore depend on the shape of the room, and how efficiently the walls actually allow the transfer of heat through/into them. – genneth Jun 22 '11 at 9:43
Without getting to complicated on the shape and dimensions of the room. I have always suspected a fan introduces more heat in to the room than what it helps dissipate. Unless the wall are cool. – Fortunato Jun 22 '11 at 21:02

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Assuming no heat transfer from a cooler outside to a warmer inside, a fan always adds more energy than it dissipates (because it dissipates no energy). However, by introducing a breeze, it accelerates evaporation off your skin, which in turn cools you off. (This is related to the wind chill factor meteorologists talk about.) How much cooler you will feel will be a function of how much you are sweating. It's important to note that pets, who don't sweat from the majority of their skin like we do, thus aren't cooled as much by a fan as we are.

Another method by which a fan can cool (as mentioned by Mitchell) is to move hot air away from a hot object, thus reducing the air's insulatory nature. This is why fans help cool off CPUs even though they don't sweat.

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Air circulation also helps by moving hot air away from your body, since air is a very good insulator. This affect applies to anything warm-blooded. – Mitchell Jun 22 '11 at 15:40
@Mitchell: Excellent point – Ben Hocking Jun 22 '11 at 16:19
@Mitchell: This point does help. basically the fan prevents pockets of hotter air. – Fortunato Jun 22 '11 at 20:57
You not only feel cooler, you ARE cooler. Evaporative cooling is a very powerful and real effect that really does pull heat away from the wetted object, resulting in a delta T. – Vintage Jun 22 '11 at 21:52
@Vintage: Another good point. I'll edit my answer to include the points that you and Mitchell have made. – Ben Hocking Jun 22 '11 at 22:31
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From my empirical experience, to dissipate 2kW of power in a room, one need 18C temperature difference above walls with one fan.

So to dissipate 0.05kW, walls need to be cooler by ~0.45C only.

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thank you that gives me some numbers to work whit. – Fortunato Jun 22 '11 at 21:05

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