Fans actually add heat to a room. One way to think about it is like this: If you have a perfectly insulated room and you put an electric fan in it, then the room will get warmer. All the electricity that is driving the fan turns directly into heat.
So a fan does not cool the room at all. What a fan does is create a wind chill effect.
When weatherpeople talk about wind chill on a cold winter day, what they are referring to is how the wind increases convective heat loss. The windchill factor is the same effect that causes you to blow on hot soup to cool it down. The movement of the air increases the soup's loss of heat by convection, so the soup cools down faster.
By blowing air around, the fan makes it easier for the air to evaporate sweat from your skin, which is how you eliminate body heat. The more evaporation, the cooler you feel.
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