Why does a ceiling fan blowing air downward cool in the summertime:
whereas a ceiling fan sucking air upwards heats in the wintertime:
Why isn't it the other way around?
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In summertime, the ceiling fan blows air downwards and cools down your body using the wind chill effect.
In wintertime, if you have an active heating system at home, it will heat up the air in the room. Hotter air moves up and accumulate near the ceiling, colder air being down. A ceiling fan in reverse direction moves cold air up pushes hot air downwards to people's level. It can do this in forward direction but then you will have the wind chill effect again.
Why does the chill effect only occur in summertime mode ?
Consider this fan :
You can try it yourself: If you stand in front of the fan you will feel a strong air stream, if you stand behind you will feel a much weaker stream. This is because the fan collects air from all directions in the back and blows it in one direction in the front.
So, in wintertime mode, wind speed above the fan will be higher than that below, there will be a weak stream of air at your level so you will not feel the chill effect.
Either way will cool you in Summer: Either way, keeps the air circulating in the room, and the moving air increases the rate at which perspiration can evaporate from your sweaty body.
Either way will warm you in Winter. Either way keeps the air circulating in the room, thereby preventing thermal stratification (i.e., it prevents all the heat from collecting up near your stately cathedral ceiling where it does you no good.)