You just want air flowing over your body more than anything, especially directly over your head and face.
The flow of air cools you more than mixing the air in the room. The differential between floor air and ceiling air isn’t huge during a hot spell. And it mixes anyways with turbulence.
Also, I’m not trying to cool the ceiling. I’m trying to cool me!
As the ceiling fan pushes the air down, the air that’s already on the ground gets squashed and moves up along the walls. Where it then gets pushed down by the ceiling fan. This process repeats.
It’s like stiring a cake mix. As you push the cake mix through the middle of the bowl, the cake mix in front of the spoon moves along the side of the bowl, to fill the space behind the spoon.
As the air flows over you it cools you down. The temperature difference between the cool air at the floor and the warm air on the ceiling is not that much anyway.
This assumes a somewhat airtight room, in reality the air will move around a little different depending on the room.
While hot air rises, there’s usually not a significant difference in air temperature between the air at the ceiling and the air at the floor, unless you’re in a very tall room or you have some way to trap the hot air up top (like an attic). So the effect of blowing the “hot” ceiling air down to the “cool” floor is not a concern. (If the air is trapped in an attic, your ceiling fan won’t move it down to you – it’s trapped.)
However, in winter you’re producing heat on the edges of the room via vents or radiators. The difference in temperature right next to the radiator versus the middle of the room is a lot greater than the difference between the ceiling and the floor in summer.
So, in winter, you want to mix the warm air coming from the radiators with the cooler air in the center. In summer, you don’t care about mixing the air because there aren’t any significant hot or cold spots, but you do want the air blowing over your skin.
(Actually, you might want to mix the air in summer if you’ve got air conditioning. So you can benefit from both the air-mixing and the breeze-on-skin effects.)
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