Hot air from a radiator doesn’t actually mix that well with the rest of the cooler air in a room.
When I give my kids a bath, I fill the tub with very hot water first (cast iron tub soaks up a lot of the heat, so we have to warm up the tub itself as well as the water). After some point we add cold water.
But adding cold water doesn’t actually make the bath water an even, cooler temp. So I have to stir the water continuously so there are no pockets of hot water.
Same for air. If there is no air movement in a room, the hot side will stay hot and the cold side will stay cold. But cold air forms a draft of cool air current because cold air wants to drop to the floor. (Cold air is denser than warm air). The movement of cold air falling to the ground creates an air current that can stir the room air.
So air moving over the radiator helps to move all of the air around the room, instead of having hot spots and cold spots.
I’ve tested this myself with electric oil radiators that we used to put on the far wall away from the window; and later learned to move it under a window or in front of a cracked interior door.
Think about what insulating is doing, keeping the warm air from going outside because that’s how you lose heat, it goes outside. It can only possibly go outside by going through an exterior wall. Therefore, heat is only required on exterior walls where the heat is escaping, only to replace the heat lost. Placing it by the worst spots, windows, gets you the most even heat distribution, the heat is only counteracting the loss, and the rest of the building stays a constant temperature because the interior isn’t losing heat to the cold exterior.
Also, this is NOT true for AC, AC counteracts the hot air outside, the hot air from all the electronics, lights, stoves, etc, and it counteracts body heat. Therefore AC needs to be distributed throughout the building, and really big buildings need so much AC that many don’t need heat even when it’s very very cold outside because their internal heat from running stuff is more than they lose through exterior walls.
I actually know the answer to this! It dates back to the 1918 influenza pandemic. Folks were told that they needed to keep their windows open to ventilate their houses. So they started putting radiators under the windows because back then you couldn’t really regulate the temperatures and that way it would still be warm but they could have the windows open as well in sick rooms. I went to an architectural Museum that explains this! So cool that I get to use this random crazy bit of knowledge.
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