Why are radiators always placed under windows? I don't know if anyone else has noticed this but in most buildings and most rooms, radiators are predominantly placed under a window. 
Now, in my eyes, that is the worst place to put them; hot air rises, reaches the window (which no matter how well insulated it's still letting out heat, in loose terms) and the thermal energy of the air disperses around the window area, thus not doing much to warm up the room. 
Am I wrong to think this? I mean, I can hold my hand close to my window and feel that it is colder there than at the other end of my room, but then again, my room does warm up when the radiator is on.
 A: The reason is because the heat loss occurs mostly in the windows and the fenestration. The idea is that you would like the incoming air to be heated up. Also, it creates an air curtain that prevents more heat from being lost through these exposed areas. Finally, it makes the temperature of the room more or less uniform. If the heaters were placed at the center of the room, you would create a large temperature gradient, resulting in drafts and discomfort for the occupant.
A: As Programmer mentions, by putting the radiator in front of the area most prone to heat loss and ingress of cold air, you are effectively screening off the room from cold air.  However, there is also the fact that radiators are often quite a bit hotter than other heat sources such as forced air.  Therefore it makes sense to put it in the coldest part of the room, not only due to efficiency reasons, but due to the fact that if it gets too hot you can easily open the window and let out some of the excess heat.
A: Since this is a physics forum I assume the OP is interested in a quantitative answer in terms of the efficiency of the system and how it differs based on the relative positioning of heat sources and heat sinks.  The math required to analyzed such a system is too much for me to manage right now, but I believe the following principles apply and are objectively correct:


*

*The dissipation of heat through the glass will increase in proportion to the difference of the indoor and outdoor temperatures; the larger the gap, the faster the loss of energy to the room.

*The dissipation of heat within the room follows the inverse square law (subject to perturbations such as drafts, etc.) in proportion to distance from the heat source.
To optimize the room for minimum heat loss, move the heat sources away from the windows.
To optimize the room for maximum heat uniformity, move the heat sources near the windows.
A: Partly practical, the wall under the windows isn't useful for anything else.
We had a house where the heaters were placed in the middle of the only empty walls, so nowhere you could put furniture, bookcases, etc.
Before double glazing there would be a draft from the windows so the idea was to heat this incoming air by having a radiator immediately below the window 
A: As the hot air goes up and the cold air goes down, the radiator is located where there is a better circulation, i.e. even though the window is double glazed, there will always be cold air entering the division by the material itself. So the cold will push the hot air inside the room.
Another explanation can be the fact that external walls can have thermal bridges and cold air can enter the room and cause heat loss. By placing the radiator on the exterior wall, the thermal bridge will still exist, but the effect of cold air entering the room, will be compensated by the heater (in environmental terms, it isn't good at all to have thermal bridges in buildings, but it is cheaper to build). Today, we can see radiators and heaters either underneath the windows or close to the maximum number of doors, as the temperature in the rooms vary and helps air circulation.
A: Reason is quite simple. If you have a window without radiator and outside is really cold, the window glass would be cold as well. This will lower temperature of the air around the window and this air will flow immediately down (physics).
So if someone want well heated room with very cold floor .. do it, put radiator to opposite side. 
That's why it is wise to put radiator under the window. ... to heat up the cold air, which is flowing from the window area. 
A: *

*Because under window is the place where delta-T (the Change in
Temperature) is largest in the whole room.

*The larger is delta-T, more efficient the system is.

*Window even when closed is still a coldest place, because it is a
thinnest wall.

*Cold air flows downwards, thus under window.
What is an efficiency of a radiator depends on whether your goal is to heat the room or cool some device. It is another question anyway.
A: As described in the other answers, putting the radiators (or hot air vents in a forced-air system) under the windows offsets the greater heat loss of the windows, but there is another reason. As room air flows over the surface of a window, it will lose heat to the window (and the outside). This can cause moisture in the air to condense out onto the window. In cold enough conditions, the window will accumulate frost or even layers of ice on the inside surface. The hot air rising off a radiator will have less tendency to deposit moisture onto the window (the glass surface will be somewhat warmer).
A: My guess would be it's there to prevent the cooling air from accumulating below the window and flowing into the rest of the room.
Anything goes to avoid cold feet ;)
A: A number of reason:
 - the wall under the window is basically useless
 - placing the heater under the window allows you have a more even temperature throughout the room: the window is the coldest place in the room, if you were to place a heater on the other side of the room and wanted to reach a certain temperature by the window, the other part of the room would have to be much hotter
A: As the hot air goes up and the cold air goes down, the radiator is located where there is a better circulation, ie, even though the window is double glazed, there will always be cold air entering the division by the material itself. So the cold will push the hot air inside the room. Another explanation can be the fact that external walls can have thermal bridges and cold air can enter the room and cause heat loss. By placing the radiator on the exterior wall, the thermal bridge will still exist, but the effect of cold air entering the room, will be compensated by the heater (in environmental terms, it isn't good at all to have thermal bridges in buildings, but it is cheaper to build). Today, we can see radiators and heaters either underneath the windows or close to the maximum number of doors, as the temperature in the rooms vary and helps air circulation. 
A: Its because the hot air that is created by the radiator heats the colder window making the glass warmer... therefore the glass is a lot less likely to condensate and at the same time keeps the room a lot warmer because the heat will radiate out wards away from the window along with any drafts or such ... also if the radiator is placed on a wall without a window the room gets a lot hotter a lot more quickly than liked... and a sudden rise in temperature unsettles the human body.
