Why are radiators always placed under windows?
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.
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.
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