When a window is open, there can be some heat loss through convection as warm air escapes and cooler air enters. However, the specific direction of the air movement will depend on several factors, including the temperature differentials, the location and size of the radiator, and the air circulation patterns within the room.
In general, hot air tends to rise because it is less dense than cold air. So if the radiator is located below the window, the warm air it produces will indeed have a natural tendency to rise. However, the air movement near the window will also be influenced by other factors, such as the pressure differences caused by wind and the indoor-outdoor temperature differentials.
When a window is open, the air circulation near the window can be complex. The movement of air depends on factors like the temperature difference between the inside and outside, the wind direction and speed, and the layout of the room. If the room is well-insulated and the temperature difference between the indoor and outdoor environments is significant, the warm air near the radiator may tend to rise and escape through the window, while cooler air from outside enters through the lower part of the window.
On the other hand, if the temperature difference is small or the room is not well-insulated, the convective heat loss through the window may not be significant compared to other modes of heat transfer, such as conduction through the walls and windows themselves.
It's worth noting that the primary purpose of radiators is to heat the room by radiating heat into the space, rather than relying solely on convective heat transfer. Radiators release radiant heat directly into the room, which warms objects and surfaces. This radiant heat can also contribute to warming the air in the room, irrespective of the window being open or closed.
In summary, if a window is open, some heat may escape through convection, but the exact air movement and heat loss will depend on various factors, including temperature differentials, insulation, and air circulation patterns.