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Let's assume we have a cold empty room (with no person in it, therefore - barely little air movement) and we want to heat it up.

In the room, we have a hot-air blower that has two fan speed-settings, but has the same number of active heating elements, no matter which speed setting has it set.

Therefore, when the fan is blowing slower (1st speed setting) the air output of is significantly hotter compared to the faster speed (2nd speed setting) where the air is slightly colder, due to the fact that the air doesn't have enough time to grab the heat from the heating-elements.

The question is: in which situation does the room heat faster? In the 1st speed setting (slow speed, hot air) or 2nd speed setting (faster speed, warm air) ? And why?

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I'd choose the higher fan speed. The movement of the air due to the fan also heats the room (even if there were no heating elements) because air has nonzero viscosity. The heat due to the heating elements is the same in both cases, so this extra contribution gives you the overall advantage.

Note however that the temperature gradient in the room will be quite different in the two cases! The volume near the fan will be hotter if you choose a lower fan speed while a higher fan speed spreads the heat better over a larger volume.

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  • $\begingroup$ Regarding no heating elements, I would think that the movement of unheated air would have a minuscule effect on the room air temperature. The heat contribution due to friction of the moving parts of the fan would be much more significant, and you could argue that the higher fan speed would involve greater friction heating. $\endgroup$
    – Bob D
    Commented Mar 7, 2019 at 13:24
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The same amount of heat will be delivered to the room, but I think the high speed might result in a better temperature distribution throughout the room than the low speed.

Hope this helps.

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