All else held equal, I think so, yeah. If you have the same temperature differential, the same manner of heat dissipation, and a smaller surface area then that should mean smaller heat dissipation, yeah?

Obviously if you go from eg. a large air-cooled motor to a smaller water-cooled motor, then the smaller motor could potentially dissipate more heat, but that's a different scenario.

▲

roelschroeven 2 days ago | parent [-]

We only know that the large and the small motor deliver the same power. I don't see how we can conclude from that the temperature differential is also equal. In fact I would expect a smaller motor to have a larger temperature differential, because the heat is produced concentrated in a smaller volume.

▲

taneq 2 days ago | parent [-]

Yep, you're getting it. Same power, same efficiency, same power dissipation, smaller motor, smaller dissipative area, higher temperature.

The other assumption I probably should have stated is that the two motors are made of similar materials with similar temperature limits. We know the ambient temperature and we know the maximum temperature of the materials used. So for a component made of those materials, existing in that ambient temperature, with an additional heat load proportional to the waste heat in the motor...

The ability to shed heat (assuming similar forced fan cooling, as we were) determines the amount of power we can deliver to the device without increasing its temperature.

	▲	roelschroeven 2 days ago \| parent [-]
		So, ok, under a whole bunch of stated and unstated unproven assumptions, a smaller motor of the same power delivery as a larger motor is more efficient. There's no relation to reality here. I don't even know why I thought the idea in your comment that started this thread was worth pursuing.