# Modeling heat build-up in air-cooled outrunners

I'm creating a thermal model for heat build-up in my outrunner motors. So far, I haven't found any online resources that discuss this. Here is the basic equations for forced convective transfer:

Q = h * A * delT, where Q is the heat transferred, A is the exposed area, delT is the temperature differential, and h is the heat transfer coefficient.

For forced air, h ranges from 1 to 1000, so it's easy to see why the devil is in this detail. A three-order of magnitude difference in cooling efficiency is huge, to put it mildly. Typical published values for forced convection are in the 10-100 range, but those seem ludicrously low for the amount of heat that a typical multirotor motor needs to shed.[*]

There are ways to calculate h from Reynolds and Prandtl relations, but without extensive modeling those are exceedingly hard to get in the turbulent flow regime around a spinning motor.

Although this particular application is a fixed-wing with a cowled motor, the basics still apply and only the airstream speed and volume changes.

Can anyone shed any insight?

[*] If you have a 100W motor that's 80% efficient, that's 20W of heat energy. To put things in perspective, it's like a 20W incandescent bulb, only much smaller. So if the heat weren't being dumped very quickly into the airstream, the motor would get excruciatingly hot. Ergo, we can conclude from all available evidence that the cooling coefficient is quite high.

• Ooh, I love this kind of stuff but fear it's too much complex physics (CFD and thermodynamics) for it to be well-answered here. IMO this might be better on Physics.SE, but I don't want to flag this. – ifconfig May 11 '20 at 17:09
• Eh, my masters was in heat transfer, so I'm good to take this on theoretically. ;) What the Physics.SE guys don't have experience with is the particularity of a drone's setup and outrunner motors. And, to be honest, I don't either. There are almost certainly some good rules of thumb which are broadly applicable to the generalized , and yet peculiar, case of a spinning heated element with forced airflow, but I don't know what they would be. (BTW, if you're into that kind of stuff, my thermo prof is one of the guys who found a closed-form N-S solution. I think at the time only 13 were known?) – Kenn Sebesta May 11 '20 at 17:36
• Huh! Well, it seems that you know what you're talking about here. I just don't know whether or not we have any more like you on the site yet. :) – ifconfig May 11 '20 at 17:42
• I'd also say you're probably better off in the Physics.SE. Maybe you have to set a bounty - if it is worth that much to you (but you sound like it is) - and if you have enough reputation. Maybe you can also post a link to your question here, so if there is someone here he/she might be able to help in some respects over there. – Bastian Springer May 11 '20 at 19:03
• That's good advice, although I would be very surprised if any of my friends or colleagues who are CFD peeps would have any intuition about this. Heat transfer is scalable, but specific. If you haven't done something similar, then your intuitions are off. Like, I can tell you all kinds of things about LN2, boiling, and evaporative heat transfer but I don't know anything at all about general orders of magnitude for outrunners. It really comes down to lots of flow interactions which you determine empirically or through complex modeling. My hope is to connect w/drone peeps who have done it. – Kenn Sebesta May 11 '20 at 23:04