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The video mentions that transferring heat to the impeller is a challenge, but it wasn't clear to me how they overcame this. Is the space between the CPU and the impeller so small that heat can be transferred efficiently?

If that is the case, I wonder how cheaply these could be produced given the incredibly tight clearance.

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There's a whitepaper available here http://prod.sandia.gov/techlib/access-control.cgi/2010/10025...

Their data suggests that the air gap provides minimal resistance to the flow of heat. As for the clearance, they've stated that unusually high-precision manufacturing is not required for the two surfaces.

Re: clearance, while .001" clearance isn't something I'd want in a design particularly, modern machine tools are good enough that you get flatness and surface finish good enough to not have problems at .001" clearance basically free on any machined surface.

Yes it's a radiative/convective coupling in the thin air gap.

Although the thermal conductivity of an air gap is normally low - which is why you have double glazed windows - it gets complicated if the gap is much less than the free path in the air

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