The heated part should be on the outside of the hair strand, or else it will just heat the outside returns.
I think it could work either way, but that this way might be slightly more efficient, but of course I’m no engineer so I can’t say for sure. But here’s my reasoning.
the coolant goes faster outwards, under higher pressure in a smaller tube with lower drag coefficient, the volume of the back-flow tube is larger so it cools the liquid in 2 ways, by reduced pressure, and by radiating through highly conductive thin walls (the inner walls are much thicker for this reason, and made of isolating materials). Since the journey back takes longer too, it should lose more heat due to that as well.
You have drawn the principle of a heat recycling system from a modern boiler chimney. The cold ambient air that returns to the burners is heated by the expelled combustion gases.
I also think that you should imagine the opposite.
And the hair cuticles would indeed play their full role.
Apparently overheating is good sometimes …
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