I'm trying to find a noncircular cylinder where the average Nusselt number is linearly proportional to the Reynolds number. So far, I've found an empirical correlation due to Hilpert where a hexagon shape gives a relation Nu ~ Re^0.782 and this is the closest I've come so far.

Anyone who has an idea what shape I can use? Or where to look for information?

Cheers / Anders

there is an other posibility: try to vary the radius of a circular pipe ( or what ever non circular pipe) in such a way that you get a lineary change of Nu against Re. that should be a parabolic shaped pipe or something like this. The Re would definetly not be constant. Might keep me in touch!

best regards

Jiannis Dotsikas.