I don't think that any definition of the length scale (or hydraulic diameter) will be universally appliccable for finned tubes. If you limit the discussion to finned circular tubes, changes in the fin shape (e.g. solid vs. serrated fins) will cause different heat transfer/pressure drop behavior, even for the same length scale. Also, factors like fin height and fin pitch will (?) impact the heat transfer/pressure drop differently,  a length scale based solely on surface area and free flow areas will not capture this. Furthermore, the relative size of the downstream recirculation zone having poor heat transfer will differ for the different fin geometries, which can (in my view) not be accounted for by any generalized length scale. (I checked possible length scales including different hydraulic diameter definitions, against a limited set of experimental data some years ago, and found that using the fin diameter collected the data best. I have, however, no reason to believe that this is more universal than any other length-scale definition)

As for the velocity: The choice of the maximum gap velocity is arbitrary, but convenient. However, as a consequence of this choice, additional corrections, such as the tube pitch-to-diameter ratio is  required to compensate for the integral change/behavior in velocity around the tube. Alternative definitions velocity definitions could be the upstream (frontal) velocity, an average velocity etc, but they would be equally arbitrary.

Mr. Erling,

thanks for your comment. We can limit discusson for two types of finned circular tubes: solid and seratted. I agree with everthing you said.

Which fin diameter your propose? Average? Which for seratted geometry.

Again, comparision with different literature is in question.

Regards

I used 'Fin diameter'='Base tube O.D.'+2*'Fin height'. When comparing to large databases, there is no length scale that singles out as being more universal than others. However for selected datasets (made by the same research groups) the potential scatter due to experimental errors is less, my comparison showed that using the fin diameter collected the data better than using ither length scales (such as hydraulic diameters). However, this comparison was not conclusive; the spread in the data for some sources was still significant.

Mr. Erling,

I read your article HEAT TRANSFER IN SERRATED-FIN TUBE BUNDLES WITH STAGGERED TUBE LAYOUTS. The article is excellent and I will cite it in my doctoral thesis.

The subject of interest in my thesis is version of serrated fins and variation of geometry to obtain optimal solution. Base variant for comparing is solid fin. I plan to make CFD and experimental work and compare it.  Of course, it must be compared with other research ...(I obtain some results for steel and Cu, difference is great).

I thinking how to connect geometry of ribs with Re. Maybe there are better solution than use fin outer diameter as lenght scale for both: solid and serrated fins. And maybe this is a good solution?

Have you additional proposals?