Such an apparatus is where the published correlations in the literature came from. Researchers performed those experiments decades ago. This is one of the most common heat exchanger calculations. Double pipes are rarely used in practice, mostly for illustration and example problems. The configuration is rarely the most cost-effective. In 40 years of climbing through all sorts of plants, I have seen no more than a half dozen, compared to countless E-shell, F-shell, G-shell, and H-shell ones. Flat plate HXs are far more common. Check out Chapter 11 of Lindon's text book. I had breakfast with him this morning. https://www.amazon.com/Lindon-C-Thomas/e/B001HOVPI4

Thanks Dr. Benton. Most text books calculate the overall heat transfer coefficient U for such types of HXs, but not Nu. My question is about Nu?.

Thanks Mr. Leader Boer. Your answer is excellent . That is why for shell and tube HEX, U is calculated not Nu.

Please check this related RG discussion:

https://www.researchgate.net/post/what_is_the_best_Nusselt_number_correlations_for_nanofluid_turbulent_flow