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I am trying to model laminar, forced convection heat exchange for water in a round pipe and rectangular duct. In both cases, a portion of tube / duct is maintained at a constant surface temperature while the rest of the tube / duct is insulated. I have two questions:

  1. Is there a reference that gives the Nusselt number for fully-developed, laminar flow in a round tube when a portion of the tube is insulated? (What I'm looking for would be similar to the results presented here: http://www.dtic.mil/dtic/tr/fulltext/u2/736260.pdf in Table 14 pg. 151, but for round pipes instead of rectangular ducts)

  2. Is there a reference that gives the Nusselt number for either Graetz flow, or simultaneously-developing flow in a tube / duct when one or more of the sides are insulated?

Thanks.

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What is the need in this case of obtaining the Nusselt number? Before the advent of powerful computers able to solve numerical solutions to the problem you describe, these adimensional numbers were used to help in obtaining analytical solutions to such problems. That's why the paper you cite was published more than 45 years ago. Now, these adimensional numbers are used to simplify problems by scaling analysis so you can quickly get an order of magnitude estimate of the solution. In your case, with the problem highly specified (shape of duct, only a portion of it insulated), to avoid being anachronistic, wouldn't it be better to just solve your problem using a package like Comsol?

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