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:
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)
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?