Abstract
Solutions to thermally developing flow (Graetz Problem) in circular and non-circular ducts are examined. It is shown that the Nusselt number based upon the square root of the crosssectional flow area is a weak function of the shape of the geometry provided an appropriate aspect ratio is defined. It is also shown that there are two distinct bounds for the fully developed Nusselt number which depend upon the shape and symmetry of the geometry. A general model which is valid for many duct configurations is developed by combining a Leveque model for the thermal entrance region with the fully developed flow asymptote. The new model is simpler than other general models and provides equal or better accuracy. Finally, it is shown that the solution for the elliptic duct geometry may be used to accurately predict results for 8 singly-connected ducts with an accuracy of ±12 percent.
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