A new model for predicting Nusselt numbers in the combined entrance region of non-circular ducts and channels is developed. This model predicts both local and average Nusselt numbers and is valid for both isothermal and isoflux boundary conditions. The model is developed using the asymptotic results for convection from a flat plate, thermally developing flows in non-circular ducts, and fully developed flow in non-circular ducts. Through the use of a novel characteristic length scale, the square root of cross-sectional area, the effect of duct shape on Nusselt number is minimized. Comparisons are made with several existing models for the circular tube and parallel plate channel and with numerical data for several non-circular ducts. Agreement between the proposed model and numerical data is within $±15percent$ or better for most duct shapes.

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