Pressure Drop in Laminar Developing Flow in Noncircular Ducts: A Scaling and Modeling Approach

A detailed review and analysis of the hydrodynamic characteristics of laminar developing and fully developed flows in noncircular ducts is presented. New models are proposed, which simplify the prediction of the friction factor–Reynolds product $fRe$ for developing and fully developed flows in most noncircular duct geometries found in heat exchanger applications. By means of scaling analysis it is shown that complete problem may be easily analyzed by combining the asymptotic results for the short and long ducts. Through the introduction of a new characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The new model has an accuracy of ±10% or better for most common duct shapes when nominal aspect ratios are used, and ±3% or better when effective aspect ratios are used. Both singly and doubly connected ducts are considered.