Heat transfer correlation for circular and non-circular ducts in the transition regime

Abstract

A new model to predict the Nusselt number in the entry region of smooth non-circular ducts and channels is developed, for both uniform heat flux and uniform wall temperature boundary conditions. The model, valid for the laminar, transition, turbulent and fully turbulent regimes, is developed using the asymptotic results for both laminar and turbulent flow in circular and non-circular ducts. The proposed model is valid for fluids with Prandtl numbers between 0.7 and 78, Reynolds numbers in the range of 890 to 248,800, and a ratio of the length of the duct to the square root of the cross-section area in the range of 0.001 to 0.03. Comparisons are made with several existing databases for circular and non-circular ducts, showing that the proposed correlation has an overall root mean square error equal to 10.0%, which is smaller than the other literature correlations. This correlation is shown to provide good predictions against the entire database, for both boundary conditions. One of the major accomplishments of this work is the versatility of the proposed equation, where for calculating the Nusselt number on circular and most common noncircular ducts a unique equation is necessary.