New Nusselt number correlations for developing and fully developed laminar flows in concentric circular annular ducts

Concentric circular annular ducts are common and important elements in fluid flow and heat transfer equipment, including chemical mixing devices and heat exchangers. There are many problems involving heat transfer in concentric annuli which require accurate heat transfer coefficients for laminar and turbulent flows. This study proposes new correlations for the local and average Nusselt numbers in hydrodynamically fully developed and thermally developing or fully developed regions of laminar flows. The correlations are developed based on the results of available series solutions for four fundamental boundary conditions. The correlations use exponential and power law functions of dimensionless axial and radial lengths; they are more accurate, easier to use, more similar to fundamental analytical solutions, and require fewer terms. The maximum and average differences between the local Nusselt numbers predicted by the proposed correlations and the analytical data are respectively 2.04% and 0.38% for fully developed flows and 9.97% and 1.35% for developing flows. Moreover, the maximum and average differences for average Nusselt numbers are 4.59% and 2.01%, respectively. The results show that the proposed correlations are more practical and they can predict the developing, fully developed, and average Nusselt numbers with very good accuracy across a wider range of flow conditions.