Axial heat conduction effects in the thermal entrance region for flows in concentric annular ducts: Correlations for the local bulk-temperature and the Nusselt number at the outer wall

Streamwise heat conduction in the flow can affect the heat transfer in ducts. This is mainly relevant for flows with small Prandtl numbers or in micro-channels. In both situations the Péclet number is small, so axial heat conduction in the fluid cannot be neglected. In literature analytical solutions of this so called extended Graetz problem are well documented. In the present paper correlations are developed for the local bulk-temperature and the local Nusselt number at the outer wall in the thermal entrance region of concentric annular ducts. Correlations are given for laminar and turbulent fully-developed flow and different thermal boundary conditions. The correlations also consider the effect of different ratios of the inner radius to the outer radius of the annular ducts.