Axial heat conduction effects in the entrance region of laminar duct flows: Correlations for the local Nusselt number

Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is low (liquid metals) or if the hydraulic diameter of the channel is very small (micro-channels). Exact analytical solutions for the extended Graetz problem for such situations are well known and documented in literature. In the present paper suitable correlations are developed for the local Nusselt number in the thermal entrance region in a parallel plate channel and in a pipe. Correlations are given for different thermal boundary conditions and for axial positions before (x < 0) and after (x > 0) the jump in wall temperature or wall heat flux.