Laminar Convection in Circular Tubes With Developing Flow

摘要

The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number Z_H ≥ 10~(-6) and for a wide range of Prandtl numbers 0.1 ≤ Pr ≤ 500. For the historical range of Z_H ≥ 5 × 10~(-4) and 0.7 ≤ Pr ≤ 50, earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr ≥ 0.5. In contrast, legacy correlations typically had a 10-20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5-10%.