Abstract

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 $ZH≥10−6$ and for a wide range of Prandtl numbers $0.1≤Pr≤500$. For the historical range of $ZH≥5×10−4$ 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%.

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