Table 5 Selected conventional heat transfer correlations from the literature

Stephan correlation [73]

\( \mathrm{Nu}=4.364+\frac{0.086{\left(\mathrm{Re} \Pr \frac{\mathrm{D}}{\mathrm{L}}\right)}^{1.33}}{1+0.1 \Pr {\left(\mathrm{Re}\frac{\mathrm{D}}{\mathrm{L}}\right)}^{0.83}} \)

Laminar flow in a circular pipe

Re < 2300

Gnielinski correlation [73]

\( \mathrm{Nu}=\frac{\left(\mathrm{f}/8\right)\left(\mathrm{Re}-1000\right) \Pr }{1+12.7\sqrt{\frac{\mathrm{f}}{8}}\left(\mathrm{P}{\mathrm{r}}^{\frac{2}{3}}-1\right)} \)

where \( f=\frac{1}{{\left(1.82 \log \left(\mathrm{Re}\right)-1.64\right)}^2} \)

Constant wall heat flux

Fully developed turbulent and transition flow

3000 < Re < 5 × 10⁴

Modified Gnielinski correlation [74]

\( \mathrm{Nu}=\frac{\left(\mathrm{f}/8\right)\left(\mathrm{Re}-1000\right) \Pr }{1+12.7\sqrt{\frac{\mathrm{f}}{8}}\left(\mathrm{P}{\mathrm{r}}^{\frac{2}{3}}-1\right)} \)

where f = 3.03 × 10^− 12 ⋅ Re³ − 3.67 × 10^− 8 ⋅ Re² + 1.46 × 10^− 4 ⋅ Re − 0.151

Constant wall heat flux

Transition flow in straight circular pipe

2300 < Re < 4500