Table 3 Correlations of the Nu and f for double twisted and smooth tubes.

Vicente et al.²³

\(\begin{gathered} N{u_o}{\text{=}}=0.403{(Re - 1500)^{0.74}}P{r_o}{\,^{{\text{0.44}}}}{{\text{(}}H/{D_{hy,o}}{\text{)}}^{{\text{0.53}}}}{{\text{(}}S/{D_{hy,o}}{\text{)}}^{{\text{-0.29}}}} \hfill \\ {f_o}{\text{=}}=1.47*R{e^{ - 0.16}}{{\text{(}}H/{D_{hy,o}}{\text{)}}^{{\text{0.91}}}}{{\text{(}}S/{D_{hy,o}}{\text{)}}^{{\text{-0.54}}}} \hfill \\ \end{gathered}\)

= 2000 ≤ Re ≤ 90,000 and = 2.5 ≤ Pr ≤ 100

Bhadouriya et al.²⁴

\(\begin{gathered} \frac{{N{u_{twisted}}}}{{N{u_{straight}}}}{\text{2.12}}R{e_o}^{{\text{0.06}}}\,Pr_{o}^{{0.6}}\,{{\text{(}}\frac{{4D_{{hy,o}}^{2}}}{{\pi d_{i}^{2}}}{\text{)}}^{{\text{0.05}}}}{{\text{(}}S/{D_{hy,o}}{\text{)}}^{{\text{0.08}}}} \hfill \\ \frac{{{f_{twisted}}}}{{{f_{straight}}}}{\text{5.8}}R{e_o}^{{{\text{-0.06}}}}{{\text{(}}\frac{{4D_{{hy,o}}^{2}}}{{\pi d_{i}^{2}}}{\text{)}}^{{\text{-0.2}}}}{{\text{(}}S/{D_{hy,o}}{\text{)}}^{{\text{-0.6}}}} \hfill \\ \end{gathered}\)

3000 ≤ Re ≤ 100,000;

10.6 ≤ \(S/{D_{hy,o}}\) ≤ 15; 0.19 ≤ \(\frac{{4D_{{hy,o}}^{2}}}{{\pi d_{i}^{2}}}\) ≤ 0.51

Gnielinski³²

\(\begin{gathered} N{u_o}{\text{=}}\frac{{(f/8)\left( {Re - 1000} \right)Pr}}{{1+12.7\sqrt {f/8} \left( {P{r^{2/3}} - 1} \right)}} \hfill \\ {f_o}={\left( {1.82\log R{e_o} - 1.64} \right)^{ - 2}} \hfill \\ \end{gathered}\)

3000 ≤ Re ≤ 5 × 10⁶