## 2 Continuous V-Rib Twisted Tapes  
The new continuous V-rib twisted tapes (CVRTs) tested in this study are shown in Figure 1a-e. Their design aims to improve heat transfer by combining continuous V-ribs with helical flow patterns, which would be an effective method that integrates geometric disruption and rotational momentum effects to enhance performance. This structure might enhance thermal performance through a synergistic interplay of turbulent flow disruption, augmented surface area, and secondary flow generation. The continuous V-rib twisted tapes were formed from 0.9 mm thick aluminum sheets because of their excellent thermal conductivity, lightweight properties, and ease of manufacturability. The sheets were cut into tapes that were 1500 mm long (\(y\)) and 60 mm wide (\(w\)). Each tape was placed between  
\begin{table}
\begin{tabular}{c c c c} \hline
**Researchers** & **Type** & **Results** & **Model or Image** \\ \hline [PERSON] et al. [17] & Solid and perforated twisted tapes with different numbers of blades. & The friction factor is reduced by 22.3\%, while the thermal performance coefficient increases by 18.1\%, compared to a TT. \\ \hline [PERSON] et al. [18] & Off-center placed twisted tape & The twisted tape placed against the wall had 3–18\% higher heat transfer than that of a tape located at the center of a tube. \\ \hline [PERSON] et al. [19] & Counter/Co-swirling flow arranged twisted tapes & The dual-counter-swirl twisted tapes with a twist ratio of 2.5 had the highest thermal performance factor, 1.39. \\ \hline [PERSON] and [PERSON] [20] & Configurations of twisted tape inside the square duct & Doubled tapes placed at the corners with counter arrangement give the highest thermal performance index, 1.38. \\ \hline [PERSON] et al. [21] & Double/triple/quadruple twisted tapes & At high Reynolds numbers and with multiple twisted tapes, the thermal performance of the system is optimal, and entropy generation is minimal. \\ \hline [PERSON] et al. [22] & Solid and perforated twisted tapes & The best performance evaluation criterion was 1.92. \\ \hline \end{tabular}
\end{table}
Table 1: \(Cont.\)two meshed gear rollers, which imprinted ribs onto the plate's surface in a rolling process. The rib attack angle is determined by the gear rollers' helix angle. This attack angle might play a critical role in influencing the fluid and heat transfer mechanisms of the testing structure. Specifically, ribs with a fixed attack angle are first rolled on one side of the tape, and the centerline is used as a reference to assure symmetry and uniformity. The tape was then flipped, and the rolling process was repeated on the opposite side, resulting in a continuous V-rib pattern that spanned both surfaces. This continuous V-rib shape not only increased the surface area but also created a more complex flow path for the working fluid, thereby enhancing turbulence and heat transfer. After the ribs were formed on the tape, the tape was transferred to a twisting machine for further processing. One end of the tape was fixed, while the other was attached to a rotating clamp. By rotating the clamp, the tape was twisted along its axis with a twist ratio of 4.0. Three CVRTs were fabricated with varying attack angles (\(\beta\)) at \(15^{\circ},30^{\circ}\), and \(45^{\circ}\) while maintaining consistent rib extrusion depth and edge distance, which would avoid introducing additional variables that could complicate the interpretation of results.  
Figure 1: Geometric features of continuous V-rib twisted tapes (CVRT). (**a**) Typical twisted tape (twist ratio, \(y/w\) = 4.0). (**b**) V-shaped ribbed tape. (**c**) Model of typical twisted tape and continuous V-rib twisted tapes. (**d**) Image of typical twisted tape and continuous V-rib twisted tapes. (**e**) Tape arrangements of continuous V-rib twisted tapes.