**1. Introduction**

Modifying heat transfer is a principal matter of concern for energy conservation and also advantageous from an economic viewpoint. Since heat exchangers are commonly used in almost all areas of industrial activities, including fuel cells [1], electronic device cooling [2], solar air collectors [3], aerospace engineering [4], flame stabilization [5], refrigeration [6], electric vehicles [7], natural gas

liquefaction [8], air dehumidification [9] and so forth, increasing the thermal performance is of vital importance. To satisfy such a need, in the last two decades, researchers have proposed different passive techniques for heat transfer augmentation, including roughness elements [10], twisted tapes [11] and wires inserts [12]. Such equipment modifies heat transfer using a higher heat transfer surface, generating a swirl flow, as well as disturbing hydrodynamic and thermal boundary layers of the fluid inside the tube, which directly improves the heat transfer coefficient.

Among the proposed passive techniques in the literature, applying twisted tape inserts with different geometries in various systems, such as solar collectors [13,14] and solar water heating systems [15–17], has been the focus of attention among experts of the field. Due to large numbers of applications, embedding the twisted tape inserts in double-pipe heat exchangers has recently been studied by many researchers. Man et al. [18] experimentally investigated twisted tape inserts in an inner tube of a double pipe with clockwise and counterclockwise swirling directions. They showed that the heat exchanger thermal performance increases in the presence of twisted tape inserts, presenting a maximum value of 1.42 for the performance evaluation criterion (PEC) number. Lim et al. [19] performed a pitch investigation of twisted tape inserts in a double pipe and reported heat transfer characteristics for different Reynolds number values. Another evaluation of thermal efficiency of a double pipe equipped with twisted tapes using the ε-NTU (Effectiveness—Number of transferred unit) method was performed by Ravi Kumar et al. [20]. They found higher values for both the effectiveness and NTU of the heat exchanger when the twisted tapes were applied. Employing nanofluids [21], hybrid nanofluids [22,23], nano-encapsulated phase change suspensions [24–26] and boiling heat transfer [27,28] are also other promising approaches to improve heat transfer.

Besides, many papers focused on the geometrical aspects of twisted tapes, such as the effects of pitch and width ratios. Jaramillo et al. [29] assessed a parabolic trough collector equipped with twisted tape. They showed that the thermal performance of the collector increased as the twisted ratio reduced at low Reynolds numbers. Mwesigye et al. [30] studied a parabolic trough collector with wall-detached twisted tape. They indicated that higher values of twist ratio and lower values of width resulted in the enhancement of the optimal Reynolds number. Esfe et al. [31] inserted the twisted tapes in a tri-lobbed tube for Reynolds numbers of 5000 to 20,000. Their results revealed that increasing the tape ratio, which is the tape radial length to pipe diameter ratio, enhances the Nusselt number, friction coefficient and overall thermal performance.

Another technique for a higher heat transfer rate using twisted tape is to increase the flow mixing and secondary flow effects by changing the geometry of the twisted tape surface. Saylroy and Eiamsa-ard [32] examined the thermohydraulic performance of a tube equipped with a square-cut twisted tape. These researchers found a maximum PEC value of 1.32 for their captured models in which the thermal performance improved 1.32 times in comparison with the classically twisted tape inserts. In another study [33], they evaluated a multi-channel twisted tape and showed laminar convection heat transfer with twisted tapes embedded in the channel. He et al. [34] examined the thermal behavior of cross hollow, twisted tape inserts in a pipe. They showed PEC values of 0.87–0.98 for Reynolds numbers of 5600–18,000. Samruaisin et al. [35] investigated numerically and experimentally the free space ratio and twisted tape arrangement for regularly spaced quadruple twisted tape inserts in a tube, in a turbulent flow regime. In the range of their operational conditions, they presented a maximum PEC number equal to 1.27. Centrally perforated twisted tape elements in a tube were investigated by Ruengpayungsak et al. [36] for convective heat transfer enhancement under laminar and turbulent flow regimes. Maximum PEC values of 8.92 and 1.33 were reported for laminar and turbulent regimes, respectively. Hasanpour et al. [37] optimized a corrugated tube heat exchanger equipped with twisted tape elements with the purpose of heat transfer modification and pressure drop reduction. They showed that the V-cut twisted tape model causes maximum heat transfer, and the perforated twisted tape model leads to the smallest pressure drop.

Despite using classical twisted tape elements with a gap between the tape and walls, the use of overlapped twisted tapes due to the lower pressure drop penalty was also studied by some researchers. Hong et al. [38] carried out an empirical study of a spiral-grooved tube equipped with twin overlapped twisted tapes in a turbulent regime with Reynolds numbers of 8000 to 22,000. They showed an enhancement in both heat transfer and friction coefficient augmented by the overlapped twisted ratio. In another study [39], they employed overlapped multiple twisted tapes in a similar experimental study. They showed that entropy generation increases and decreases due to friction resistance and heat transfer, respectively, as the tape number changes and overlapped twisted ratio decreases. Eiamsa-Ard and Samravysin [40] carried out an empirical study to investigate the thermal performance of a tube heat exchanger equipped with overlapped quadruple twisted tape inserts compared to typical quadruple twisted tape elements with a Reynolds number ranging from 5000 to 20,000, under a turbulent regime. They reported a maximum value of 1.58 for the PEC number in the case of overlapped quadruple counter tapes in a cross arrangement at a Reynolds number of 5000. Later, overlapped dual twisted tapes, along with Al2O<sup>3</sup> nanofluid, were studied by Rudrabhiramu et al. [41], with the objective of improving the thermal performance of a heat exchanger. They reported that using 1% nanofluid volume concentration and twisted tape with a twist ratio of two causes the best result.

Some researchers also benefited from compound techniques of heat transfer enhancement using nanofluid along with twisted tape inserts. Qi et al. [42] experimentally investigated the convective nanofluid heat transfer in a tube using rotating and static built-in twisted tape elements. They reported a 101.6% enhancement in heat transfer by using rotating twisted tape inserts along with the nanofluid. In another empirical study, Sunder et al. [43] examined the thermal performance of a solar water heater employing nanofluid and twisted tape inserts as the heat transfer enhancement techniques. They showed a 49.75% improvement using the best configuration of twisted tape.

The above literature review indicates that there are a substantial number of papers using twisted tape inserts in different ways and techniques to reach a model for heat transfer rate maximization and pressure drop minimization. However, reviewing the preceding papers reveals that the hydrothermal investigation of truncated twisted tapes in tubes has not been studied so far. Motivated by this research gap, this study examines the twisted tape truncation percentage and its position in the tube at different pitch values and Reynolds numbers. This paper provides guidelines for the novel usage of twisted tapes in tubes toward higher performance.
