## 1 Introduction  
Vortex generators (VGs) have received extensive attention by researchers [1; 2; 3; 4; 5] as devices for obtaining high thermal performance by enhancing the heat-transfer coefficients of a tube heat exchanger. VGs are also regarded as potential heat-transfer augmentation devices because they create vortices that lead to high heat-transfer rates [5]. VGs are used to induce secondary flow, which disturbs or cuts off the thermal boundary layer developed along the wall and removes heat from the wall to the core of the flow by means of large-scale turbulence [6]. VGs that form longitudinal vortices are extremely attractive because they experience only a small pressure drop penalty. These longitudinal vortices can be generated by using wing or winglet type VGs, which create flow separation at the leading edge of the wing [7]. Generally, wing/winglet type VGs function like a fin and are fabricated by punching out or mounting onto a strip/base fin. Considerable improvements in convective heat transfer using the wing/winglet VGs have been demonstrated [8; 9; 10; 11; 12; 13; 14; 15]. An experimental and numerical study on a rectangular channel fitted with a delta-winglet vortex generator was conducted by [PERSON] and [PERSON] [8]. The attack angles were varied (15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\)) to obtain an optimum heat-transfer profile for the channel. A large attack angle was found to exhibit a high heat-transfer rate, which was due to a disruption of the air flow in the lower channel by the transverse flow through the punched holes. [PERSON] et al. [9] also conducted a numerical study on heat-transfer augmentation by investigating the mechanism of the flow structure. Variation in the attack angle, row number, and placement of rectangular winglet pairs was discussed in detail. They found that by altering the position of the winglet, pressure drop could be reduced without decreasing heat transfer. The effect of variations in the profile of rectangular winglets (i.e., wavy-up and wavy-down) on the heat-transfer performance of a fin-and-tube heat exchanger was numerically investigated and compared with that of a conventional rectangular channel without a winglet by [PERSON] et al. [10]. The wavy-up and wavy-down rectangular winglets were found to exhibit better heat-transfer performance. Moreover, the effect of the wavy-up configuration was more significant than the wavy-down configuration. [PERSON] et al. [11] experimentally studied the influence of various delta-winglet arrangements (one side cut with one delta-winglet, one side cut with two delta winglets, two sides cut with two delta winglets, and two sides cut with four delta winglets) on the heat-transfer augmentation of a tube and compared that to the performance of a plain tube. The results showed that a tube with delta winglets had better thermal performance than a plain tube, and that the arrangements of two sides cut with four delta winglets outperformed all other arrangements. A combined winglet pair (a rectangular wing and a trapezoidal wing) proposed as a novel longitudinal VG was numerically investigated by [PERSON] et al. [12]. Compared with a rectangular winglet pair, the combined winglet pair showed considerable improvement in heat transfer with a moderate pressure drop penalty. [PERSON] and [PERSON] [13] numerically studied the optimization parameters (shape and attack angle) of a winglet VG. They showed that at low Reynolds number, attack angle modification did not significantly improve performance; in contrast, for a high Reynolds number, variation in the attack angle considerably influenced performance because the angle could increase drag. Moreover, among the different VG shapes (traditional vortex generator, delta vortex generator, rectangular vortex generator, and trapezoidal vortex generator), the rectangular vortex generator was found to provide the best heat-transfer performance because it had a large facing flow area.