Vortex generators (VGs) are utilized in heating and cooling systems to enhance heat transfer efficiency for energy savings. This study investigates the thermo-hydraulic performance of using the rectangular vortex generators (RVG) and the sinusoidal vortex generator (SVG) with and without holes on the annular side of a double-pipe heat exchanger (DPHE) for turbulent regimes. The numerical analysis is conducted for different angles of attack (α) (15°, 45°, and 75°) and spacings between VGs (60, 100, and 300 mm). By comparing the heat transfer behavior for a given α, the RVG cases present a higher heat transfer when compared to the SVG cases, with an exception for the 15° case. The configuration with a low α and slight curvature augments flow velocities and vortex strength, thereby enhancing heat transfer efficiency. Moreover, the 15° SVGs-hole case demonstrates a higher Nusselt number compared to the no-hole case. Adding holes in the VG significantly reduces the pressure drop for the 45° and 75° cases, while it remains the same at the 15° case. Additionally, the 75° RVG case yields the highest Nusselt number among the studied cases, with an enhancement of 42.4% when compared to the smooth pipe at the Reynolds number of 5,711. The best performance evaluation criterion (PEC) is achieved by the 15° SVGs-hole case. When the effect of different spacings is examined, the spacing of 60 mm provides the highest PEC of 1.22. In short, the present study provides valuable insights for optimizing VG design and enhancing overall system performance in DPHEs.