## 1 Introduction
[PERSON] and [PERSON] [20] conducted a numerical analysis using a large eddy simulation to investigate the impact of different impingement heights on the local HT of a slot jet-cooled channel at REs of 4000, 8000, and 12000. They concluded that the Nusselt number (Nu) increased with the increase in the Reynolds number (Re) and that, at a constant Re, the Nu increased with decreasing distance between the slot jet and the target plate. However, they noted that variations in Re had a more pronounced effect on the Nu than changes in the jet-to-target distance. [PERSON] and [PERSON] [21] investigated eleven distinct characteristics over three levels each to determine the ideal conditions for multi-jet impingement applications. The Nu served as the performance measure, and an L\({}_{27}\)(3\({}^{11}\)) orthogonal array was chosen as the experimental design. Optimal results were obtained when the Nu was computed using the nozzle diameter under the following specified conditions: a pipe diameter of 40 mm, air velocity of 9 m/s, vertical spacing between fins of 20 mm, heat flux of 400 W, fin width of 15 mm, fin angle of 30\({}^{\circ}\), horizontal spacing between slices of 15 mm, heat receiver angle of 10\({}^{\circ}\), horizontal spacing between fins of 20 mm, and a nozzle-to-heat receiver distance ratio (h/d) of eight. A comparison of the finned, optimum heat receiver versus a flat surface under ideal circumstances showed a 28.61% enhancement in heat transmission using the finned heat receiver. [PERSON] et al. [22] used computational and experimental techniques to examine the HT and flow characteristics of a heat sink with optimized rectangular fins subjected to a single impingement jet using the Taguchi experimental L\({}_{\text{IS}}\)(2\({}^{1}\)* 3\({}^{7}\)) design approach. The heat sink, designed for jet impingement cooling, was evaluated at six jet velocities (4, 5, 6, 7, 8, and 9 m/s), four nozzle diameters (D = 40, 50, 63, and 75 mm), and three nozzle-to-target distances (h/d = 1, 2, and 3). Alterations in the mean target surface temperature were assessed, and fluctuations in Nus and Res were calculated. The findings were numerically simulated with ANSYS Fluent 19 software. Experimental and numerical findings were compared using Nu-Re diagrams, demonstrating that the average Nu increased proportionately with Re. The Nu decreased as the distance between the nozzle and the heat receiver grew. The agreement between the experimental and numerical findings was validated. [PERSON] et al. [23] conducted a numerical analysis of the HT and flow characteristics of hexagonal finned heat sinks optimized by the Taguchi experimental L\({}_{\text{IS}}\)(2\({}^{1}\)* 3\({}^{7}\)) design technique for channel flow. The ANSYS Fluent Icepak module was used for computational fluid dynamics research on two optimized heat sinks, including three distinct fin heights and five varying flow velocities. For all fin heights, the Nusselt number rose with the Reynolds number for the OH-1 and OH-2 heat sinks. Furthermore, the findings indicated a reduction in the friction factor with an increase in the Reynolds number for all fin heights. CFD data were used to derive changes in Nu-Re and f-Re, which were then compared to the experimental findings. It was concluded that the numerical and experimental findings were congruent. [PERSON] et al. [24; 25] compared the HT characteristics of standard and inclined jet arrays. Their findings indicated that inclined jet designs exhibited superior HT performance compared to standard jet configurations. However, strong crossflow in the downstream jet regions significantly reduced HT. [PERSON] et al. [26] conducted a theoretical study to evaluate jet inclination angles. Their study, aimed at optimizing the placement of inclined impingement jets, found that an injection hole angle of approximately 60\({}^{\circ}\) on a concave surface achieved the highest cooling efficiency.