## 2 Materials and Methods  
### Experimental Parameters and Planning  
On the basis of this study, controllable parameters were chosen due to the influence they might have on the HT characteristics. All the parameters were chosen to be at 3 levels, and accordingly, the L\({}_{27}\)(3\({}^{11}\)) orthogonal series shown in Table 1 was chosen as the experimental plan [21]. \begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \multicolumn{6}{l}{**EXPERIMENTS**} \\ \hline  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** & **I** & **J** & **K** \\ \hline
1 & 25 mm & 6 & 5 m/s & 10\({}^{\circ}\) & 15\({}^{\circ}\) & 2222 W/m\({}^{2}\) & 15 mm & 10 mm & 10 mm & 10 mm & 10 mm \\
2 & 25 mm & 6 & 5 m/s & 10\({}^{\circ}\) & 30\({}^{\circ}\) & 3333 W/m\({}^{2}\) & 30 mm & 15 mm & 15 mm & 15 mm & 15 mm \\
3 & 25 mm & 6 & 5 m/s & 10\({}^{\circ}\) & 45\({}^{\circ}\) & 4444 W/m\({}^{2}\) & 45 mm & 20 mm & 20 mm & 20 mm & 20 mm \\
4 & 25 mm & 7 & 7 m/s & 20\({}^{\circ}\) & 15\({}^{\circ}\) & 2222 W/m\({}^{2}\) & 15 mm & 15 mm & 15 mm & 15 mm & 20 mm \\
5 & 25 mm & 7 & 7 m/s & 20\({}^{\circ}\) & 30\({}^{\circ}\) & 3333 W/m\({}^{2}\) & 30 mm & 20 mm & 20 mm & 20 mm & 10 mm \\
6 & 25 mm & 7 & 7 m/s & 20\({}^{\circ}\) & 45\({}^{\circ}\) & 4444 W/m\({}^{2}\) & 45 mm & 10 mm & 10 mm & 10 mm & 15 mm \\
7 & 25 mm & 8 & 9 m/s & 30\({}^{\circ}\) & 15\({}^{\circ}\) & 2222 W/m\({}^{2}\) & 15 mm & 20 mm & 20 mm & 20 mm & 15 mm \\
8 & 25 mm & 8 & 9 m/s & 30\({}^{\circ}\) & 30\({}^{\circ}\) & 3333 W/m\({}^{2}\) & 30 mm & 10 mm & 10 mm & 10 mm & 20 mm \\
9 & 25 mm & 8 & 9 m/s & 30\({}^{\circ}\) & 45\({}^{\circ}\) & 4444 W/m\({}^{2}\) & 45 mm & 15 mm & 15 mm & 15 mm & 10 mm \\
10 & 32 mm & 6 & 7 m/s & 30\({}^{\circ}\) & 15\({}^{\circ}\) & 3333 W/m\({}^{2}\) & 45 mm & 10 mm & 15 mm & 20 mm & 10 mm \\
11 & 32 mm & 6 & 7 m/s & 30\({}^{\circ}\) & 30\({}^{\circ}\) & 4444 W/m\({}^{2}\) & 15 mm & 20 mm & 10 mm & 15 mm \\
12 & 32 mm & 6 & 7 m/s & 30\({}^{\circ}\) & 45\({}^{\circ}\) & 2222 W/m\({}^{2}\) & 30 mm & 20 mm & 10 mm & 15 mm & 20 mm \\
13 & 32 mm & 7 & 9 m/s & 10\({}^{\circ}\) & 15\({}^{\circ}\) & 3333 W/m\({}^{2}\) & 45 mm & 15 mm & 20 mm & 10 mm & 20 mm \\
14 & 32 mm & 7 & 9 m/s & 10\({}^{\circ}\) & 30\({}^{\circ}\) & 4444 W/m\({}^{2}\) & 15 mm & 20 mm & 10 mm & 15 mm & 10 mm \\
15 & 32 mm & 7 & 9 m/s & 10\({}^{\circ}\) & 45\({}^{\circ}\) & 2222 W/m\({}^{2}\) & 30 mm & 10 mm & 15 mm & 20 mm & 15 mm \\
16 &Thanks to the Taguchi experimental design, only 27 experiments were conducted using the L2(31) experimental plan rather than conducting 311 = 177,147 experiments using the traditional experimental design methods and complete factorial design. In these experiments, to observe the effects of disruptive and random factors, each experiment was conducted twice at different times, and 54 experiments were conducted in total. \"Performance statistic\" was shown as the optimization criterion. Performance values of the Nusselt number were calculated to observe the effects of parameters on the optimization criterion. As seen in Table 2, optimum results were achieved with a 40 mm nozzle diameter, 9 m/s air velocity, 20 mm vertical distance between slices, 4444 W/m\({}^{2}\) heat flux, 20 mm vertical distance between fins, 15 mm fin width, 30\({}^{\circ}\) fin angle, 15 mm horizontal distance between slices, 10\({}^{\circ}\) heat sink angle, 20 mm horizontal distance between fins, and 8 h/d (the ratio of the nozzle diameter to the nozzle-heat sink distance) [21]. In this study, the HT characteristics of a rectangular finned heat sink, previously optimized using the Taguchi L2(31) experimental design method, were investigated under angular and multi-impingement jet conditions. For the optimized heat sink, the effects of varying heat sink angles, nozzle diameters, h/d ratios, and velocity values under constant heat flux conditions were analyzed.