## 2 Materials and Methods
### Data Reduction  
The steady-state condition of the HT through the air may be stated as given below [23]:  
\[\mathrm{Q_{tot}=Q_{conv}+Q_{rad}+Q_{cond}} \tag{1}\]  
\[\mathrm{\dot{Q}_{conv}=\dot{m}C_{p}(T_{out}-T_{in})=V^{2}/R=VI} \tag{2}\]  
The HT from the test unit by convection can be calculated as follows [13]:  
\[\mathrm{Q_{conv}=h_{ave}A_{s}(T_{yave}-T_{jet})} \tag{3}\]  
The metal base plate and fins were meticulously cleaned and polished. The operational temperature was maintained within standard parameters. In this context, the radiative heat loss was deemed to be below 5% of the total input to the pin-fin arrays. Consequently, the radiative heat loss from this component may be disregarded. Considering these findings and the effective insulation of the section, together with the thermocouple readings at the outside surface of the heating section, which are almost equivalent to the ambient temperature, the last two elements of Equation (1) may be disregarded. These assumptions are shortened in Equation (1) given as follows:  
\[\mathrm{Q_{total}=Q_{conv}} \tag{4}\]  
The average HT coefficient was attained from Equations (1)-(3) given as follows:  
\[\mathrm{h_{ave}=\frac{Q_{conv}}{A_{s}(T_{yave}-T_{jet})}} \tag{5}\]  
Previous studies employed both the projection area and total HT area as metrics for the HT surface area. The whole HT region was used in the current investigation. This region pertains to the overall HT area, including both fins and the base plate, and may be delineated as follows [2,14]:  
\[\mathrm{A_{s}=WL+N[(2 bh_{k}+(2 th_{k})]} \tag{6}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Explanation** & **Value** \\ \hline a & \begin{tabular}{c} The horizontal distance \\ between fins (mm) \\ \end{tabular} & 20 \\ b & \begin{tabular}{c} Fin width (mm) \\ \end{tabular} & 15 \\ c & \begin{tabular}{c} The vertical distance between \\ fins (mm) \\ \end{tabular} & 20 \\ e & \begin{tabular}{c} The vertical distance between \\ slices (mm) \\ \end{tabular} & 20 \\ f & \begin{tabular}{c} The horizontal distance \\ between slices (mm) \\ \end{tabular} & 15 \\ h\({}_{k}\) & \begin{tabular}{c} Fin height (mm) \\ \end{tabular} & 100 \\ \(\alpha\) & \begin{tabular}{c} Fin angle (degree) \\ \end{tabular} & 30\({}^{\circ}\) \\ \(\beta\) & \begin{tabular}{c} Angle of heat sink (degree) \\ \end{tabular} & 10\({}^{\circ}\)-20\({}^{\circ}\)-30\({}^{\circ}\) \\ h/d & \begin{tabular}{c} Dimensionless distance \\ between the nozzle-heat sink \\ \end{tabular} & 6-7-8 \\ d & \
\begin{tabular}{c} Nozzle diameter (mm) \\ \end{tabular} & 25-32-40 \\ V &
\begin{tabular}{c} Velocity of fluid (m/s) \\ \end{tabular} & 5-6-7-8-9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variables analyzed in the experiments. where W denotes the width of the base plate, L signifies its length, N represents the number of fins, b indicates the fin breadth, t relates to the thickness of the heat sink, and h\({}_{\text{k}}\) pertains to the height of the rectangular fins. Although most jet-impinging applications are turbulent, laminar jets are also encountered in many industrial applications, such as microelectronic devices, miniature geometry, and jets of highly viscous fluid. Most of the published studies on jet impingement cooling consider forced convection a heat transfer mode. In these studies, the Buoyancy effect is neglected. Therefore, the Buoyancy effect is neglected in this study. However, it cannot be neglected for the low Reynolds number laminar flow. For laminar jet flows, the impinging regime may fall into natural, forced, or mixed convection, depending on the relative strengths of the inertia/viscous forces and the buoyancy forces involved [31; 32]. The Prandtl number is independent of temperature. In the experiments conducted in this study, the air temperature was approximately 20 \({}^{\circ}\)C. Nu served as a performance metric.