## 3 Experimental Methodology
### Basic Principles in FFD Building  
In chemometric applications, it is essential to set the levels of these factors correctly to ensure that the response variable is maximized. This process involves finding the ideal levels for each factor. Thus, before beginning the optimization process, it is necessary to identify which factors and respective interactions significantly impact the response variable. It is also beneficial to determine which factors have minimal or no effect to avoid wasting time and resources on unnecessary experiments. All calculations and graphical analyses were performed with the Statistica software package, version 6 [40]. The statistical significance of the results was tested at the \(p<0.05\) level. In this study, the choice of factors was based on their expected impact on the heat dissipation efficiency, evaluated by the \(G_{TR}\) (\({}^{\circ}\)C\(\cdot\)W\({}^{-1}\)) and the convective heat transfer coefficient \(h\) (W\(\cdot\)m\({}^{-2.\circ}\)C\({}^{-1}\)). Therefore, power supply, temperature, and flow rate (labeled as A, B, and C, respectively, in Table 3) were identified as key variables that could influence cooling efficiency (2\({}^{3}\) FFD). For two-level designs, it is customary to identify the higher and lower levels with (+) and (-) signs, respectively. These levels were determined based on practical operating ranges and prior knowledge of the system. This binary coding simplifies the chemometric treatment of data, allowing for the straightforward calculation of main effects and their interactions. In this setup, we have three factors, each with two levels, resulting in 2\({}^{3}\) = 8 combinations. The \(G_{TR}\) and \(h\) values observed from these runs, which were conducted in a random order and in duplicate (for a total of 16 experiments), are presented in Table 4, in which the design matrix and results of the full 2\({}^{3}\) designs are displayed. The number in parenthesis following each response value indicates the order in which the run was conducted. In experimental design, particularly in factorial experiments, a contrast matrix is a powerful tool for analyzing the main effects and interactions between factors. Constructing a contrast matrix involves defining the factors and levels, creating a design matrix of all possible combinations, adding columns for main effects and interactions, and then interpreting these columns to understand the significance of each factor and interaction. To form a contrast matrix, new columns for the main effects and interactions (Table 3) are required, in which the effect or interaction is represented by a new column. The main effects of factors A, B, and C are straightforward, but it is also important to consider the two-factor interactions (AB, AC, BC) and the three-factor interaction (ABC). The signs in these interaction columns are determined by multiplying the signs of the relevant factors. For instance, the column for interaction AB is generated by multiplying the signs from the columns for A and B. Similarly, the column for the three-factor interaction ABC is the product of the signs from the columns for A, B, and C, as illustrated in Table 5. This table presents the contrast matrix for the 2\({}^{3}\) factorial design. The last column contains the average values of \(G_{TR}\) and \(h\) obtained from the experimental runs, as shown in Table 4.  
Conducting this factorial design and calculating the main effects and interactions allows for a comprehensive assessment of the influence of each factor and their combinations on the responses. The duplication of experiments enhances the robustness of the results, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factors** & **(–)** & **(+)** \\ \hline (A) Power supply (W) & 30 & 65 \\ \hline (B) Ambient temperature (\({}^{\circ}\)C) & 22 & 29 \\ \hline (C) Flow rate (L\(\cdot\)min\({}^{-1}\)) & 2.50 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Factors and levels of the 2\({}^{3}\) FFD.