## 2 Materials and Methods
### Design of Experiments for Optimized Conformal Channels  
A design of experiments approach is used to guide the design of conformal cooling channels. Typically, the thickness of molded plastic parts varies within a range of 0-6 mm. Different shapes, sizes, and thicknesses of the part would require different configurations of optimized conformal  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wall Thickness of** & **Channel Diameter, D (mm)** & **Pitch Distance, P (mm)** & **Channel Centerline to Mold** \\
**Molded Part (mm)** & & & **Wall Distance, L (mm)** \\ \hline
0–2 & 4–8 & 2D–3D & 1.5D–2D \\
2–4 & 8–12 & 2D–3D & 1.5D–2D \\
4–8 & 12–14 & 2D–3D & 1.5D–2D \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation amongst design parameters of conformal cooling channels [37].  
cooling channels. As such, only one basic shape of plastic parts, namely cylindrical, is considered. Three different thicknesses are modeled: one mm, 3.5 mm, and six mm. Thus, three sets of DOEs are prepared: DOE-1 for the thickness of one mm; DOE-2 for the thickness of 3.5 mm; and DOE-3 for the thickness of six mm.  
The information regarding the part thickness provides the basic outline for channel design parameters such as diameter (in circular channels), pitch distance, channel centerline to mold wall distance, etc. The range of analysis for each DOE has been determined from the literature and the general rule of thumb of mold designers [36]. After deciding on the design variables (pitch, wall to wall distance, etc.), the channel cross-section is selected. This research group found that a rectangular cross-section of conformal cooling channels provides effective thermal performance in injection molds. As a result, all of the design cases in the above-mentioned DOEs are created with rectangular-shaped cooling channels. The DOE parameter details are mentioned in Table 2. The design cases are designated as 1.1, 1.2..., 2.1..., 3.1, 3.2,... 3.18.  
For DOE-1, the plastic part thickness is one mm. According to the guidelines in Table 1, the channel diameter should be in the range of four to eight mm. The perimeter of such channels would be 12.6 mm to 25.13 mm. Keeping the perimeter the same, the circular channels are converted into rectangular ones, and their cross-sectional dimensions are calculated. For example, the circular channel with a diameter of four-mm was converted to a rectangular channel with a cross-section of 3.8 mm \(\times\) 2.5 mm, and the channel with a diameter of eight mm is converted into a 7.5 mm \(\times\) 5 mm section channel. There are three design variables in each DOE 1, 2 and 3. These are the channel cross-section (a \(\times\) b), pitch distance (P), and mold wall to channel centerline distance (L). The first two variables have three levels of design, and the third one has two levels of design. As a result, DOE-1 has 3 \(\times\) 3 \(\times\) 2 = 18 design cases (Table 2, column 1). Similarly, DOE-2 has 18 cases (Table 1, column 5), and DOE-3 also has 18 design cases (Table 2, column 9). The channel design parameters, such as pitch distance and cross-section dimensions, are the same for both the cavity and core in a single design case. In all of the DOEs mentioned here (DOE 1, 2 and 3), as well as the other ones (DOE 4, 5, 6, 7, 8 and 9) discussed in the latter part of the paper, a full factorial method is used to formulate the design of experiments.