## 2 Theoretical Analysis and Fabrication of Lens and Heatsink for the Seaport Luminaire
### Theoretical Analysis and Fabrication of Heatsink for High-Power LED Module  
The LED module was designed for rated power of 250 W with 48 LED PKGs (4 LED PKGs in serial \(\times\) 12 LED PKGs in parallel). The operating voltage and current for each LED PKG is 11.7 V and 400 mA, respectively. In order to effectively dissipate the heat generated from the LED chip, the LED is attached to the heat dissipation pattern on the upper side of the PCB with vertical via hole that reduces the heat primarily, and the vertical via hole is in contact with the heat dissipation coating layer at the bottom of the PCB. It is designed so that heat is secondarily conducted to the lower surface, which is close to the aluminum die-casting body with a high heat dissipation coefficient [26]. The thermal characteristics of heatsink were investigated with Solidworks flow software, as shown in Figure 4. A total of four types of heatsink (type A with vertical fin, type B with horizontal fin, type C with triangle fin, and type D with hexagonal fin) were analyzed, and the results are summarized in Table 3. In the simulation, the total amount of fins for type C and D was 118. As a result of these numerical analyses, the heatsink type D with a hexagonal fin shows the best thermal characteristics of 58.4 \({}^{\circ}\)C at the top of the heatsink, and this means an improvement of 6.8 K in thermal dissipation performance compared to that of type A.  
To measure the real thermal characteristics, four LED modules were fabricated with each heatsink type A, B, C, and D, respectively. The 3D dimension of each heatsink was 565 mm \(\times\) 185 mm \(\times\) 81 mm. Five thermocouples (from point 1 to point 3: near the LED PKGs top side of the heatsink, point 4 and 5: on the bottom of the heatsink) were attached to monitor the temperature of each heatsink, as shown in Figure 5.  
The results of temperature measurement are summarized in Table 4, and as expected from the numerical analysis, heatsink type D shows the best thermal characteristics of 48.6 \({}^{\circ}\)C at point 5. The temperature difference between type D (best case) and type A (worst case) is 7.1 K at the bottom of the heatsink (position 5), and these results are very similar to those of the simulated data temperature difference of 6.8 K at the same position, as shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{4}{c}{**Type of Lens**} \\ \cline{2-5}  & **A** & **B** & **C** & **D** \\ \hline Minimum illuminance & 35.4 k & 48.0 lx & 41.1 lx & 66.9 lx \\ Average illuminance & 73 lx & 90.6 lx & 91.3 lx & 91.8 lx \\ Overall uniformity & 0.48 & 0.53 & 0.45 & 0.73 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Illuminance simulation results of LED seaport lighting using each type of lens.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Measuring Point**} & \multicolumn{4}{c}{**Type of Heatsink**} \\ \cline{2-5}  & **A** & **B** & **C** & **D** \\ \hline top of heatsink & 66.3 \({}^{\circ}\)C & 65.8 \({}^{\circ}\)C & 62.7 \({}^{\circ}\)C & 61.3 \({}^{\circ}\)C \\ bottom of heatsink & 65.2 \({}^{\circ}\)C & 63.4 \({}^{\circ}\)C & 60.7 \({}^{\circ}\)C & 58.4 \({}^{\circ}\)C \\ end-point of fin & 50.3 \({}^{\circ}\)C & 48.9 \({}^{\circ}\)C & 46.2 \({}^{\circ}\)C & 44.3 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of thermal analysis of four types of heatsink.  
Figure 4: Heatsink design and thermal analysis result of type A with vertical fin (**a**), type B with horizontal fin (**b**), type C with triangle fin (**c**), and type D with hexagonal fin (**d**).  
Figure 5: Positions of three thermocouples to monitor the temperature on the top side of the heatsink (**a**) and two thermocouples on the bottom side of the heatsink (**b**).