## 1 Introduction
Because this study aimed to create devices with a high capacity for heat dissipation, various types of ALFHS and CUFHS using different materials were examined. Although they have fundamental differences, this study used ALFHSs and CUFHSs to develop optimal heat sinks with high dissipation capacities. LED lifetime is subject to junction temperature. Lower junction temperatures tend to produce longer lifetimes. Therefore, LED cooling is necessary. Heat sinks have an important role in the natural convection cooling of LED lighting. Selecting suitable materials and determining appropriate dimensions are the main factors. In this study, the dimensions were determined by simulating the different height of the materials. The CUFHS height was determined first, followed by the ALFHS height. Of 5 mm, 10 mm, and 17 mm height copper foam materials, the 17 mm material was selected because of its higher heat dissipation capacity. Simulation and testing were then conducted before and after INST. ALFHSs with heights of 16 mm, 20 mm, and 23 mm were simulated and tested to compare them with the 17 mm CUFHS. To compare the heat dissipation behavior with both heat sinks, the 23 mm ALFHS was then examined. Finally, the 23 mm ALFHS and 17 mm CUFHS were selected. A comparison of the temperature of the solder point (\(T_{\text{sp}}\)) for the ALFHS and CUFHS before and after INST is presented in Table 1. Before INST, for case 1, the \(T_{\text{sp}}\) values of the ALFHS and CUFHS both with 17 mm height were very similar. For cases 2 and 3, the \(T_{\text{sp}}\) values of the 20 and 23 mm height CUFHS were higher than those of the ALFHS by 1.6 \({}^{\circ}\)C and 3.2 \({}^{\circ}\)C, respectively. After INST, for cases 1 and 2, the \(T_{\text{sp}}\) values of the ALFHS were higher than those of the CUFHS by 8.4 \({}^{\circ}\)C and 2.8 \({}^{\circ}\)C, respectively. For case 3, the same \(T_{\text{sp}}\) was obtained for both the ALFHS and CUFHS. These results indicate that (1) The 17 mm height ALFHS and CUFHS exhibited a very similar capacity for heat dissipation before INST. The high conductivity of the copper foam material compensates for its higher fluid flow resistance caused by its increased pressure drop; (2) For the same height, the ALFHS \(T_{\text{sp}}\) was higher than that of the CUFHS after INST because the heat dissipation concentrated centrally above the heat sink with higher velocity. Unlike in the ALFHS, the heat accumulated along the heat sink to the cover of the test box, resulting in less efficient transfer of heat from inside the ambient of the test box to the outside atmosphere. The copper foam can potentially increase the heat transfer rates from solid surfaces by conducting heat to the material struts and inducing a high interaction between the struts and a through-flowing fluid [11]; and (3) After INST, the same \(T_{\text{sp}}\) was obtained for the ALFHS and CUFHS by increasing the height of the ALFHS to 23 mm, which was 6 mm higher than that of the CUFHS, thereby increasing the efficiency of fin performance. This facilitated comparing the heat dissipation behavior of the heat sinks. The \(T_{\text{sp}}\) of both heat sinks was 91.7 \({}^{\circ}\)C, which is a suitable heat dissipation capacity for the purpose of this study. The simulated \(T_{\text{sp}}\) values for ALFHSs with heights of 16 mm, 20 mm, and 23 mm were 104.0 \({}^{\circ}\)C, 95.7 \({}^{\circ}\)C, and 91.7 \({}^{\circ}\)C, respectively. The 23 mm heights ALFHS was then used in this study because of its higher heat dissipation capacity and its heights being acceptable for CLRDL design. Figure 1 illustrates the length of the thermal dissipation path around the LED junction, solder point, metal core printed circuit board (MCPCB), aluminum housing, heat sink (ALFHS or CUFHS), and test box (plywood, 13 mm thick, 105 mm \(\times\) 105 mm \(\times\) 100 mm, \(L\times W\times H\)) to the atmosphere. Another path involved dissipation from the aluminum housing, through the trim (a decorated flange of CLRDL exposed below the ceiling) to the atmosphere.