## 5 Results and Discussion
### Experimental Results
The correlation between \(T_{\rm trim}\) and \(T_{\rm sp}\) can be determined using thermal resistance equations. Therefore, \(T_{\rm j}\) can be predicted using the thermal resistance model by using the measured temperature at a reference point of \(T_{\rm trim}\). Figure 9a,b as well as Table 9 demonstrate that the heat transfer coefficient and Nusselt number increased with the inlet velocity. The highest heat transfer coefficient was achieved by the PTFHS, followed by MFLHS and TTFHS. Figure 9a,b indicates that the PTFHS exhibits the highest heat transfer performance, followed by MFLHS and TTFHS in the lower or higher Reynolds number turbulent air flow, because the PTFHS exhibits increased heat transfer surface area and less air flow obstruction. Figure 10a illustrates the experimental results of the thermal resistance for cases 1-9 based on Tables 6-8. The groups A, B, and C denote cases 1-3, 4-6, and 7-9, respectively. In all cases, the PTFHS exhibits the highest heat dissipation performance, followed by MFLHS and TTFHS. The optimal geometry effect enhances heat transfer. Moreover, thermal resistance difference among heat sinks are remarkable at a high inlet velocity. The experimental results in Figure 10b-d were compared with numerical simulations for thermal resistance. Thermal resistance of TTFHS in Figure 10b is based on the case studies of higher inlet velocity, lower inlet velocity, and additional housing which denoted as groups D, E, and F, respectively. Figure 10c denotes thermal resistance of PTFHS on case studies of high inlet velocity, low inlet velocity, and additional housing which denoted as groups G, H, and I, respectively. Figure 10d denotes MFLHS for the cases studies of higher inlet velocity, lower inlet velocity, and additional housing denoted as groups J, K, and L, respectively. Based on the comparisons, the experimental results concur with the numerical simulation results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Type**} & \(\mathbf{T_{\rm sp}}\) & \(\mathbf{T_{\rm b}}^{\prime}\) & \(\mathbf{T_{\rm hs}}\) & \(\mathbf{T_{\rm jet}}\) & \(\mathbf{T_{\rm trim}}\) & \(\mathbf{R_{\rm sp\text{-}jet}}\) \\  & & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)C) & (\({}^{\circ}\)W\({}^{\text{-1}}\)) \\ \hline
7 & TTFHS & 45.3 & 33.8 & 33.6 & 25.0 & 32.9 & 2.71 \\
8 & PTFHS & 39.9 & 32.8 & 30.3 & 25.0 & 32.5 & 1.99 \\
9 & MFLHS & 42.0 & 32.3 & 30.1 & 25.0 & 32.0 & 2.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experimental validation results of cases 7-9 for TTFHS, PTFHS, and MFLHS with LED and housing under inlet velocity of 6.13 m s\({}^{-1}\), Re = 14916. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Heat Sink Type** & **PTFHS** & **MFLHS** \\ \hline Nusselt number increase, \% & 10.3 & 7.7 \\ Thermal resistance reduction, \% & 40.3 & 13.0 \\ Weight reduction, \% & 23.6 & 24.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Nusselt number increase, thermal resistance reduction and weight reduction comparing PTFHS and MFLHS with TTFHS. Figure 8: Temperature rise test results of cases 1–9.