## 3 Results
Therefore, as shown in Figure 8a,b, the base temperature of each heat sink is found to be higher with no vibration conditions, limiting the cooling effect. However, as shown in Figure 8c-f, the base temperature of each heat sink reduced with the increase in vibrational frequency for both conventional and thin plate-fin heat sinks. Induced flow recirculation zones around heat sink fins enhance the heat transfer of fin surfaces. This leads to a lower temperature in the heat sink base, indicating a higher cooling effect. Moreover, Figure 8d,f shows that the application vibration with higher frequency leads to a higher reduction in the heat-sink base temperature of the thin plate-fin heat sink as compared to the conventional heat sink (Figure 8c,e) owing to the flapping motion of thin plate fins which induced strong flow recirculation zones. As shown in Figure 8e-h, an increase in vibrational amplitude leads to a further reduction in base temperature in both heat sinks. As expected, as seen in Figure 8h, a higher decrease in heat-sink base temperature is recorded with the thin plate-fin heat sink compared to the conventional heat sink, indicating a higher cooling effect. As seen in Figure 9a, with low vibrational frequencies (\(f<30\) Hz), the increase in Nusselt number is insignificant. This might be due to the small frequency values, which are not adequate to formulate the recirculation zones within the flow field, resulting in limited heat transfer. Moreover, this threshold frequency is common for both conventional and thin plate-fin heat sinks. When heat sinks vibrate with higher frequencies (\(f>30\) Hz), an increase in frequency leads to a higher Nusselt number. It is noteworthy that an enhancement in Nusselt number is prominent with the thin plate-fin heat sink in comparison with the  
Figure 8: Temperature profiles of heat sink base at \(Re=1000\). (**a**) static (conventional); (**b**) static (thin plate); (**c**) \(f=50\) Hz, \(A_{b}=0.0015\) m (conventional); (**d**) \(f=50\) Hz, \(A_{b}=0.0015\) m (thin plate); (**e**) \(f=100\) Hz, \(A_{b}=0.0015\) m (conventional); (**f**) \(f=100\) Hz, \(A_{b}=0.0015\) m (thin plate); (**g**) \(f=100\) Hz, \(A_{b}=0.003\) m (conventional); (**h**) \(f=100\) Hz, \(A_{b}=0.003\) m (thin plate). conventional heat sink. The Nusselt numbers are increased up to a maximum of 16% and 12% with the conventional heat sink and thin plate-fin heat sinks, respectively. The variation in the Nusselt value with an increase in vibrational amplitude is shown in Figure 9. As amplitude increases, the Nusselt value increases due to the flow disturbance and recirculation zones caused by the higher vibrational amplitude. As expected, the vibration of the thin plate-fin heat sink provides higher Nu enhancement than the conventional heat sink, due to the stronger recirculation zones induced by the translation and flapping motion of the heat sink fins. The thin plate-fin heat sink achieved a maximum of 20% enhancement in Nusselt value, while the conventional heat sink recorded a maximum 15% increase in Nusselt number compared to its static conditions. Since the application of vibration provides a higher heat-transfer enhancement in the thin plate-fin heat sink as compared to the conventional heat sink, the thin plate-fin heat sink is selected to investigate the effect of varying Reynolds numbers on the vibration-assisted thermal performance. Figure 9 shows the variation in the Nusselt value with the vibrational frequency at different Reynold numbers under a constant amplitude of 0.0015 m. It can be seen that the enhancement of the Nusselt value is insignificant when the vibrational frequency is less than 30 Hz. However, when the frequency exceeds 30 Hz, the Nusselt value increases exponentially with the increase in vibrational frequency. It can be seen in Figure 9 that Nusselt number values increase at higher Reynolds values. The  
Figure 9: Time-averaged Nusselt number variations with vibrational characteristics.