## 3 Results  
After validating each simulation model, the CFD modeling was initially performed with heat sinks in static conditions at a Reynolds number of 1000. Then, conventional and thin plate-fin heat sinks were subjected to sinusoidal vibration with a range of vibrational frequency and amplitude of 0-100 Hz and 0-0.003 m, respectively. After performing the comparative analysis of the vibration-assisted thermal performance of conventional and thin plate-fin heat sinks, the Reynolds number of the thin plate-fin heat sink model was varied between 1000 and 2000 and we determined the effect of vibration on the heat-transfer enhancement of thin plate-fin heat sinks under different Reynolds numbers. Vibration induces secondary flows within the flow regime, resulting in a mixing effect and consequently enhancing heat transfer. Thus, a brief discussion is presented on the effect of vibration on the flow profiles shed from an oscillating conventional and thin plate fin. The end-view schematic of the conventional and thin plate-fin heat sink is presented in Figure 5.  
Figure 6 shows the velocity profiles of non-vibrating and vibrating heat sinks at a vibrational frequency of 100 Hz and an amplitude of 0.0025 m. When a conventional or thin plate-fin heat sink is not subjected to vibration, the flow moves smoothly from the inlet to the outlet, and no secondary flows are induced within the flow field, as shown in Figure 6a,b. When the conventional heat sink is at the start of the first quarter of the sinusoidal vibration, the velocity vector at the tip of the heat sink shows that the flow recirculation appears near the trailing edges of both fins (Figure 6c). Furthermore, the velocity vector at the cross-section of the heat sink shows that the clockwise two-flow recirculation zones near each fin tip and airflow within the channel area follow the movement direction of the heat sinks and hit the inner surface of fin 1. However, when vibration is subjected to a thin plate-fin heat sink, as shown in Figure 6g, as compared to the conventional heat sink, stronger recirculation zones are formed near the trailing edges of both fins and a stronger counterclockwise recirculation zone is formed near the tip of the fins due to the flapping motion of the thin fins. Moreover, flow within the channel area hits the inner surface of fin 1. At the start of the second quarter, the heat sink moves to the maximum positive amplitude, inducing flow recirculation near the trailing edge of the heat sinks (as shown in Figure 6d). Moreover, two counterclockwise zones and one clockwise recirculation zone tend to appear near the tip of the conventional heat sink. However, the vibration of the thin plate-fin heat sink induces stronger recirculation zones near the trailing edge of the  
Figure 5: End view of heat sink models. (**a**) conventional heat sink (**b**) thin plate-fin heat sink. fins, and two stronger counterclockwise and clockwise recirculation zones are formed near the tip of the fins (Figure 6h). At the start of the quarter of the sinusoidal vibration (Figure 6e,i), the motion of both heat sinks induces the recirculation zones near the trailing edge of the fins, and one counterclockwise recirculation zone is formed near the tip of both heat sink fins. Moreover, the flow between the channel area follows the movement direction of the heat sinks and hits the inner surface of fin 2 in both heat sinks. However, as expected, induced recirculation zones are found to be stronger with thin plate fins due to the flapping motion of the fins. Figure 6: Velocity vector profile passing through the tip and cross-section of the heat sink.