## 3 Results  
CFD modelling is initially performed for the static heat sink (shown in Figure 2) at a Reynolds number of 1000. Then, \(Re=1000\) is used in the investigation of the vibration and amplitude variation effect on heat transfer. The airflow and vibrating directions are shown in the black arrows in the top view of the heat sink (Figure 7). The vibration of the heat sink improves heat transfer by inducing randomness of the airflow profile and recirculation in the flow field. Thus, investigating the velocity profile  
Figure 6: Time-averaged Nusselt number validation against experimental measurements of [PERSON], et al. [37]. Figure 7: Top view of the heat sink. shed from the vibrating heat sink is important. The effect of using the sinusoidal and square wave-shaped vibrations on the flow profile is expected to be different. Investigating the transient development of the velocity profile under each type of vibration compared with the velocity profile of the stationary heat sink is therefore important. The velocity profile of the nonvibrating heat sink and the transient development of air velocity vectors on a plane passing through the top section of the heat sink at different vibration cycle stages for sinusoidal and square wave shapes are presented. The air velocity vectors shown in Figure 8b-i are obtained with sinusoidal and square wave-shaped vibrations at frequencies of 100 Hz at a constant peak-to-peak amplitude of 0.003 m. In each figure, the two fins of the vibrating heat sink are shown as red surfaces. After performing the validation of the model, the heat sink shown in Figure 2 is modeled under normal and vibration conditions under the range of vibrational frequencies and amplitudes for both sinusoidal and square wave shapes. At the beginning of the sinusoidal motion, the heat sink moves to a positive Y direction. Figure 8b shows that, at the end of the first quarter of the cycle, the vibrating fins induce airflow recirculation near the trailing edges of the fins, whereas the flow between the two fins moves upward toward fin 1 following the vibration displacement direction and hitting the surface of fin 1. At the end of the second and third quarter of the vibration cycle, Figure 8c,d show that the recirculation of air at the trailing edges of the fins continues. However, the airflow in the middle channel between the two fins changes its direction and hits the interior surfaces, especially the interior surface of fin 2. This induced flow change in direction becomes more noticeable at the end of the third quarter of the cycle. When the vibration continues at the  
Figure 8: Velocity vectors in the vicinity of the vibrating heat sink at different phases of a cycle of sinusoidal and square wave-shaped vibration at \(f\) = 100 Hz, \(Amp\) = 0.003 m, and \(Re\) = 1000 (**a**) without vibration, (**b**) sinusoidal at 1 st quarter of the cycle, (**c**) sinusoidal at 2 nd quarter of the cycle, (**d**) sinusoidal at 3 rd quarter of the cycle, (**e**) sinusoidal at 4 th quarter of the cycle, (**f**) square at 1 st quarter of the cycle, (**g**) square at 2 nd quarter of the cycle, (**h**) square at 3 rd quarter of the cycle, and (**i**) square at 4 th quarter of the cycle. end of the cycle, it can be seen in Figure 8e that the flow direction and recirculation become similar to Figure 8c. At the beginning of the square wave-shaped motion, the heat sink reaches its maximum positive amplitude almost instantly. As a result, Figure 8f shows that the square wave excitation of the fins induces strong air recirculation near the trailing edges of fins compared to the sinusoidal motion at the end of the first quarter of the vibration cycle. With increasing time, the heat sink moves to the end of the second quarter of the cycle (Figure 8g). The impulsive motion of the heat sink gives a higher air velocity magnitude to the air particles. Thus, the fluid adjacent to it gains noticeable movement path changes.