## 3 Results
This leads to the formation of strong clockwise and counter-clockwise recirculation zones near the leading and trailing edges of both fins. Afterward, the heat sink moves in the negative y-direction continuously at the start of the third quarter of the vibration cycle. As indicated in Figure 8h, the flow circulation zones are found to be similar to those mentioned earlier at the end of the second quarter. However, the strength of the circulation zones near the leading and trailing edges of the fins decreases gradually at the end of the third quarter of the vibration cycle. As vibration continuous, the heat sink moves to the positive y-direction at the end of the vibration cycle (Figure 8i), and the flow direction and recirculation zones are found to be opposite to those, as shown in Figure 8g. Compared with the nonvibrating heat sink shown in Figure 8a, air velocity vectors under the vibration effect are not straight streamlines. When the heat sink vibrates with some frequency and amplitude, the airflow direction continuously changes toward the fins' surface, which is expected to improve the fins' thermal performance. When the heat sink vibrates under a square wave shape, strong recirculation zones and secondary flows are formed around both fins at each quadrant of the vibration cycle owing to the sudden movement of the heat sink, causing a noticeable velocity increase in the flow field. By comparing air velocity vectors between the square shape and sinusoidal vibration, the velocity magnitude and strength of the recirculation zones are higher under square-shaped vibration. This phenomenon induces more disruption to the developed thermal boundary layer, thereby further enhancing the thermal performance of the heat sink. Figure 9 shows the temperature contours of the nonvibrating heat sink compared with other cases of increasing frequency and amplitude at each type of vibrational wave shape. To avoid repetition, only one representing case for vibration frequency and amplitude under each wave shape is selected to show the effect of vibration on the thermal boundary layer. As seen in Figure 8a, the nonvibrating heat sink has a uniform airflow distribution in the direction of the flow field. Thus, the temperature gradient is high between the air stream and near the fin surfaces (Figure 9a), showing that the effect of the heat resistance of the thermal boundary layer causes and limits the cooling effect. However, when vibration is applied, it causes a rapid change in the air velocity distribution and randomness and recirculation, causing the fluid to move directly toward the heated fin surfaces, as shown in Figure 8. This phenomenon consequently ruptures the thermal boundary layer. As seen in Figure 9b,c, applying vibration on the heat sink induces a disturbance to the continuous thermal wake. It leads to a widespread decrease in air temperature near the fin surfaces, which tends to have a higher cooling effect than the static fin. This randomness and recirculation are more noticeable with a higher air velocity magnitude when a square-shaped vibration is used. Figure 8f-i show that using a square wave-shaped vibration induces stronger recirculation zones, leading to a higher mixing effect within the flow field. Thus, the overall spread of thermal disturbance and lower air temperature becomes more noticeable when square wave excitation is applied compared with the sinusoidal wave shape. The cooling effect of the square shape vibration can be seen in Figure 9c, where it causes a widespread low-temperature region at both fin surfaces, indicating a further cooling effect. When the peak-to-peak amplitude is increased from 0.003 to 0.005 m at a constant frequency of 100 Hz, the recirculation zones and randomness of the airflow profile increase as the peak-to-peak amplitude increases. As a result, the thermal boundary layer is disturbed further, resulting in increased heat transfer.