## 1 Introduction
Given that the application of external vibration is beneficial to thermal performance, it may also cause an adverse effect on the reliability of the system. There are studies that have investigated the reliability of the electronic systems under the vibration that occurs during shipping, handling, and the service life of the system. The reliability assessment of electronic assemblies under shock, harmonic, and random vibration has been performed experimentally [38] and analytically [39, 40] to investigate the strains and stresses of printed circuit boards (PCBs) and the solder interconnect. Moreover, finite element modeling analysis (FEA) has been performed by several studies [41, 42, 43] to investigate the fatigue performance and failure modes of electronic products under vibrating conditions. However, no research has been performed to investigate the reliability of electronic systems due to the application of external vibration. Thus, a special consideration on the relatability of the system may be required in designing a vibrating system. As mentioned, vibration has been a viable method to enhance heat transfer, and further investigation has been warranted to increase the enhancement. Although previous research has focused on the effect of sinusoidal vibration on forced convective heat transfer in heated geometries, new vibration methods by introducing different vibrational wave shapes on thermal systems are needed. The vibrating heated surface enhances heat transfer mainly by setting the fluid in motion and consequently disrupting the thermal boundary layer [14]. However, the motion of the fluid particles depends not only on the vibrational characteristics but also on the type of vibrational wave shape. The different vibrational wave shapes may have a distinct effect on the flow profile, potentially affecting the thermal performance of the heat sink. This effect has not been considered in previous studies and is worth investigating. In fact, [PERSON], et al. [44] conducted an experimental study to investigate the effect of vibration modes on the detachment of low-rank coal particles from oscillating bubbles. The authors found that different vibration modes of oscillating bubbles have a distinct effect on path changes, and applying square wave excitations leads to the highest dramatic movement path changes due to its impulsive motion. In addition, the authors claimed that the square wave-shaped vibration induces the greatest acceleration within the particles compared to other vibration modes at similar vibrational frequencies and amplitudes. On the other hand, several experimental studies have been performed by utilizing a square wave-shaped vibration using a piezo-shaker [45], vibrators [44], and piezoelectrical actuators [46]. As applying square wave-shaped vibration has resulted in the highest movement path change as compared with the sinusoidal wave, utilizing square wave vibrations in heat sinks may result in a higher heat transfer enhancement, which has not been previously utilized in electronic systems and could be considered a new implementation to further enhance heat transfer. As seen in the vibrational wave plot (Figure 1), square wave-shaped vibration causes a sudden impulsive motion of the heated geometry, potentially causing rapid velocity changes. Therefore, introducing the new square wave-shaped vibration in comparison with sinusoidal vibration may produce a higher heat transfer enhancement and consequently further reduce the size of the cooling system. To the best of the author's knowledge, the application of square wave-shaped vibration on a heat sink to improve the thermal performance of the heat sink is new and has not yet been investigated by previous researchers. The present study investigates the heat transfer enhancement resulting from a vibrating heat sink under the influence of the newly introduced square wave shape and sinusoidal wave shape using ANSYS/FLUENT CFD software. The examined heat sink structure is subjected to different vibration levels.