## 1 Introduction
Moreover, past studies investigated the potential of mechanical vibration for enhancing the thermal efficiency of fins or heat sinks. For instance, the vibration-assisted heat transfer of 2D fins has been numerically investigated by [PERSON] and [PERSON] [37], [PERSON] and [PERSON] [38] and [PERSON] et al. [30]. These studies show that vibration induces the secondary flows within the flow regime, which disrupts the thermal boundary layer, resulting in enhanced heat transfer. [PERSON] et al. [39] investigated the effect of sinusoidal vertical vibration on heat sinks. Their findings revealed that vibrational frequency enhances heat transfer, and the Nu value is increased by up to a maximum of 6.5% compared with the static conditions due to the fluid flow circulation caused by the vibration. Moreover, [PERSON] et al. [40] investigated the thermal performance of horizontally vibrating conventional heat sinks under sinusoidal and square wave-shaped vibrations, and they observed a maximum of 25% enhancement in the Nusselt number. There is a growing interest among researchers in enhancing the heat transfer of fins or heat sinks through the utilization of piezoelectric actuators to induce movement in heated solid bodies. Piezoelectric technology is widely suitable for electronic cooling purposes due to its suitability in terms of power densities, operating frequencies, and compactness [41]. [PERSON] et al. [42] conducted an experimental study on heat-transfer augmentation using piezo-actuated single and triple thin fins, which are oscillated by piezoelectric actuator patches connected to the base of the fin. The study revealed that vibration enhances heat transfer and achieves a maximum temperature reduction of 35% at the fin tip. In their numerical investigation, [PERSON] et al. [43] examined the thermal performance of six piezo-actuated fins and observed an 11.6% enhancement in thermal effectiveness. Another numerical study by [PERSON] and [PERSON] [44] focused on the impact of piezo-actuated fin motion with a static substrate on heat-transfer enhancement. They reported a 98.7% increase in the Nusselt value by utilizing higher vibrational characteristics. Theyattributed this enhancement to the formation of two counter-rotating vortices at the tip of the fin, and it tends to enhance heat transfer. The application of vibration on a thin plate-fin heat sink can cause a flapping motion within the fins, which may positively contribute to the formation of excessive secondary flows and additional mixing effects within the flow field. The induced secondary flows and the mixing effect may result in disturbing the thermal boundary layer, enhancing heat transfer further. As a result, the size of the cooling system or heat sink can be reduced. Moreover, thin plate fins have a small thickness compared to conventional heat sinks, resulting in material saving, weight reduction and more compactness. In fact, applying vibration to a thin plate-fin heat sink provides a more feasible way to achieve actuator motion within the thin fins. However, to the authors' best knowledge, no research has been conducted to demonstrate the heat-transfer enhancement and potential cooling system size reduction of thin plate-fin heat sinks under sinusoidal vibration or to compare their thermal performance with vibrating conventional heat sinks to determine which heat sink is more superior in terms of thermal performance. This study aims to analyze and compare the heat-transfer enhancement of conventional and thin plate-fin heat sinks subjected to sinusoidal vibrations using ANSYS/FLUENT V 2021 R2 CFD software. The vibration of a conventional heat sink causes the heat sink to vibrate within the vibration wave frequency and amplitude range; however, for thin fins, the vibration causes a flapping motion. Commercial CFD software does not model by default vibration. Therefore, User-Defined Function (UDF) codes using C++ need to be developed to simulate each vibration and then incorporated into the CFD model.