## 1 Introduction  
Continued development in the electronic industry has led to a significant increase in energy consumption [1, 2]. A higher percentage of this energy is converted into heat [3]. In addition, reducing the size of electronic components is on the rise, making the cooling of these components smaller whilst maintaining the compactness of the system a challenge. Among numerous cooling enhancements, one mechanism is the fan-based cooling system, a well-known method due to its high performance-to-cost ratio [4]. However, the thermal performance of fan-based electronic cooling systems is saturated by the formation of the thermal boundary layer, which is found to hinder the heat transfer between the cooling fluid and heated surface [5]. In addition, increasing cooling requires increasing fan size, which compromises the compactness of electronic components. Consequently, researchers have implemented different mechanisms in electronic cooling systems to overcome the limited thermal performance. In the literature, the most popular passive thermal enhancement techniques in electronic cooling have been investigated, such as utilizing foam-based heat sinks [6, 7], and optimizing the heat sink shape, size, arrangement, and artificial roughness [8, 9, 10]. Various approaches by enhancing the mixing process of working fluid with vortex generators [4, 11, 12], vortex tubes [13], mixing promoters [14], or flow-induced vibration [15, 16] have also been attempted by many researchers. However, the benefits of electronic cooling by utilizing passive technologies have been found to be inefficient for high-power dissipation electronic systems. Therefore, active cooling methods have been utilized to enhance the electronic cooling, including the projection of air at high speed toward a heated surface using air jets [17, 18, 19, 20] or spray [14, 21], investigated to enhance the thermal performance. Furthermore, using heat pipes [22] or adding oscillating heat pipes [23] and utilizing nanofluids in conjunction with a heat sink [24, 25] as well as electronic cooling systems [26, 27] have shown to be promising techniques for the thermal management of electronic systems. However, another effective technique has been used; applying external vibrations to the heated object has also been studied as a heat transfer intensification technique. To prove the concept of vibrational heat transfer augmentation, experimental and numerical studies have been performed with different geometries, including gauge wire [28], spheres [29], and cylinders [30, 31, 32, 33]. These studies noted that forced convective heat transfer is significantly influenced by external vibration. Due to the need to reduce the size of electronic components and cooling systems, applying vibration on fins and heat sinks could be a viable option to achieve a reduction in the electronic cooling system. Thus, several studies have considered the influence of vibrational frequency and amplitude variation on heat transfer augmentation. [PERSON] and [PERSON] [34] investigated the heat transfer of a vibrating 2D pin fin numerically and observed an increase in heat transfer coefficient with frequency. An analysis detailing the influence of a vibrating 2D plate-fin on the flow field was reported by [PERSON] and [PERSON] [35]. The maximum heat transfer was obtained at the highest vibrational characteristics. [PERSON] and [PERSON] [5] numerically investigated the heat transfer augmentation of a vibrating actuated 3D fin. The authors obtained limited enhancement with lower vibrational characteristics. However, they noted an enhanced thermal performance with an increase in vibrational characteristics. [PERSON], et al. [36] experimentally studied the thermal performance of piezo-actuated cooling fins and observed a higher heat transfer with the increase in vibrational frequency. [PERSON], et al. [37] conducted an experimental study indicating a potential increase in the thermal performance of the vibrating heat sink at higher frequencies.