## 5 Conclusions  
Numerical simulations are conducted to investigate the effect of vibration on the heat transfer performance of a heat sink. A parametric study is performed by using vibrational frequency, amplitude, and wave shapes to quantify the dependence of thermal performance on each parameter. When the vibrational frequency is lower than the critical frequency (\(f<30\) Hz), the thermal performance of the heat sink is not influenced by the vibration. However, after exceeding the critical frequency, an increase in amplitude and frequency leads to a higher enhancement in thermal performance at each vibrational wave shape. This result enables the identification of the appropriate operating envelope of the vibrational characteristics, thereby enhancing the heat transfer of the heat sink. Using square wave-shaped excitations provides more benefit to heat transfer than does sinusoidal vibration at every frequency and amplitude level. A maximum increase of 14.2% in Nusselt number values is recorded with sinusoidal vibration, while a maximum enhancement of 25% is obtained with square wave-shaped vibration. Thus, using a square wave-shaped vibration on the heat sink at the frequency of 100 Hz and amplitude of 0.005 m is found to achieve the highest thermal performance of the system over the range of the evaluated parameters. The process results in a 42.2% reduction in Reynolds number, making using the square wave-shaped vibration beneficial in reducing the conventional cooling system and achieve the compactness needed in modern electronic systems.  
However, the current study is performed at a single Reynolds number and power input. Future research could be performed on a range of Reynolds numbers and power inputs. Moreover, this current study could be extended with experimental work and investigating the energy used to vibrate the fins as compared with heat transfer enhancement. This research could also be extended to investigate the reliability of the system due to the vibration of the heat sink.  
Conceptualization, A.H.D.K.R. and M.S.N.; methodology, A.H.D.K.R. and M.S.N.; software, M.S.N.; validation, A.H.D.K.R. and M.S.N.; formal analysis, A.H.D.K.R. and M.S.N.; investigation, A.H.D.K.R. and M.S.N.; resources, M.S.N.; data curation, A.H.D.K.R., M.S.N., W.P. and R.A.-W.; writing--original draft preparation, A.H.D.K.R.; writing--review and editing, M.S.N., W.P. and R.A.-W.; visualization, A.H.D.K.R. and M.S.N.; supervision, M.S.N., W.P. and R.A.-W.; project administration, M.S.N.; funding acquisition, M.S.N. All authors have read and agreed to the published version of the manuscript.  
The Ministry of Higher Education, Malaysia (MoHE) through The Fundamental Research Grant (FRGS)--grant number FRGS/1/2018/TK03/UTP/02/7.  
Not applicable.  
The data presented in this study are available on request from the corresponding authors. The data are not publicly available, due to privacy.  
The authors would like to thank the Ministry of Higher Education (MOHE), Malaysia for providing financial assistance under the Fundamental Research grant Scheme (FRGS/1/2018/TK03/UTP/02/7) and Universiti Teknologi PETRONAS for providing the required facilities to conduct this research work.  
The authors declare no conflict of interest.