## 4 Conclusions  
A numerical study is performed to value and compare the effect of sinusoidal vibration on the thermal performance of conventional and thin plate-fin heat sinks. It was found that at a vibration frequency below 30 Hz, an enhancement in the Nusselt value is insignificant with both heat sinks. However, an increase in frequency beyond the threshold value and amplitude increases the Nusselt number. Moreover, the effect of the vibration on the heat-transfer enhancement was proved to be stronger with the thin plate-fin heat sink than the conventional heat sinks due to the induced flapping motion of the fins, which positively contributes to the formation of higher recirculation zones within the flow field. Compared to the non-vibrating heat sink, the thin plate-fin heat sink achieved a maximum increase in 20% in Nusselt values, while a 15% maximum enhancement in the Nusselt number is recorded with the conventional heat sink. Moreover, the effect of the Reynolds number on the vibration-assisted thermal performance of the thin plate-fin heat sink is investigated, and it was found that an increase in the Reynolds number leads to a reduction in the thermal performance of the heat sink at vibrating conditions. At a base frequency and amplitude of 100 Hz and 0.0015 m, the maximum enhancement in the Nusselt value of the vibrating thin plate-fin heat sink is recorded as 16%, 9% and 6% at Reynolds numbers of 1000, 1500 and 2000, respectively. Furthermore, a possible reduction of the size of the cooling system is estimated using a percentage reduction of the Reynolds number, and a 28% and 33.3% maximum enhancement in PR\({}_{\rm Re}\) is recorded with conventional and thin plate-fin heat sinks, respectively, in comparison with non-vibrating heat sinks at a Reynolds value of 1000. 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. and R.A.-W.; writing--original draft preparation, A.H.D.K.R. ; writing--review and editing, M.S.N. and R.A.-W.; visualization, A.H.D.K.R. and M.S.N. ; supervision, M.S.N. 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. Figure 11: Percentage reduction in Reynolds number variation with vibrational characteristics at \(Re=1000\). **(a)** frequency at \(Ap=0.0015\) m; **(b)** amplitude at \(f=100\) Hz. **Funding:** The Ministry of Higher Education, Malaysia (MoHE) through The Fundamental Research Grant (FRGS)--grant number FRGS/1/2018/TK03/UTP/02/7, and Yayasan Universiti Teknologi PETRONAS (YUTP) research grant number 015 LC0-480. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding authors. The data are not publicly available, due to privacy. **Acknowledgments:** 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 also would like to acknowledge the financial assistance provided by Universiti Teknologi PETRONAS through its Yayasan Universiti Teknologi PETRONAS (YUTP) research grant number 015 LC0-480 for the supplementary funding of the publication fee. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**