The Heat Dissipation Effect of Liquid Cooling Heat Sink Based on Triply Periodic Minimal Surface Structure

Abstract:

This study explores the use of Triply Periodic Minimal Surface (TPMS) structures, Schwarz Primitive, Diamond, and Gyroid, as liquid cooling heat sinks to enhance heat dissipation. Both uniform and graded-density designs were evaluated through numerical simulations and validated via metal additive manufacturing using AlSi10Mg alloy. The results show that increasing TPMS density improves thermal conductivity, while graded-density configurations offer a balanced performance between conduction and convection. Among the tested models, the graded-density Gyroid structure demonstrated the most efficient heat transfer, suggesting that TPMS-based heat sinks, particularly with density gradation, hold strong potential for next-generation thermal solutions in high heat flux environments.

• Periodical: Key Engineering Materials (Volume 1059)
• Pages: 57-64
• DOI: https://doi.org/10.4028/p-4DryyJ
• Online since: June 2026
• Authors: Shien Kai Liao, Jun Zin Zhang, Hung Yuan Li, Cheng Hsien Kuo*
• Keywords: Graded Density Structures, Numerical Simulation, Thermal Management, Triply Periodic Minimal Surfaces (TPMS)

References

[1] Zulfiqar Khattak, Hafiz Muhammad Ali, Air cooled heat sink geometries subjected to forced flow: A critical review, International Journal of Heat and Mass Transfer, 2019.

DOI: 10.1016/j.ijheatmasstransfer.2018.08.048

[2] Xilei Wu, Jialiang Yang, Ying Liu, Yuan Zhuang, Song Luo, Yuhao Yan, Longhuang Xiao, Xiaohong Han, Investigations on heat dissipation performance and overall characteristics of two-phase liquid immersion cooling systems for data center, International Journal of Heat and Mass Transfer, April 2025.

DOI: 10.1016/j.ijheatmasstransfer.2024.126575

[3] Hamdi E. Ahmed , B.H. Salman, A.Sh. Kherbeet , M.I. Ahmed, Optimization of thermal design of heat sinks: A review. International Journal of Heat and Mass Transfer, 2018.

DOI: 10.1016/j.ijheatmasstransfer.2017.10.099

[4] Md Atiqur Rahman, S. M. Mozammil Hasnain, Prabhu Paramasivam, Abinet Gosaye Ayanie, Advancing thermal management in electronics:a review of innovative heat sink designs and optimization techniques, RSC Advances, 2024.

DOI: 10.1039/d4ra05845c

[5] David Southall, Renaud Le Pierres, Stephen John Dewson, Stephen John Dewson, Design Considerations for Compact Heat Exchangers, Proceedings of ICAPP '08, 2008.

[6] Mohamed G. Gado, Thermal management and heat transfer enhancement of electronic devices using integrative phase change material (PCM) and triply periodic minimal surface (TPMS) heat sinks, Applied Thermal Engineering, 2025.

DOI: 10.1016/j.applthermaleng.2024.124504

[7] Muhammad Usman Shahid, Muhammad Mahabat Khan, Muhammad Noman Shahid, Numerical Investigation of the Heat Transfer Rate and Fluid Flow Characteristics of Conventional and Triply Periodic Minimal Surface (TPMS)-Based Heat Sinks, MDPI Engineering proceedings, 2024.

DOI: 10.3390/engproc2024075035

[8] Schwarz, H.A., Gesammelte Mathematische Abhandlungen, Julius Springer, 1890.

[9] Schoen, A.H., Infinite periodic minimal surfaces without self-intersections, Electronics Research Center Cambridge, Mass, 1970.

[10] Zo-Han Lin, Jyun-Hong Pan, Hung-Yuan Li, Mechanical Strength of Triply Periodic Minimal Surface Lattices Subjected to Three-Point Bending, Polymers, 2022.

DOI: 10.3390/polym14142885

[11] S. Catchpole-Smith , R.R.J. Sélo, A.W. Davis, I.A. Ashcroft, C.J. Tuck, A. Clare, Thermal conductivity of TPMS lattice structures manufactured via laser powder bed fusion, Additive Manufacturing, 2019.

DOI: 10.1016/j.addma.2019.100846

[12] Nada Baobaid, Mohamed I. Ali, Kamran A. Khan, Rashid K. Abu Al-Rub, Fluid flow and heat transfer of porous TPMS architected heat sinks in free convection environment, Case Studies in Thermal Engineering, 2022.

DOI: 10.1016/j.csite.2022.101944

[13] Wei Tang, Hua Zhou, Yun Zeng, Minglei Yan, Chenglu Jiang, Ping Yang, Qing Li, Zhida Li, Junheng Fu, Yi Huang, Yang Zhao, Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroid and Iwp, International Journal of Heat and Mass Transfer, 2023.

DOI: 10.1016/j.ijheatmasstransfer.2022.123642

[14] Guanghan Yan, Mingrui Sun, Yiqiang Liang, Shuai Li, Zhaoda Zhang, Xiaokai Zhang, Yongchen Song, Yu Liu, Jiafei Zhao, Simulation and experimental study on flow and heat transfer performance of sheet-network and solid-network disturbance structures based on triply periodic minimal surface, International Journal of Heat and Mass Transfer, 2024.

DOI: 10.1016/j.ijheatmasstransfer.2023.124905

[15] Eric A. Lord, Alan L. Mackay, Periodic Minimal Surfaces of Cubic Symmetry, Current Science, 2003.

[16] H.G. von Schnering, R. Nesper , Nodal surfaces of Fourier series: Fundamental invariants of structured matter, Zeitschrift für Physik B Condensed Matter, 1991.

DOI: 10.1007/bf01313411

[17] Albert E. Patterson, Nasiha Muna, Simple 3-D Visualization of Some Common Mathematical Minimal Surfaces using MATLAB. Illinois Digital Environment for Access to Learning and Scholarship, 2018.

[18] Lorna J. Gibson, Michael F. Ashby, Cellular Solids: Structure and Properties, 2ed., Cambridge University Press, 1997.

[19] Dong-Jin Yoo, Advanced Porous Scaffold Design using Multi-Void Triply Periodic Minimal Surface Models with High Surface Area to Volume Ratios, International Journal of Precision Engineering and Manufacturing, 2014.

DOI: 10.1007/s12541-014-0516-5

[20] Mohamad Ziad Saghir, Mohammad M. Rahman, Effectiveness in Cooling a Heat Sink in the Presence of a TPMS Porous Structure Comparing Two Different Flow Directions, Fluids, 2024.

DOI: 10.3390/fluids9120297