Experimental Measurement and Numerical Modelling of Solid Network-Based Schoen’s I-Graph—Wrapped Package (I-WP) toward Cooling Heat Sink

M. Yahya; A. Yahya; M. Z. Saghir

Abstract

Triply Periodic Minimal Surfaces (TPMS) are periodic implicit surfaces with zero-mean curvature. Zero-mean surfaces are those that locally have minimum surface area for a given boundary. This study investigates the thermal performance of a TPMS geometry, Schoen’s I-graph Wrapped Package (I-WP), for application as a compact heat sink. While most prior work focuses on gyroid-based TPMS structures, this research explores the less-studied I-WP architecture fabricated from copper with a fixed porosity of 0.7. The influence of unit cell size on convective heat transfer and flow resistance is examined both experimentally and numerically. Experimental testing was conducted for unit cell sizes of 4 mm, 6 mm and 8 mm, while numerical simulations using COMSOL Multiphysics extended the analysis to sizes of up to 14 mm. Strong agreement between the measured and simulated results (within a 3% temperature deviation and 7% for the local Nusselt number) validated the numerical model. Empirical correlations for the average Nusselt number were developed based on both experimental and numerical data. The novelty of this paper lies in the performance of the experiment for different flow rates and unit cell sizes. The study identified 12 mm as the optimal unit cell size, yielding the highest Performance Evaluation Criterion (PEC) and demonstrating an effective balance between thermal enhancement and hydraulic performance. Furthermore, uniform temperature distributions observed across the flow direction underscore the advantages of TPMS structures over conventional metal foams. These findings establish the I-WP geometry as a promising candidate for next-generation, geometrically tunable heat exchangers that can be enabled by additive manufacturing.

References

1.
Ahamed, M.K.; Wang, H.; Hazell, P.J. From biology to biomimicry: Using nature to build better structures–A review. Constr. Build. Mater. 2022, 320, 126195.
2.
Ahmed, N.; Barsoum, I.; Abu Al-Rub, R.K. Numerical investigation on the effect of residual stresses on the effective mechanical properties of 3D-printed TPMS lattices. Metals 2022, 12, 1344.
3.
Al-Ketan, O.; Abu Al-Rub, R.K. MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Mater. Des. Process. Commun. 2021, 3, e205.
4.
Al-Ketan, O.; Al-Rub, R.K.A.; Rowshan, R. The effect of architecture on the mechanical properties of cellular structures based on the I-WP minimal surface. J. Mater. Res. 2018, 33, 343–359.
5.
Baobaid, N.; Ali, M.I.; Khan, K.A.; et al. Fluid flow and heat transfer of porous TPMS architected heat sinks in free convection environment. Case Stud. Therm. Eng. 2022, 33, 101944.
6.
Su, X.; Zhang, Y.; Rao, Y.; et al. Experimental and Numerical Study on Flow and Heat Transfer Characteristics of Additively Manufactured Triply Periodic Minimal Surface (TPMS) Heat Exchangers for Micro Gas Turbine. Aerospace 2025, 5, 416.
7.
Wang, J.; Chen, K.; Zeng, M.; et al. Investigation on flow and heat transfer in various channels based on triply periodic minimal surfaces (TPMS). Energy Convers.Manag. 2023, 283, 116955.
8.
Tang, W.; Zhou, H.; Zeng, Y.; et al. Analysis on the convective heat transfer process and performance evaluation of Triply Periodic Minimal Surface (TPMS) based on Diamond, Gyroi (TPMS) based on Diamond, Gyroid and Iwp. Int. J. Heat Mass Transf. 2023, 201, 123642.
9.
Gandy, P.J.; Bardhan, S.; Mackay, A.L.; et al. Nodal surface approximations to the P, G, D and I-WP triply periodic minimal surfaces. Chem. Phys. Lett. 2001, 336, 187–195.
10.
Kobayashi, Y.; Ohnuki, R.; Yoshioka, S. Discovery of I-WP minimal-surface-based photonic crystal in the scale of a longhorn beetle. J. R. Soc. Interface 2021, 18. https://doi.org/10.1098/rsif.2021.0505.
11.
Montazerian, H.; Zhianmanesh, M.; Davoodi, E.; et al. Longitudinal and radial permeability analysis of additively manufactured porous scaffolds: Effect of pore shape and porosity. Mater. Des. 2017, 122, 146–156.
12.
Tang, W.; Zou, C.; Guo, J.; et al. Experimental Investigation on the Convective Heat Transfer Performance of Five Triply Periodic Minimal Surfaces (TPMS): Gyroid, Diamond, Iwp, Primitive, and Fischer-Koch-S. SSRN 2023. https://doi.org/10.2139/ssrn.4648952.
13.
Zhang, C.; Qiao, H.; Yang, L.; et al. Vibration characteristics of additive manufactured IWP-type TPMS lattice structures. Compos. Struct. 2024, 327, 117642.
14.
Men, Z.; Chen, W.; Li, Q.; et al. Topology optimization of the I-WP triply periodic minimal surfaces (TPMS) heat sink based on porous media effective model. Int. J. Heat Mass Transf. 2025, 240, 126657.
15.
Rajkumar, R.; Ramkumar, J.; Balani, K. Design of TPMS-based Uniform and Hybrid Graded Lattice Structures: A Fluid Flow Analysis. MATEC Web Conf. 2024, 401, 11001.
16.
Qureshi, Z.A.; Al-Omari, S.A.B.; Elnajjar, E.; et al. Using triply periodic minimal surfaces (TPMS)-based metal foams structures as skeleton for metal-foam-PCM composites for thermal energy storage and energy management applications. Int. Commun. Heat Mass Transf. 2021, 124, 105265.
17.
Ouda, M.; Al-Ketan, O.; Sreedhar, N.; et al. Novel static mixers based on triply periodic minimal surface (TPMS) architectures. J. Environ. Chem. Eng. 2020, 85, 104289.
18.
Yeranee, K.; Rao, Y. A review of recent investigations on flow and heat transfer enhancement in cooling channels embedded with triply periodic minimal surfaces (TPMS). Energies 2022, 15, 8994.
19.
Saghir, M.Z.; Yahya, M.; Ortiz, P.D.; et al. Heat Enhancement of Ethylene Glycol/Water Mixture in the Presence of Gyroid TPMS Structure: Experimental and Numerical Comparison. Processes 2025, 13, 228.
20.
Saghir, M.Z.; Yahya, M. Convection Heat Transfer and Performance Analysis of a Triply Periodic Minimal Surface (TPMS) for a Novel Heat Exchanger. Energies 2024, 17, 4275.
21.
COMSOL Software, Version 6.2; COMSOL, Inc.: Burlington, MA, USA, 2024.

Scilight Press

Author Information

Abstract

Keywords

References

About Scilight

Journals

Publishing Policies

Contact Us