The thermal tortuosity driven model of effective thermal conductivity and its application to triply periodic minimal surface structures

Novel biomimetic tortuous porous architectures, represented by triply periodic minimal surface (TPMS) structures, exhibit excellent thermal management potential. However, their geometric tortuosity complicates heat conduction paths, contradicting fundamental assumptions in many pre-existing models. In this paper, we established the correlation between geometric tortuosity and thermal tortuosity, demonstrating that thermal tortuosity prolongs conductive paths and impairs heat transfer efficiency. Accounting for thermal tortuosity effects, we propose the thermal tortuosity driven model for the effective thermal conductivities of porous structures and apply it to vacuum and water-filled TPMS structures. This is convenient for the study of heat transfer in porous structures and water-cooling devices. Both numerical studies and experiment reveal that the effective thermal conductivities of TPMS structures can be accurately predicted by the thermal tortuosity driven model. Comparative analysis shows that the overhangs in TPMS structures lead to more complex thermal tortuosity and reduce effective thermal conductivity. Consequently, the Gyroid structure exhibits the lowest effective thermal conductivities at the same porosity among TPMS structures. Graded porosity TPMS structures can achieve thermal insulation in high-porosity regions while enhance heat dissipation in low-porosity zones. This work provides a reliable effective thermal conductivities model for TPMS structures, which promotes their research and applications in thermal management of porous structures.