Skip to main content
SpringerLink
Log in

Effective Thermal Conductivity Measurement of Additively Manufactured Lattice Structures by Application of Modified Temperature Profile Method

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

This study aims to establish a general-purpose thermal conductivity measurement method that can take into account the effect of heat loss under atmospheric conditions for measuring the effective thermal conductivity of lattice structures, and to clarify the effective thermal conductivity of lattice structures with different wire diameters. In this paper, calculations by finite element method and measurements using steady state comparative-longitudinal heat flow method and modified temperature profile method were performed to clarify the effective thermal conductivity of the five truncated octahedron unit-cell lattice structures with different wire diameters fabricated by additive manufacturing. The modified temperature profile method is developed to take into account the effect of interfacial thermal resistance in the measurement apparatus. The effective thermal conductivity measured using the steady state comparative-longitudinal heat flow method and calculated with finite element method analysis showed good agreement, confirming that the effective thermal conductivity is strongly dependent on the wire diameter. The effective thermal conductivity obtained by the modified temperature profile (MTP) method was 3 % to 24 % smaller than that obtained by the steady state comparative-longitudinal heat flow method, and the measurement was able to take heat loss into account more concretely. Furthermore, measurements using the MTP method enabled us to obtain reasonable values for the ratio of heat loss in each section, the fin efficiency of the sample, the heat transfer coefficient to the surroundings, and the interfacial thermal resistance between the rods and the sample.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data Availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(Q_{R}\) :

Amount of heat flow of rod (W)

\(k_{R}\) :

Thermal conductivity of rod (W⋅m−1⋅K−1)

\(A_{R}\) :

Cross-sectional area of rod (m2)

\(Q_{UR}\) :

Amount of heat flow of upper rod (W)

\(Q_{LR}\) :

Amount of heat flow of lower rod (W)

\(k_{eff}\) :

Effective thermal conductivity of sample for conventional method (W⋅m−1⋅K−1)

\(A_{S}\) :

Cross-sectional area of sample (m2)

\(Q_{C}\) :

Amount of heat flow through interface (W)

\(A_{g}\) :

Contact area of the interface (m2)

\(k_{exp}\) :

Effective thermal conductivity of sample for MTP method (W⋅m−1⋅K−1)

\(T_{UC}\) :

Temperature difference of upper cartridge block from the surroundings (K)

\(T_{LC}\) :

Temperature difference of lower cartridge block from the surroundings (K)

\(Q_{SLOS}\) :

Heat loss from sample to the surroundings (W)

\(Q_{ULOS}\) :

Heat loss from the rod and cartridge blocks at the upper side of the sample to the surroundings (W)

\(Q_{LLOS}\) :

Heat loss from the rod and cartridge blocks at the lower side of the sample to the surroundings (W)

\(S_{S}\) :

Surface area of the sample (m2)

\(S_{R}\) :

Surface area of the rod (m2)

\(S_{C}\) :

Surface area of the cartridge block (m2)

\(h\) :

Heat transfer coefficient giving the heat loss to the surroundings (W⋅m−2⋅K−1)

\(\phi\) :

Fin efficiency (–)

\(T_{US}\) :

Temperature difference of upper surface of the sample from the surroundings (K)

\(T_{LS}\) :

Temperature difference of lower surface of the sample from the surroundings (K)

\(Q_{LOS}\) :

Total heat loss to the surroundings (W)

\(R_{C}\) :

Interfacial thermal resistance of upper and lower interface of sample in case of assuming the interfacial thermal resistance of the upper and lower interface is the same for MTP method (km2⋅W−1)

\(Q_{UC}\) :

Amount of heat flow into sample (W)

\(Q_{LC}\) :

Amount of heat flow out of sample (W)

\(t_{C}\) :

Thickness of cartridge block (m)

\(k_{C}\) :

Thermal conductivity of cartridge block (W⋅m−1⋅K−1)

\(A_{C}\) :

Cross-sectional area of cartridge block (m2)

\(T_{x}\) :

Temperature rise profile in the direction of heat flow in the sample (K)

\(L_{S}\) :

Thickness of sample (m)

\(x\) :

Axial position on sample (m)

\(m^{ - 1}\) :

Thermal healing length (m)

\(P_{S}\) :

Perimeter of sample (m)

\(R^{2}\) :

Coefficient of determination (–)

\(T_{s1}\) :

Temperature raise of the measurement point closest to the upper rod at the sample (K)

\(T_{s3}\) :

Temperature raise of the measurement point closest to the lower rod at the sample (K)

\(x_{s1}\) :

Position of the measurement point closest to the upper rod at the sample (m)

\(x_{s3}\) :

Position of the measurement point closest to the lower rod at the sample (m)

\(R_{U}\) :

Interfacial thermal resistance between upper rod and sample in case of assuming the interfacial thermal resistance of the upper and lower interface is different for MTP method (m2⋅K−1⋅W−1)

\(R_{L}\) :

Interfacial thermal resistance between sample and lower rod in case of assuming the interfacial thermal resistance of the upper and lower interface is different for MTP method (m2⋅K−1⋅W−1)

References

  1. M.E. Korkmaz, M.K. Gupta, G. Robak, K. Moj, G.M. Krolczyk, M. Kuntoğlu, Development of lattice structure with selective laser melting process: a state of the art on properties, future trends and challenges. J. Manuf. Process. 81, 1040–1063 (2022)

    Article  Google Scholar 

  2. B.K. Nagesha, V. Dhinakaran, M. Varsha Shree, K.P. Manoj Kumar, D. Chalawadi, T. Sathish, Review on characterization and impacts of the lattice structure in additive manufacturing. Mater. Today Proc. 21, 916–919 (2020)

    Article  Google Scholar 

  3. L.-Y. Chen, S.-X. Liang, Y. Liu, L.-C. Zhang, Additive manufacturing of metallic lattice structures: unconstrained design, accurate fabrication, fascinated performances, and challenges. Mater. Sci. Eng. R Rep. 146, 100648 (2021)

    Article  Google Scholar 

  4. N. Lebaal, Y. Zhang, F. Demoly, S. Roth, S. Gomes, A. Bernard, Optimised lattice structure configuration for additive manufacturing. CIRP Ann. 68(1), 117–120 (2019)

    Article  Google Scholar 

  5. L. Zhang, B. Song, J.J. Fu, S.S. Wei, L. Yang, C.Z. Yan, H. Li, L. Gao, Y.S. Shi, Topology-optimized lattice structures with simultaneously high stiffness and light weight fabricated by selective laser melting: design, manufacturing and characterization. J. Manuf. Process. 56, 1166–1177 (2020)

    Article  Google Scholar 

  6. K. Kitazono, R. Tada, Y. Sugiyama, T. Miura, Effects of cell morphology and heat treatment on impact energy absorption property of porous aluminum used for landing gears of a small satellite. Aerosp. Technol. Jpn. 17, 115–119 (2018)

    ADS  Google Scholar 

  7. V. Acanfora, S. Saputo, A. Russo, A. Riccio, A feasibility study on additive manufactured hybrid metal/composite shock absorbers. Compos. Struct. 268, 113958 (2021)

    Article  Google Scholar 

  8. X.Z. Zhang, M. Leary, H.P. Tang, T. Song, M. Qian, Selective electron beam manufactured Ti–6Al–4V lattice structures for orthopedic implant applications: current status and outstanding challenges. Curr. Opin. Solid State Mater. Sci. 22(3), 75–99 (2018)

    Article  ADS  Google Scholar 

  9. Y. Koizumi, A. Okazaki, A. Chiba, T. Kato, A. Takezawa, Cellular lattices of biomedical Co–Cr–Mo-alloy fabricated by electron beam melting with the aid of shape optimization. Addit. Manuf. 12, 305–313 (2016)

    Google Scholar 

  10. R. Hatakenaka, T. Kinjo, M. Saitoh, H. Sugita, T. Yamamoto, Heat-transfer characteristics of a lightweight, fin-integrated PCM Unit manufactured by additive manufacturing. in Proceeding of 47th International Conference on Environmental Systems (2017). http://hdl.handle.net/2346/73104

  11. Y. Guo, H. Yang, G. Lin, H. Jin, X. Shen, J. He, J. Miao, Thermal performance of a 3D printed lattice-structure heat sink packaging phase change material. Chin. J. Aeronaut. 34(5), 373–385 (2021)

    Article  Google Scholar 

  12. J.Y. Ho, K.C. Leong, T.N. Wong, Experimental and numerical investigation of forced convection heat transfer in porous lattice structures produced by selective laser melting. Int. J. Therm. Sci. 137, 276–287 (2019)

    Article  Google Scholar 

  13. M. Khalil, M.I.H. Ali, K.A. Khan, R.A. Al-Rub, Forced convection heat transfer in heat sinks with topologies based on triply periodic minimal surfaces. Case Stud. Therm. Eng. 38, 102313 (2022)

    Article  Google Scholar 

  14. T. Dixit, E. Al-Hajri, M.C. Paul, P. Nithiarasu, S. Kumar, High performance, microarchitected, compact heat exchanger enabled by 3D printing. Appl. Therm. Eng. 210, 118339 (2022)

    Article  Google Scholar 

  15. A. Takezawa, X. Zhang, M. Kato, M. Kitamura, Method to optimize an additively-manufactured functionally-graded lattice structure for effective liquid cooling. Addit. Manuf. 28, 285–298 (2019)

    Google Scholar 

  16. 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. Addit. Manuf. 30, 100846 (2019)

    Google Scholar 

  17. D. Muñoz Codorníu, J.J. Moyano, M. Belmonte, M.I. Osendi, P. Miranzo, Thermal conduction in three-dimensional printed porous samples by high resolution infrared thermography. Open Ceram. 4, 100028 (2020)

    Article  Google Scholar 

  18. R.R. Sélo, S. Catchpole-Smith, I. Maskery, I. Ashcroft, C. Tuck, On the thermal conductivity of AlSi10Mg and lattice structures made by laser powder bed fusion. Addit. Manuf. 34, 101214 (2020)

    Google Scholar 

  19. J.-H. You, K. Park, Design and additive manufacturing of thermal metamaterial with high thermal resistance and cooling capability. Addit. Manuf. 41, 101947 (2021)

    Google Scholar 

  20. T. Ogushi, N. Iwamoto, Steady state longitudinal thermal conductivity measurement method of a thick specimen with low thermal conductivity MTP Method. J. Jpn. Inst. Electron. Packag. 21(2), 108–113 (2018)

    Article  Google Scholar 

  21. EOS GmbH—Electro Optical Systems, Material Data Sheet EOS Aluminium AlSi10Mg (2011). http://www.hvd.co.jp/assets/img/service/3d-printer/Aluminum.pdf

  22. Japanese Standards Association, JIS H 7903 (2008)

  23. H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd edn. (Oxford University Press, Oxford, 1959), p.139

    Google Scholar 

  24. J.E. Graebner, K. Azar, Thermal conductivity measurements in printed wiring boards. J. Heat Transfer 119, 401–405 (1997)

    Article  Google Scholar 

  25. Japan Society of Thermophysical Properties, Thermophysical Properties Handbook (2008), p. 213

  26. T. Ogushi, S. Yanaura, S. Watanabe, T. Hirata, Thermal conductivity measurement method for isotropic conductive adhesives. Netsu Bussei 28(1), 22–28 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical System Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, 464-8601, Japan

    Ryo Umemoto, Ai Ueno & Hosei Nagano

  2. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa, 252-5210, Japan

    Masatsugu Otsuki

  3. Advanced Knowledge Laboratory Inc., Heat Transfer & Cooling La., 1619, Kamiuchigami, Sanda, Hyougo, 669-1338, Japan

    Tetsuro Ogushi

Authors
  1. Ryo Umemoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ai Ueno
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hosei Nagano
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Masatsugu Otsuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tetsuro Ogushi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

RU: Conceptualization, Methodology, Investigation, Formal analysis, preparing figures, Writing—Original Draft. AU: Investigation, Resources, Writing—Review & Editing. HN: Conceptualization, Resources, Writing—Review & Editing, Funding acquisition. MO: Preparing test specimens, Review & Editing. TO: Conceptualization, Methodology, Supervision, Review & Editing.

Corresponding author

Correspondence to Hosei Nagano.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Umemoto, R., Ueno, A., Nagano, H. et al. Effective Thermal Conductivity Measurement of Additively Manufactured Lattice Structures by Application of Modified Temperature Profile Method. Int J Thermophys 44, 95 (2023). https://doi.org/10.1007/s10765-023-03206-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-023-03206-1

Keywords

Search

Navigation