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Technical Brief

An Analytical and Numerical Estimation of the Effective Thermal Conductivity of Complex Metal Frame Core Structures

[+] Author and Article Information
X. Bai

Graduate School of Science and Technology,
Shizuoka University,
3-5-1 Johoku,
Naka-ku,
Hamamatsu 432-8561, Japan

A. Nakayama

Faculty of Engineering,
Shizuoka University,
3-5-1 Johoku,
Naka-ku,
Hamamatsu 432-8561, Japan;
School of Civil Engineering and Architecture,
Wuhan Polytechnic University,
Wuhan 430023, Hubei, China
e-mail: nakayama.akira@shizuoka.ac.jp

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 15, 2018; final manuscript received November 5, 2018; published online December 13, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 141(2), 024504 (Dec 13, 2018) (5 pages) Paper No: HT-18-1673; doi: 10.1115/1.4041957 History: Received October 15, 2018; Revised November 05, 2018

An analytical and numerical study was conducted for estimation of the effective thermal conductivities of curved metal frame core structures, which can replace metal foams, in views of their advantages over the metal foams for both load bearing and heat dissipation. The trajectory of the frame ligament and its cross-sectional area were allowed to vary arbitrarily in the three-dimensional (3D) space. The analytical formula obtained by extending the formula previously proposed by Bai et al. (2017, “A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures,” ASME J. Heat Transfer, 140(5), p. 052001) was examined by comparing it with the numerical results directly obtained from full 3D numerical computations. An air layer partially filled with a collection of coiled circular rods was treated both analytically and numerically. Furthermore, the effect of lattice nodes on the effective thermal conductivity was investigated by introducing an analytical model with the lattice ligaments merging together at one nodal point. The analytical expressions thus derived for the lattice structures with nodes were applied to tetrahedral structure and octet-truss structure to find their effective thermal conductivities, which are found to agree closely with the 3D numerical results. Thus, the present analytical expressions can be used to customize the structure to meet its desired thermal performance.

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References

Dukhan, N. , 2013, Metal Foams: Fundamentals and Applications, DEStech Publications, Lancaster, PA.
Han, X. H. , Wang, Q. , Park, Y. G. , Tjoen, C. , Sommers, A. , and Jacobi, A. , 2012, “ A Review of Metal Foam and Metal Matrix Composites for Heat Exchangers and Heat Sinks,” Heat Transfer Eng., 33(12), pp. 991–1009. [CrossRef]
Lu, T. J. , Stone, H. A. , and Ashby, M. F. , 1998, “ Heat Transfer in Open-Cell Metal Foams,” Acta Mater., 46, pp. 3619–3635. [CrossRef]
Lemlich, R. , 1987, “ A Theory for the Limiting Conductivity of Polyhedral Foam at Low Density,” J. Colloid Interface Sci., 64(1), pp. 107–110. [CrossRef]
Krishnan, S. , Murthy, J. Y. , and Garimella, S. V. , 2006, “ Direct Simulation of Transport in Open-Cell Metal Foam,” ASME J. Heat Transfer, 128(8), pp. 793–799. [CrossRef]
Yang, C. , and Nakayama, A. , 2010, “ A Synthesis of Tortuosity and Dispersion in Effective Thermal Conductivity of Porous Media,” Int. J. Heat Mass Transfer, 53, pp. 3222–3230. [CrossRef]
Bai, X. , Hasan, C. , Mobedi, M. , and Nakayama, A. , 2017, “ A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures,” ASME J. Heat Transfer, 140(5), p. 052001.
Joo, J. H. , Kang, K. J. , Kim, T. , and Lu, T. J. , 2011, “ Forced Convective Heat Transfer in All Metallic Wire-Woven Bulk Kagome Sandwich Panels,” Int. J. Heat Mass Transfer, 54, pp. 5658–5662. [CrossRef]
Wadley, H. N. G. , 2006, “ Multifunctional Periodic Cellular Metals,” Phil. Trans. R. Soc. A, 364(1838), pp. 31–68. [CrossRef]
Evans, A. G. , Hutchinson, J. W. , Fleck, M. F. , Ashby, M. F. , and Wadley, H. N. G. , 2001, “ The Topological Design of Multifunctional Cellular Metals,” Mater. Sci., 46(3–4), pp. 309–327.
Krishnan, S. G. , Bolda, K. K. , Weibel, J. A. , and Garimella, S. V. , 2014, “ Numerical Investigation of Fluid Flow and Heat Transfer in Periodic Porous Lattice-Frame Materials,” 15th International Heat Transfer Conference, Kyoto, Japan, Aug. 10--15, pp. 6651–6665.
Kim, T. , Zhao, C. Y. , Lu, T. J. , and Hodson, H. P. , 2004, “ Convective Heat Dissipation With Lattice-Frame Materials,” Mech. Mater., 36(8), pp. 767–780. [CrossRef]
Kim, T. , Hodson, H. P. , and Lu, T. J. , 2004, “ Fluid-Flow and Endwall Heat-Transfer Characteristics of an Ultralight Lattice-Frame Material,” Int. J. Heat Mass Transfer, 47(6–7), pp. 1129–1140. [CrossRef]
Tian, J. , Kim, T. , Lu, T. J. , Hodson, H. P. , and Queheillalt, D. T. , 2004, “ The Effects of Topology Upon Fluid-Flow and Heat-Transfer Within Cellular Copper Structures,” Int. J. Heat Mass Transfer, 47(14–16), pp. 3171–3186. [CrossRef]
Yan, H. B. , Zhang, Q. C. , Lu, T. J. , and Kim, T. , 2015, “ A Lightweight X-Type Metallic Lattice in Single-Phase Forced Convection,” Int. J. Heat Mass Transfer, 83, pp. 273–283. [CrossRef]
Haydn, N. , Wadley, G. , and Queheillalt, D. T. , 2007, “ Thermal Applications of Cellular Lattice Structures,” Mater. Sci. Forum, 539–543, pp. 242–247.
Lu, T. J. , Xu, F. , and Wen, T. , 2013, Thermo-Fluid Behavior of Periodic Cellular Metals, Springer Press, Beijing, China.
Mobedi, M. , 2018, Private Communication.
Bai, X. , 2018, “ A Theoretical and Experimental Study of Ion Transport in Electrodialysis,” Ph.D. thesis, Shizuoka University, Shizuoka, Japan.
Bai, X. , and Nakayama, A. , 2018, “ A Numerical Investigation of Charged Ion Transport in Electrodialyzers With Spacers,” Desalination, 445, pp. 29–39. [CrossRef]
Deshpande, V. S. , Fleck, N. A. , and Ashby, M. P. , 2001, “ Effective Properties of the Octet-Truss Lattice Material,” J. Mech. Phys. Solids, 49(8), pp. 1747–1752. [CrossRef]
Dong, L. , Deshpande, V. , and Wadley, H. , 2015, “ Mechanical Response of Ti-6Al-4V Octet-Truss Lattice Structures,” Int. J. Solids Struct., 60–61, pp. 107–124. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Air layer with metal frames

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Fig. 2

Lattice ligaments merging at a node: (a) three ligaments merging at a node and (b) nodal model

Grahic Jump Location
Fig. 3

Air layer with a collection of coiled circular rods: (a) collection and (b) unit

Grahic Jump Location
Fig. 4

Effective thermal conductivity for a collection of coiled circular rods

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Fig. 5

Tetrahedral structure: (a) structural arrangement and (b) unit

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Fig. 6

Effective thermal conductivity for tetrahedral structure

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Fig. 7

Octet-truss structure

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Fig. 8

Effective thermal conductivity for octet-truss structure

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