Research Papers: Conduction

Pore Scale Investigation of Heat Conduction of High Porosity Open-Cell Metal Foam/Paraffin Composite

[+] Author and Article Information
Yuanpeng Yao

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: yaoyuanpeng@sjtu.edu.cn

Huiying Wu

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: whysrj@sjtu.edu.cn

Zhenyu Liu

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhenyu.liu@sjtu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 17, 2016; final manuscript received March 12, 2017; published online May 9, 2017. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 139(9), 091302 (May 09, 2017) (11 pages) Paper No: HT-16-1751; doi: 10.1115/1.4036526 History: Received November 17, 2016; Revised March 12, 2017

In this paper, a numerical model employing an approximately realistic three-dimensional (3D) foam structure represented by Weaire–Phelan foam cell is developed to study the steady-state heat conduction of high porosity open-cell metal foam/paraffin composite at the pore-scale level. The conduction problem is considered in a cubic representative computation unit of the composite material with a constant temperature difference between one opposite sides of the cubic unit (the other outer surfaces of the cubic unit are thermally insulated). The effective thermal conductivities (ETCs) of metal foam/paraffin composites are calculated with the developed pore-scale model considering small-scale details of heat conduction, which avoids using adjustable free parameters that are usually adopted in the previous analytical models. Then, the reason why the foam pore size has no evident effect on ETC as reported in the previous macroscopic experimental studies is explored at pore scale. Finally, the effect of air cavities existing within solid paraffin in foam pore region on conduction capacity of metal foam/paraffin composite is investigated. It is found that our ETC data agree well with the reported experimental results, and thus by direct numerical simulation (DNS), the ETC data of different metal foam/paraffin composites are provided for engineering applications. The essential reason why pore size has no evident effect on ETC is due to the negligible interstitial heat transfer between metal foam and paraffin under the present thermal boundary conditions usually used to determine the ETC. It also shows that overlarge volume fraction of air cavity significantly weakens the conduction capacity of paraffin, which however can be overcome by the adoption of high conductive metal foam due to enhancement of conduction.

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Liu, Z. , Yao, Y. , and Wu, H. , 2013, “ Numerical Modeling for Solid–Liquid Phase Change Phenomena in Porous Media: Shell-and-Tube Type Latent Heat Thermal Energy Storage,” Appl. Energy, 112, pp. 1222–1232. [CrossRef]
Nithyanandam, K. , and Pitchumani, R. , 2014, “ Computational Studies on Metal Foam and Heat Pipe Enhanced Latent Thermal Energy Storage,” ASME J. Heat Transfer, 136(5), p. 051503. [CrossRef]
Allen, M. J. , Bergman, T. L. , Faghri, A. , and Sharifi, N. , 2015, “ Robust Heat Transfer Enhancement During Melting and Solidification of a Phase Change Material Using a Combined Heat Pipe-Metal Foam or Foil Configuration,” ASME J. Heat Transfer, 137(10), p. 102301. [CrossRef]
Mancin, S. , Diani, A. , Doretti, L. , Hooman, K. , and Rossetto, L. , 2015, “ Experimental Analysis of Phase Change Phenomenon of Paraffin Waxes Embedded in Copper Foams,” Int. J. Therm. Sci., 90, pp. 79–89. [CrossRef]
Xiao, X. , Zhang, P. , and Li, M. , 2013, “ Preparation and Thermal Characterization of Paraffin/Metal Foam Composite Phase Change Material,” Appl. Energy, 112, pp. 1357–1366. [CrossRef]
Chen, J. , Yang, D. , Jiang, J. , Ma, A. , and Song, D. , 2014, “ Research Progress of Phase Change Materials (PCMs) Embedded With Metal Foam (A Review),” Procedia Mater. Sci., 4, pp. 389–394. [CrossRef]
Shiina, Y. , 2006, “ Reduction of Temperature Changes in Heat Transfer Fluid by the Use of Latent Heat Storage Technology,” Trans. At. Energy Soc. Jpn., 5(3), pp. 190–199. [CrossRef]
Hong, S. T. , and Herling, D. R. , 2007, “ Effects of Surface Area Density of Aluminum Foams on Thermal Conductivity of Aluminum Foam‐Phase Change Material Composites,” Adv. Eng. Mater., 9(7), pp. 554–557. [CrossRef]
Lafdi, K. , Mesalhy, O. , and Shaikh, S. , 2007, “ Experimental Study on the Influence of Foam Porosity and Pore Size on the Melting of Phase Change Materials,” J. Appl. Phys., 102(8), p. 083549. [CrossRef]
Xiao, X. , Zhang, P. , and Li, M. , 2014, “ Effective Thermal Conductivity of Open-Cell Metal Foams Impregnated With Pure Paraffin for Latent Heat Storage,” Int. J. Therm. Sci., 81, pp. 94–105. [CrossRef]
Yao, Y. , Wu, H. , and Liu, Z. , 2015, “ A New Prediction Model for the Effective Thermal Conductivity of High Porosity Open-Cell Metal Foams,” Int. J. Therm. Sci., 97, pp. 56–67. [CrossRef]
Calmidi, V. V. , and Mahajan, R. L. , 1999, “ The Effective Thermal Conductivity of High Porosity Fibrous Metal Foams,” ASME J. Heat Transfer, 121(2), pp. 466–471. [CrossRef]
Bhattacharya, A. , Calmidi, V. V. , and Mahajan, R. L. , 2002, “ Thermophysical Properties of High Porosity Metal Foams,” Int. J. Heat Mass Transfer, 45(5), pp. 1017–1031. [CrossRef]
Boomsma, K. , and Poulikakos, D. , 2011, “ Corrigendum for the Paper: K. Boomsma, D. Poulikakos, On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam [International Journal of Heat and Mass Transfer, 44 (2001) 827–836],” Int. J. Heat Mass Transfer, 54(1–3), pp. 746–748. [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]
Goodall, R. , Weber, L. , and Mortensen, A. , 2006, “ The Electrical Conductivity of Microcellular Metals,” J. Appl. Phys., 100(4), p. 044912. [CrossRef]
Assis, E. , Ziskind, G. , and Letan, R. , 2009, “ Numerical and Experimental Study of Solidification in a Spherical Shell,” ASME J. Heat Transfer, 131(2), p. 024502. [CrossRef]
Sundarram, S. S. , and Li, W. , 2014, “ The Effect of Pore Size and Porosity on Thermal Management Performance of Phase Change Material Infiltrated Microcellular Metal Foams,” Appl. Therm. Eng., 64(1–2), pp. 147–154. [CrossRef]
Hu, X. , Wan, H. , and Patnaik, S. S. , 2015, “ Numerical Modeling of Heat Transfer in Open-Cell Micro-Foam With Phase Change Material,” Int. J. Heat Mass Transfer, 88, pp. 617–626. [CrossRef]
Phelan, R. , Weaire, D. , and Brakke, K. , 1995, “ Computation of Equilibrium Foam Structures Using the Surface Evolver,” Exp. Math., 4(3), pp. 181–192. [CrossRef]
Kamath, P. M. , Balaji, C. , and Venkateshan, S. , 2013, “ Convection Heat Transfer From Aluminium and Copper Foams in a Vertical Channel—An Experimental Study,” Int. J. Therm. Sci., 64, pp. 1–10. [CrossRef]
Banhart, J. , 2006, “ Metal Foams: Production and Stability,” Adv. Eng. Mater., 8(9), pp. 781–794. [CrossRef]
Bock, J. , and Jacobi, A. M. , 2013, “ Geometric Classification of Open-Cell Metal Foams Using X-Ray Micro-Computed Tomography,” Mater. Charact., 75, pp. 35–43. [CrossRef]
Boomsma, K. , Poulikakos, D. , and Ventikos, Y. , 2003, “ Simulations of Flow Through Open Cell Metal Foams Using an Idealized Periodic Cell Structure,” Int. J. Heat Fluid Flow, 24(6), pp. 825–834. [CrossRef]
Kopanidis, A. , Theodorakakos, A. , Gavaises, E. , and Bouris, D. , 2010, “ 3D Numerical Simulation of Flow and Conjugate Heat Transfer Through a Pore Scale Model of High Porosity Open Cell Metal Foam,” Int. J. Heat Mass Transfer, 53(11), pp. 2539–2550. [CrossRef]
de Carvalho, T. P. , Morvan, H. P. , and Hargreaves, D. , 2014, “ Pore-Level Numerical Simulation of Open-Cell Metal Foams With Application to Aero Engine Separators,” ASME Paper No. GT2014-26402.
Calmidi, V. , and Mahajan, R. , 2000, “ Forced Convection in High Porosity Metal Foams,” ASME J. Heat Transfer, 122(3), pp. 557–565. [CrossRef]
Incropera, F. P. , 2011, Fundamentals of Heat and Mass Transfer, Wiley, New York.
Pettes, M. T. , Sadeghi, M. M. , Ji, H. , Jo, I. , Wu, W. , Ruoff, R. S. , and Shi, L. , 2015, “ Scattering of Phonons by High-Concentration Isotopic Impurities in Ultrathin Graphite,” Phys. Rev. B, 91(3), p. 035429
Hosseinizadeh, S. F. , Darzi, A. A. R. , and Tan, F. L. , 2012, “ Numerical Investigations of Unconstrained Melting of Nano-Enhanced Phase Change Material (NEPCM) Inside a Spherical Container,” Int. J. Therm. Sci., 51, pp. 77–83. [CrossRef]
Mózes, G. , ed., 1983, Paraffin Products, Vol. 14, Elsevier, New York.
Tian, Y. , and Zhao, C. Y. , 2011, “ A Numerical Investigation of Heat Transfer in Phase Change Materials (PCMs) Embedded in Porous Metals,” Energy, 36(9), pp. 5539–5546. [CrossRef]


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Fig. 1

Metal foam/paraffin composites: (a) copper foam/paraffinand (b) nickel foam/paraffin [5]

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Fig. 2

Microscopic images of realistic structure of open-cell metal foams: (a) nickel foam [5], (b) aluminum foam [21], and (c) copper foam

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Fig. 3

Representative foam cells: (a) Kelvin foam cell and (b) Weaire–Phelan foam cell

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Fig. 4

The Weaire–Phelan structures: (a) dry foam with foam cells included in a cubic unit cell and (b) wet foam

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Fig. 5

Open-cell metal foam structures having different porosities created with Weaire–Phelan cell

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Fig. 6

Metal foams with different pore sizes: (a) dfp = 4.34 mm and (b) dfp = 2.68 mm

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Fig. 7

Comparison between numerical results and predicted results by correlation (1) for asf of metal foam

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Fig. 8

Heat conduction problem of metal foam/paraffin composite at pore scale

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Fig. 9

Influences of pore size, porosity and material of metal foam on the ETC

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Fig. 10

ETCs of copper foam/paraffin composite obtained by the present pore-scale numerical model, pore-scale model in the literature [19], experiments in the literature [10,11], and analytical models in the previous studies [1214]

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Fig. 11

Temperature fields of metal foam/paraffin composite (ε = 0.949, dfp = 2.54 mm): (a) copper foam and (b) paraffin

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Fig. 12

Heat flux distributions in the heat transfer surfaces of metal foam/paraffin composite (ε = 0.949, dfp = 2.54 mm)

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Fig. 13

Influences of pore size, porosity, and material of metal foam on Qi/Qp and Qi/Qmf

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Fig. 14

Schematical diagram of influences of pore size and porosity on tortuous conduction paths of metal foam: (a) ε = 0.94, dfp = 2.54 mm; (b) ε = 0.94, dfp = 1.27 mm; and (c) ε = 0.98, dfp = 2.54 mm

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Fig. 15

Distribution of air cavity in cubic unit cell of metal foam/paraffin composite (the spherical surface shows the interface between paraffin and air cavity)

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Fig. 16

Variations of keff, kmf, and kfp with fac



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