Open-cell porous metals for thermal management applications: Fluid flow and heat transfer

Abstract

Porous metals are produced by a wide range of industrially applied techniques, and the resulting porous structure is a characteristic of the manufacturing method chosen. This review firstly provides an overview of the different techniques to manufacture open-cell porous metals, highlighting the distinction between the resulting porous structures. The effects of the structural parameters on the fluid flow properties and heat transfer in porous metals are also discussed. It was evident from literature that there exist optimum structural parameters which offered maximum thermal exchange performance. Therefore, the last part of this review outlines the current research on porous metals for thermal management applications, which focuses on optimising the design of the porous metal structure to improve the heat transfer performance.

This review was submitted as part of the 2016 Materials Literature Review Prize of the Institute of Materials, Minerals and Mining run by the Editorial Board of MST. Sponsorship of the prize by TWI Ltd is gratefully acknowledged

Keywords

Porous metals Open-cell Fluid flow Heat transfer Thermal management

Get full access to this article

View all access options for this article.

References

Dukhan

: ‘Metal foams: fundamentals and applications'; 2013, Lancaster, PA, DEStech Publications, Inc.

Ashby

M. F.

, Evans

A. G.

, Fleck

N. A.

, Gibson

L. J.

, Hutchinson

J. W.

and Wadley

H. N. G.

: ‘Metal foams: a design guide’; 2000, Burlington, Butterworth-Heinemann.

Banhart

: ‘Manufacture, characterisation and application of cellular metals and metal foams', Prog. Mater. Sci., 2001, 46, (6), 559–632. doi: 10.1016/S0079-6425(00)00002-5

Banhart

, Ashby

and Fleck

: ‘Metal foams and porous metal structures'; 1999, Breman, Germany, MIT.

Ghosh

: ‘How good Is open-cell metal foam as heat transfer surface?’, J. Heat Trans., 2009, 131, (10), 101004-1–101004-8. DOI 10.1115/1.3160537. doi: 10.1115/1.3160537

, Zhang

H.-W.

, Li

Y.-X.

, Liu

, Chen

and He

: ‘Fabrication and wettability of monolithic bimodal porous Cu with Gasar macro-pores and de-alloying nano-pores', Appl. Surf. Sci., 2015, 353, (30), 804–810. doi: 10.1016/j.apsusc.2015.07.020

Harte

A. M.

, Fleck

N. A.

and Ashby

M. F.

: ‘Fatigue failure of an open cell and a closed cell aluminium alloy foam’, Acta Mater., 1999, 47, (8), 2511–2524. doi: 10.1016/S1359-6454(99)00097-X

Sharafat

, Ghoniem

, Sawan

, Ying

and Williams

: ‘Breeder foam: an innovative low porosity solid breeder material’, Fusion Eng. Des., 2006, 81, (1–7), 455–460. doi: 10.1016/j.fusengdes.2005.06.374

Fujibayashi

, Neo

, Kim

H. M.

, Kokubo

and Nakamura

: ‘Osteoinduction of porous bioactive titanium metal’, Biomaterials, 2004, 25, (3), 443–450. doi: 10.1016/S0142-9612(03)00551-9

10.

Eisenmann

: ‘ASM handbook’; 1998, Novelty, OH, ASM International.

11.

Gladysz

G. M.

and Chawla

K. K.

: ‘Voids in materials: from unavoidable defects to designed cellular materials'; 2015, Amsterdam, Elsevier.

12.

Bram

, Stiller

, Buchkremer

H. P.

, Stöver

and Baur

: ‘High-porosity titanium, stainless steel, and superalloy parts', Adv. Eng. Mater., 2000, 2, (4), 196–199. doi: 10.1002/(SICI)1527-2648(200004)2:4<196::AID-ADEM196>3.0.CO;2-K

13.

Zhao

Y. Y.

, Fung

, Zhang

L. P.

and Zhang

F. L.

: ‘Lost carbonate sintering process for manufacturing metal foams', Scr. Mater., 2005, 52, (4), 295–298. doi: 10.1016/j.scriptamat.2004.10.012

14.

, Yang

Q. M.

and Zhitomirsky

: ‘Nickel foam-based manganese dioxide–carbon nanotube composite electrodes for electrochemical supercapacitors', J. Power Sources, 2008, 185, (2), 1569–1574. doi: 10.1016/j.jpowsour.2008.07.057

15.

Liu

P. S.

and Chen

G. F.

: ‘Chapter 1 – general introduction to porous materials’ in ‘Porous Materials’, (ed. Chen

P. S. L. F.

), 1–20; 2014, Boston, MA, Butterworth-Heinemann.

16.

Shapovalov

V. I.

: ‘Porous and cellular materials for structural applications', MRS Symp. Proc., San Francisco, California, USA, 13–15 April, 1998, 281–290.

17.

Pal

, Joyce

M. K.

and Fleming

P. D.

: ‘A simple method for calculation of the permeability coefficient of porous media’, Tappi J., 2006, 5, (9), 10–16.

18.

Darcy

: ‘Les fontaines publiques de la ville de dijon’; 1856, Paris, Dalmont.

19.

Tiab

and Donaldson

E. C.

: ‘Chapter 7 – applications of Darcy's law’ in ‘Petrophysics’, 2nd edn. (ed. D. Tiab and E. Donaldson), 419–483; 2012, Boston, MA, Gulf Professional Publishing.

20.

Preziosi

and Farina

: ‘On Darcy's law for growing porous media’, Int. J. Non-Linear Mech., 2002, 37, (3), 485–491. doi: 10.1016/S0020-7462(01)00022-1

21.

Gibson

A. G.

: ‘Modification of Darcy's law to model mould interface effects in composites processing’, Comp. Manuf., 1992, 3, (2), 113–118. doi: 10.1016/0956-7143(92)90123-C

22.

Davis

P. A.

, Olague

N. E.

and Goodrich

M. T.

: ‘Application of a validation strategy to Darcy's experiment’, Adv. Water Resour., 1992, 15, (3), 175–180. doi: 10.1016/0309-1708(92)90022-T

23.

Wright

: ‘Nonlinear flow through granular media’, J. Hydraul. Div., 1968, 94, (4), 851–872.

24.

Cornell

and Katz

D. L.

: ‘Flow of gases through consolidated porous media’, Ind. Eng. Chem., 1953, 45, (10), 2145–2152. doi: 10.1021/ie50526a021

25.

Geertsma

: ‘Estimating the coefficient of inertial resistance in fluid flow through porous media’, Soc. Petrol. Eng. J., 1974, 14, (5), 445–450. doi: 10.2118/4706-PA

26.

Liu

, Civan

and Evans

R. D.

: ‘Correlation of the non-Darcy flow coefficient’, J. Can. Petrol. Tech., 1995, 34, (10), 50–54.

27.

and Engler

T. W.

: ‘Literature review on correlations of the non-Darcy coefficient’, SPE Permian Basin Oil and Gas Recovery Conference, Midland, TX, 15–17 May 2001, Society of Petroleum Engineers ; 2001.

28.

White

: ‘Fluid mechanics’, 7th edn; 2009, New York, McGraw-Hill.

29.

Kececioglu

and Jiang

: ‘Flow through porous media of packed spheres saturated with water’, J. Fluid Eng., 1994, 116, (1), 164–170. doi: 10.1115/1.2910229

30.

Farkas

, Zhong

and Guiochon

: ‘Validity of Darcy's law at low flow-rates in liquid chromatography’, J. Chromatogr. A, 1999, 849, (1), 35–43. doi: 10.1016/S0021-9673(99)00482-3

31.

Ergun

and Orning

A. A.

: ‘Fluid flow through randomly packed columns and fluidized beds', Ind. Eng. Chem., 1949, 41, (6), 1179–1184. doi: 10.1021/ie50474a011

32.

Hassanizadeh

S. M.

and Gray

: ‘High velocity flow in porous media’, Transp. Porous. Med., 1987, 2, (6), 521–531. doi: 10.1007/BF00192152

33.

Blick

E. F.

and Civan

: ‘Porous-media momentum equation for highly accelerated flow’, SPE Reserv. Eng., 2013, 3, (3), 1048–1052. doi: 10.2118/16202-PA

34.

Du Plessis

J. P.

and Masliyah

: ‘Mathematical modelling of flow through consolidated isotropic porous media’, Transp. Porous. Med., 1988, 3, (2), 145–161. doi: 10.1007/BF00820342

35.

Thauvin

and Mohanty

K. K.

: ‘Network modelling of non-Darcy flow through porous media’, Transp. Porous. Med., 1998, 31, (1), 19–37. doi: 10.1023/A:1006558926606

36.

Zeng

and Grigg

: ‘A criterion for non-Darcy flow in porous media’, Transp. Porous. Med., 2006, 63, (1), 57–69. doi: 10.1007/s11242-005-2720-3

37.

Bonnet

J. P.

, Topin

and Tadrist

: ‘Flow laws in metal foams: compressibility and pore size effects', Transp. Porous. Med., 2008, 73, (2), 23–254. doi: 10.1007/s11242-007-9169-5

38.

Despois

J. F.

and Mortensen

: ‘Permeability of open-pore microcellular materials', Acta Mater., 2005, 53, (5), 1381–1388. doi: 10.1016/j.actamat.2004.11.031

39.

Boomsma

and Poulikakos

: ‘The effects of compression and pore size variations on the liquid flow characteristics in metal foams', J. Fluid Eng., 2001, 124, (1), 263–272. doi: 10.1115/1.1429637

40.

Dukhan

, Bağcı

Ö.

and Özdemir

: ‘Metal foam hydrodynamics: flow regimes from pre-Darcy to turbulent’, Int. J. Heat Mass Transf., 2014, 77, 114–123. doi: 10.1016/j.ijheatmasstransfer.2014.05.017

41.

Zhong

, Li

, Liu

, Tao

, Lu

and Kagawa

: ‘Measurement and correlation of pressure drop characteristics for air flow through sintered metal porous media’, Transp. Porous. Med., 2014, 101, (1), 53–67. doi: 10.1007/s11242-013-0230-2

42.

Dukhan

and Ali

: ‘Strong wall and transverse size effects on pressure drop of flow through open-cell metal foam’, Int. J. Therm. Sci., 2012, 57, 85–91. doi: 10.1016/j.ijthermalsci.2012.02.017

43.

Baloyo

J. M.

and Zhao

: ‘Heat transfer performance of micro-porous copper foams with homogeneous and hybrid structures manufactured by Lost Carbonate Sintering’, MRS Online Pro. Lib. Arch., 2015, 1779, 39–44. doi: 10.1557/opl.2015.699

44.

Costa

: ‘Permeability-porosity relationship: a re-examination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption’, Geophys. Res. Lett., 2006, 33, (2). doi: 10.1029/2005GL025134

45.

Ghabezloo

, Sulem

and Saint-Marc

: ‘Evaluation of a permeability–porosity relationship in a low-permeability creeping material using a single transient test’, Int. J. Rock Mech. Min., 2009, 46, (4), 761–768. doi: 10.1016/j.ijrmms.2008.10.003

46.

Moreira

E. A.

, Innocentini

M. D. M.

and Coury

J. R.

: ‘Permeability of ceramic foams to compressible and incompressible flow’, J. Eur. Ceram. Soc., 2004, 24, (10–11), 3209–3218. doi: 10.1016/j.jeurceramsoc.2003.11.014

47.

Davies

and Zhen

: ‘Metallic foams: their production, properties and applications', J. Mater. Sci., 1983, 18, (7), 1899–1911. doi: 10.1007/BF00554981

48.

Khayargoli

, Loya

, Lefebvre

and Medraj

: ‘The impact of microstructure on the permeability of metal foams', CSME Forum, 2004, 2004, 220–228.

49.

Bhattacharya

, Calmidi

V. V.

and Mahajan

R. L.

: ‘Thermophysical properties of high porosity metal foams', Int. J. Heat Mass Trans., 2002, 45, (5), 1017–1031. doi: 10.1016/S0017-9310(01)00220-4

50.

Xiao

and Zhao

: ‘Heat transfer coefficient of porous copper with homogeneous and hybrid structures in active cooling’, J. Mater. Res., 2013, 28, (17), 2545–2553. doi: 10.1557/jmr.2013.190

51.

Sun

, Tang

and Cheng

: ‘Numerical simulation for tortuosity of porous media’, Micro. Meso. Mater., 2013, 173, 37–42. doi: 10.1016/j.micromeso.2013.01.035

52.

Matyka

and Koza

: ‘How to calculate tortuosity easily?’, AIP Conf. Proc., 2012, 1453, (1), 17–22. doi: 10.1063/1.4711147

53.

Liu

P. S.

: ‘A new method for calculating the specific surface area of porous metal foams', Philos. Mag. Lett., 2010, 90, (6), 447–453. doi: 10.1080/09500831003745571

54.

Liu

J. F.

, Wu

W. T.

, Chiu

W. C.

and Hsieh

W. H.

: ‘Measurement and correlation of friction characteristic of flow through foam matrixes', Exp. Therm. Fluid Sci., 2006, 30, (4), 329–336. doi: 10.1016/j.expthermflusci.2005.07.007

55.

Richardson

J. T.

, Peng

and Remue

: ‘Properties of ceramic foam catalyst supports: pressure drop’, Appl. Catal. A Gen., 2000, 204, (1), 19–32. doi: 10.1016/S0926-860X(00)00508-1

56.

Garboczi

E. J.

: ‘Permeability, diffusivity, and microstructural parameters: a critical review’, Cement Concrete Res., 1990, 20, (4), 591–601. doi: 10.1016/0008-8846(90)90101-3

57.

: ‘Review of permeability evolution model for fractured porous media’, J. Rock Mech. Geotech. Eng., 2015, 7, (3), 351–357. doi: 10.1016/j.jrmge.2014.12.003

58.

Alkan

: ‘Percolation model for dilatancy-induced permeability of the excavation damaged zone in rock salt’, Int. J. Rock Mech. Min., 2009, 46, (4), 716–724. doi: 10.1016/j.ijrmms.2008.08.002

59.

Dienes

J. K.

: ‘Permeability, percolation and statistical crack mechanics', Proc. 23rd Symp. on ‘Rock Mech. Am. Inst. Min. Metall. Petrol. Eng.’, New York, USA, 1983, 86.

60.

Sahimi

: ‘Linear and nonlinear, scalar and vector transport processes in heterogeneous media: fractals, percolation, and scaling laws', Chem. Eng. J. Biochem. Eng. J., 1996, 64, (1), 21–44. doi: 10.1016/S0923-0467(96)03103-X

61.

Bayles

G. A.

, Klinzing

G. E.

and Chiang

S.-H.

: ‘Fractal mathematics applied to flow in porous systems', Part. Part. Sys. Char., 1989, 6, (1–4), 168–175. doi: 10.1002/ppsc.19890060128

62.

Rodriguez

, Giacomelli

and Vazquez

: ‘Permeability-porosity relationship in RTM for different fiberglass and natural reinforcements', J. Compos. Mater., 2004, 38, (3), 259–268. doi: 10.1177/0021998304039269

63.

Zhu

and Wong

T.-F.

: ‘The transition from brittle faulting to cataclastic flow: permeability evolution’, J. Geophys. Res. Solid Earth, 1997, 102, (B2), 3027–3041. doi: 10.1029/96JB03282

64.

Nelson

P. H.

: ‘Permeability–porosity relationships in sedimentary rocks', Log Analyst, 1994, 35, (3), 38–62.

65.

Bethke

C. M.

: ‘A numerical model of compaction-driven groundwater flow and heat transfer and its application to the paleohydrology of intracratonic sedimentary basins', J. Geophys.Res. Solid Earth, 1985, 90, (B8), 6817–6828. doi: 10.1029/JB090iB08p06817

66.

Morris

J. P.

, Lomov

I. N.

and Glenn

L. A.

: ‘A constitutive model for stress-induced permeability and porosity evolution of berea sandstone’, J. Geophys. Res. Solid Earth, 2003, 108, (B10). doi: 10.1029/2001JB000463

67.

Yang

and Aplin

A. C.

: ‘A permeability–porosity relationship for mudstones', Mari. Petrol. Geol., 2010, 27, (8), 1692–1697. doi: 10.1016/j.marpetgeo.2009.07.001

68.

Walsh

J. B.

and Brace

W. F.

: ‘The effect of pressure on porosity and the transport properties of rock’, J. Geophys. Res. Solid Earth, 1984, 89, (B11), 9425–9431. doi: 10.1029/JB089iB11p09425

69.

DeWitt

, Incropera

, Bergman

and Lavine

: ‘Introduction to heat transfer’; 2007, Hoboken, NJ, John Wiley & Sons.

70.

Ashby

M.G. L.

: ‘Cellular solids technology’; 1998, Oxford, Pergamon Press.

71.

Zhao

C. Y.

, Lu

T. J.

, Hodson

H. P.

and Jackson

J. D.

: ‘The temperature dependence of effective thermal conductivity of open-celled steel alloy foams', Mater. Sci. Eng. A, 2004, 367, (1–2), 123–131. doi: 10.1016/j.msea.2003.10.241

72.

Kaviany

: ‘Principles of heat transfer in porous media’; 1995, New York, Springer.

73.

Nield

and Bejan

: ‘Forced convection’ in ‘Convection in porous media’, (ed. D. Nield and A. Bejan), 69–143; 2013, New York, Springer.

74.

Calmidi

V. V.

and Mahajan

R. L.

: ‘The effective thermal conductivity of high porosity fibrous metal foams', J. Heat Trans., 1999, 121, (2), 466–471. doi: 10.1115/1.2826001

75.

Boomsma

and Poulikakos

: ‘On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam’, Int. J. Heat Mass Trans., 2001, 44, (4), 827–836. doi: 10.1016/S0017-9310(00)00123-X

76.

Dai

, Nawaz

, Park

Y. G.

, Bock

and Jacobi

A. M.

: ‘Correcting and extending the Boomsma–Poulikakos effective thermal conductivity model for three-dimensional, fluid-saturated metal foams', Int. Commun. Heat Mass Trans., 2010, 37, (6), 575–580. doi: 10.1016/j.icheatmasstransfer.2010.01.015

77.

Paek

J. W.

, Kang

B. H.

, Kim

S. Y.

and Hyun

J. M.

: ‘Effective thermal conductivity and permeability of aluminium foam materials', Int. J. Thermophys., 2000, 21, (2), 453–464. doi: 10.1023/A:1006643815323

78.

Babcsán

, Mészáros

and Hegman

: ‘Thermal and electrical conductivity measurements on aluminium foams', Materwiss. Werksttech., 2003, 34, (4), 391–394. doi: 10.1002/mawe.200390081

79.

Ding

X. R.

, Lu

L. S.

, Chen

, He

Z. S.

and Ou

D. S.

: ‘Heat transfer enhancement by using four kinds of porous structures in a heat exchanger’, Appl. Mech. Mater., 2011, 52–54, 1632–1637. doi: 10.4028/www.scientific.net/AMM.52-54.1632

80.

Hunt

M. L.

and Tien

C. L.

: ‘Effects of thermal dispersion on forced convection in fibrous media’, Int. J. Heat Mass Trans., 1988, 31, (2), 301–309. doi: 10.1016/0017-9310(88)90013-0

81.

Kim

S. Y.

, Paek

J. W.

and Kang

B. H.

: ‘Flow and heat transfer correlations for porous fin in a plate-fin heat exchanger’, J. Heat Trans., 2000, 122, (3), 572–578. doi: 10.1115/1.1287170

82.

Hwang

J. J.

, Hwang

G. J.

, Yeh

R. H.

and Chao

C. H.

: ‘Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams', J. Heat Trans., 2001, 124, (1), 120–129. doi: 10.1115/1.1416690

83.

Seyf

H. R.

and Layeghi

: ‘Numerical analysis of convective heat transfer from an elliptic pin fin heat sink with and without metal foam insert’, J. Heat Trans., 2010, 132, (7), DOI 071401-1-071401-9. doi: 10.1115/1.4000951

84.

Zhao

C. Y.

, Kim

, Lu

T. J.

and Hodson

H. P.

: ‘Thermal transport in high porosity cellular metal foams', J. Thermophys. Heat Trans., 2004, 18, (3), 309–317. doi: 10.2514/1.11780

85.

Mancin

, Zilio

, Diani

and Rossetto

: ‘Experimental air heat transfer and pressure drop through copper foams', Exp. Therm. Fluid Sci., 2012, 36, 224–232. doi: 10.1016/j.expthermflusci.2011.09.016

86.

Tamayol

and Hooman

: ‘Thermal assessment of forced convection through metal foam heat exchangers', J. Heat Trans., 2011, 133, (11), 111801-1–111801-7. DOI 10.1115/1.4004530. doi: 10.1115/1.4004530

87.

Mahdi

R. A.

, Mohammed

H. A.

, Munisamy

K. M.

and Saeid

N. H.

: ‘Review of convection heat transfer and fluid flow in porous media with nanofluid’, Renew. Sust. Energ. Rev., 2015, 41, 715–734. doi: 10.1016/j.rser.2014.08.040

88.

Ejlali

, Ejlali

, Hooman

and Gurgenci

: ‘Application of high porosity metal foams as air-cooled heat exchangers to high heat load removal systems', Int. Commun. Heat Mass Trans., 2009, 36, (7), 674–679. doi: 10.1016/j.icheatmasstransfer.2009.03.001

89.

Boomsma

, Poulikakos

and Zwick

: ‘Metal foams as compact high performance heat exchangers', Mech. Mater., 2003, 35, (12), 1161–1176. doi: 10.1016/j.mechmat.2003.02.001

90.

Mao

, Love

, Leanos

and Rodriguez-Melo

: ‘Correlation studies of hydrodynamics and heat transfer in metal foam heat exchangers', App. Therm. Eng., 2014, 71, (1), 104–118. doi: 10.1016/j.applthermaleng.2014.06.035

91.

Tuckerman

D. B.

and Pease

R. F. W.

: ‘High-performance heat sinking for VLSI’, IEEE Electron Dev. Lett., 1981, 2, (5), 126. doi: 10.1109/EDL.1981.25367

92.

Zhang

H. Y.

, Pinjala

, Joshi

Y. K.

, Wong

T. N.

, Toh

K. C.

and Iyer

M. K.

: ‘Fluid flow and heat transfer in liquid cooled foam heat sinks for electronic packages', IEEE Trans. Compo. Pack. Technol., 2005, 28, (2), 272–280. doi: 10.1109/TCAPT.2005.848528

93.

Hutter

, Büchi

, Zuber

and Rudolf von Rohr

: ‘Heat transfer in metal foams and designed porous media’, Chem. Eng. Sci., 2011, 66, (17), 3806–3814. doi: 10.1016/j.ces.2011.05.005

94.

Bejan

: ‘Designed porous media: maximal heat transfer density at decreasing length scales', Int. J. Heat Mass Trans., 2004, 47, (14–16), 3073–3083. doi: 10.1016/j.ijheatmasstransfer.2004.02.025

95.

Carpenter

K. P.

and da Silva

A. K.

: ‘A combined hydro-thermal characterization of high-porosity metal foam test sections with discrete pore-size gradients', Int. J. Heat Mass Trans., 2014, 77, 770–776. doi: 10.1016/j.ijheatmasstransfer.2014.05.057

96.

Zaragoza

and Goodall

: ‘Metal foams with graded pore size for heat transfer applications', Adv. Eng. Mater., 2013, 15, (3), 123–128. doi: 10.1002/adem.201200166

97.

Oun

and Kennedy

: ‘Tailoring the pressure-drop in multi-layered open-cell porous Inconel structures', J. Porous Mater., 2015, 22, 1–7. doi: 10.1007/s10934-015-0046-2

98.

Baril

, Mostafid

, Lefebvre

L. P.

and Medraj

: ‘Experimental demonstration of entrance/exit effects on the permeability measurements of porous materials', Adv. Eng. Mater., 2008, 10, (9), 889–894. doi: 10.1002/adem.200800142

99.

T. J.

: ‘Heat transfer efficiency of metal honeycombs', Int. J. Heat Mass Trans., 1999, 42, (11), 2031–2040. doi: 10.1016/S0017-9310(98)00306-8