Abstract
The effective thermal conductivity of open-pore metal foams in combination with the fluids air and water have been investigated in an extended range in relative density and selection of material. This study is conducted to estimate the influence of the thermal conductivities of the combination “metal foam — fluid” λs and λfl on the effective thermal conductivity λe of the open-pore metal foam. Therefore, open-pore metal foams (ρrel = 12.7 % in average) of different base materials are manufactured by respect of significant differences in the thermal conductivity of their bulk material in a range of 24.80 W × (m × K)−1≤λs≤ 402.13 W × (m × K)−1. These samples are saturated by air and water and the effective thermal conductivities of the corresponding combinations are determined. The thereto used method is a transient one and is based on the theory of inturbide temperature fields. The impact of the fluid type on λe is evaluated and its dependence on λs is identified, resulting in a simple expression for estimating the effective thermal conductivity as a function of λfl, λs and ρrel applicable for air and water.
Kurzfassung
Die effektive Wärmeleitfähigkeit von offenporigen Metallschäumen in Kombination mit Luft und Wasser wurden für einen erweiterten Bereich der relativen Dichte sowie der Werkstoffauswahl untersucht. Dies wurde durchgeführt, um den Einfluss der jeweiligen Wärmeleitfähigkeiten der Kombination „Metallschaum — Fluid“ λs und λfl auf die effektive Wärmeleitfähigkeit der offenporigen Metallschäume λe zu bestimmen. Dazu sind offenporige Metallschäume mit einer durchschnittlichen relativen Dichte von ρrel = 12,7 % aus unterschiedlichen Basiswerkstoffen hergestellt worden, die im Hinblick auf große Unterschiede in ihrer Wärmeleitfähigkeit in einem Bereich von 24,80 W × (m × K)−1≤λs≤402,13 W × (m × K)−1 ausgewählt wurden. Diese Proben wurden mit Luft und Wasser gesättigt, wobei die messtechnische Ermittlung der Wärmeleitfähigkeiten der jeweiligen Kombinationen erfolgte. Es wurde hierzu ein transientes Verfahren gewählt, das auf der Theorie der inturbiden Temperaturfelder beruht. Der Einfluss des Fluides auf die effektive Wärmeleitfähigkeit der offenporigen Metallschäume λe wurde bestimmt, sowie dessen Zusammenhang mit der Wärmeleitfähigkeit des Basiswerkstoffes λs aufgezeigt. Daraus resultiert eine einfache Gleichung zur Berechnung der effektiven Wärmeleitfähigkeit als Funktion von λs, λfl und ρrel, welche für die Fluide Luft und Wasser anwendbar ist.
References
1 J.Banhart: Light-metal foams: History of innovation and technological challenges, Advanced Engineering Materials15 (2013), pp. 82–11110.1002/adem.201200217Search in Google Scholar
2 M. F.Ashby: The mechanical properties of cellular solids, Metallurgical Transactions A14 (1983), pp. 1755–176910.1007/BF02645546Search in Google Scholar
3 L. J.Gibson: Mechanical behavior of metallic foams, Annual Review of Materials Science30 (2000), pp. 191–22710.1146/annurev.matsci.30.1.191Search in Google Scholar
4 W.-Y.Jang, S.Kyriakides: On the crushing of aluminum open-cell foams: Part I – Experiments, International Journal of Solids and Structures46 (2009), pp. 617–63410.1016/j.ijsolstr.2008.09.008Search in Google Scholar
5 Y.Er, E.Unsaldi: The production of nickel-chromium-molybdenum alloy with open-pore structure as an implant and the investigation of its biocompatibility in vivo, Advances in Materials Science and Engineering2013, Art. 568479, pp. 1–710.1155/2013/568479Search in Google Scholar
6 G.Lewis: Properties of open-cell porous metals and alloys for orthopaedic applications, Journal of Materials Science: Materials in Medicine24 (2013), pp. 2293–232510.1007/s10856-013-4998-ySearch in Google Scholar PubMed
7 D. W.Müller, A. M.Matz, N.Jost: Casting open porous Ti foam suitable for medical applications, Bioinspired, Biomimetic and Nanobiomaterials2 (2013), pp. 76–8310.1680/bbn.12.00023Search in Google Scholar
8 S. M.Tabaatabaai, M. S.Rahmanifar, S. A.Mousavi, S.Shekofteh, J.Khonsari, A.Oweisi, M.Hejabi, H.Tabrizi, S.Shirzadi, B.Cheraghi: Lead-acid batteries with foam grids, Journal of Power Sources158 (2006), pp. 879–88410.1016/j.jpowsour.2005.11.017Search in Google Scholar
9 Q.-X.Low, W.Huang, X.-Z.Fu, J.Melnik, J.-L.Luo, K. T.Chuang, A. R.Sanger: Copper coated nickel foam as current collector for H2S-containing syngas solid oxide fuel cells, Applied Surface Science258 (2013), pp. 1014–102010.1016/j.apsusc.2011.07.133Search in Google Scholar
10 J. R.González, F.Nacimiento, R.Alcántara, G. F.Ortiz, L. J.Tirado: Electrodeposited CoSn2 on nickel open-cell foam: Advancing towards high power lithium ion and sodium ion batteries, Crystal Engineering Communications15 (2013), pp. 9196–920210.1039/c3ce41368cSearch in Google Scholar
11 X.-H.Han, Q.Wang, Y.-G.Park, C.T'joen, A.Sommers, A.Jacobi: A review of metal foam and metal matrix composites for heat exchangers and heat sinks, Heat Transfer Engineering33 (2012), pp. 1–2010.1080/01457632.2012.659613Search in Google Scholar
12 A. A.Sertkaya, K.Altınısık, K.Dincer: Experimental investigation of thermal performance of aluminum finned heat exchangers and open-cell aluminum foam heat exchangers, Experimental Thermal and Fluid Science36 (2012), pp. 86–9210.1016/j.expthermflusci.2011.08.008Search in Google Scholar
13 C. Y.Zhao: Review on thermal transport in high porosity cellular metal foams with open cells, International Journal of Heat and Mass Transfer55 (2012), pp. 3618–363210.1016/j.ijheatmasstransfer.2012.03.017Search in Google Scholar
14 S. T.Hong, D. R.Herling: Open-cell aluminum foams filled with phase change materials as compact heat sinks, Scripta Materialia55 (2006), pp. 887–89010.1016/j.scriptamat.2006.07.050Search in Google Scholar
15 J.Vicente, F.Topin, J.-V.Daurelle: Open celled material structural properties measurement: From morphology to transport properties, Materials Transactions47 (2006), pp. 2195–220210.2320/matertrans.47.2195Search in Google Scholar
16 S.Mahjoob, K.Vafai: A synthesis of fluid and thermal transport models for metal foam heat exchangers, International Journal of Heat and Mass Transfer51 (2008), pp. 3701–371110.1016/j.ijheatmasstransfer.2007.12.012Search in Google Scholar
17 I.Kurtbas, N.Celik: Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel, International Journal of Heat and Mass Transfer52 (2009), pp. 1313–132510.1016/j.ijheatmasstransfer.2008.07.050Search in Google Scholar
18 C. Y.Zhao, L. N.Dai, G. H.Tang, Z. G.Qu, Z. Y.Li: Numerical study of natural convection in porous media (metals) using lattice Boltzmann method (LBM), International Journal of Heat and Fluid Flow31 (2010), pp. 925–93410.1016/j.ijheatfluidflow.2010.06.001Search in Google Scholar
19 A.Bhattacharya, R. L.Mahajan: Finned metal foam heat sinks for electronics cooling in forced convection, Journal of Electronic Packaging124 (2002), pp. 155–16310.1115/1.1464877Search in Google Scholar
20 J.-J.Hwang, G.-J.Wang, R.-H.Yeh, C.-H.Chao: Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams, Journal of Heat Transfer124 (2001), pp. 120–12910.1115/1.1416690Search in Google Scholar
21 A. J.Fuller, T.Kim, H. P.Hodson, T. J.Lu: Measurement and interpretation of the heat transfer coefficients of metal foams, Journal of Mechanical Engineering Science219 (2005), pp. 183–19110.1243/095440605X8414Search in Google Scholar
22 L. B.Younis, R.Viskanta: Experimental determination of the volumetric heat transfer coefficient between stream of air and ceramic foam, International Journal of Heat and Mass Transfer36 (1993), pp. 1425–143410.1016/S0017-9310(05)80053-5Search in Google Scholar
23 M. L.Hunt, C. L.Tien: Effects of thermal dispersion on forced convection in fibrous media, International Journal of Heat and Mass Transfer31 (1998), pp. 301–30910.1016/0017-9310(88)90013-0Search in Google Scholar
24 D.-F.Lee, K.Vafai: Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media, International Journal of Heat and Mass Transfer42 (1999), pp. 423–43510.1016/S0017-9310(98)00185-9Search in Google Scholar
25 M. S.Phanikumar, R. L.Mahajan: Non-Darcy natural convection in high porosity metal foams, International Journal of Heat and Mass Transfer45 (2002), pp. 3781–379310.1016/S0017-9310(02)00089-3Search in Google Scholar
26 R.Rachedi, S.Chikh: Enhancement of electronic cooling by insertion of foam materials, Heat and Mass Transfer37 (2001), pp. 371–37810.1007/s002310100192Search in Google Scholar
27 V. V.Calmidi, R. L.Mahajan: The effective thermal conductivity of high porosity fibrous metal foams, Journal of Heat Transfer121 (1999), pp. 466–47110.1115/1.2826001Search in Google Scholar
28 J. W.Paek, B. H.Kang, S. Y.Kim, J. M.Hyun: Effective thermal conductivity and permeability of aluminum foam materials, International Journal of Thermophysics21 (2002), pp. 453–46410.1023/A:1006643815323Search in Google Scholar
29 A.Bhattacharya, V. V.Calmidi, R. L.Mahajan: Thermophysical properties of high porosity metal foams, International Journal of Heat and Mass Transfer45 (2002), pp. 1017–103110.1016/S0017-9310(01)00220-4Search in Google Scholar
30 S.-T.Hong, D. R.Herling: Effects of surface area density of aluminum foams on thermal conductivity of aluminum foam-phase change material composites, Advanced Engineering Materials9 (2007), pp. 554–55710.1002/adem.200700023Search in Google Scholar
31 R.Dyga, S.Witczak: Investigation of effective thermal conductivity aluminum foams, Procedia Engineering42 (2012), pp. 1088–109910.1016/j.proeng.2012.07.500Search in Google Scholar
32 A. D.Sullins, K.Daryabeigi: Effective thermal conductivity of high porosity open cell nickel foam, Proc. of the 35th AIAA Thermophysics Conference (2001), pp. 1–1110.2514/6.2001-2819Search in Google Scholar
33 C. Y.Zhao, T. J.Lu, H. P.Hodson, J. D.Jackson: The temperature dependence of effective thermal conductivity of open-celled steel alloy foams, Materials Science and Engineering: A367 (2004), pp. 123–13110.1016/j.msea.2003.10.241Search in Google Scholar
34 R.Coquard, M.Lorentz, D.Baillis: Conductive heat transfer in metallic/ceramic open-cell foams, Advanced Engineering Materials10 (2008), pp. 323–33710.1002/adem.200700331Search in Google Scholar
35 R.Coquard, D.Rochais, D.Baillis: Experimental investigations of the coupled conductive and radiative heat transfer in metallic/ceramic foams, International Journal of Heat and Mass Transfer52 (2009), pp. 4907–491810.1016/j.ijheatmasstransfer.2009.05.015Search in Google Scholar
36 J. A.Reglero, M. A.Rodríguez-Pérez, D.Lehmhus, M.Windmann, J. A.de Saja, A.Fernández: An experimental study on the inhomogeneities of aluminum foams measuring the thermal conductivity by using the transient plane source method, Materials Science Forum480 – 481 (2005), pp. 133–13810.4028/www.scientific.net/MSF.480-481.133Search in Google Scholar
37 O.Reutter, J.Sauerhering, T.Fend, R.Pitz-Paal, S.Angel: Characterization of heat and momentum transfer in sintered metal foams, Advanced Engineering Materials10 (2008), pp. 812–81510.1002/adem.200800095Search in Google Scholar
38 E.Solórzano, J. A.Reglero, M. A.Rodríguez-Pérez, D.Lehmhus, M.Wichmann, J. A.de Saja: An experimental study on the thermal conductivity of aluminum foams by using the transient plane source method, International Journal of Heat and Mass Transfer51 (2008), pp. 6259–626710.1016/j.ijheatmasstransfer.2007.11.062Search in Google Scholar
39 E.Solórzano, M. A.Rodríguez-Pérez, J. A.de Saja: Thermal conductivity of cellular metals measured by the transient plane sour method, Advanced Engineering Materials10 (2008), pp. 371–37710.1002/adem.200700337Search in Google Scholar
40 G.Laschet, J.Sauerhering, O.Reutter, T.Fend, J.Scheele: Effective permeability and thermal conductivity of open-cell metallic foams via homogenization on a microstructure model, Computational Materials Science45 (2008), pp. 1–710.1016/j.commatsci.2008.06.023Search in Google Scholar
41 S.Brendelberger, S.Hötker, T.Fend, R.Pitz-Paal: Macroscopic foam model with effective material properties for high heat load applications, Applied Thermal Engineering47 (2012), pp. 34–4010.1016/j.applthermaleng.2012.03.017Search in Google Scholar
42 V.Kathare, J. H.Davidson, F.A.Kulacki: Natural convection in water-saturated metal foam, International Journal of Heat and Mass Transfer51 (2008), pp. 3794–380210.1016/j.ijheatmasstransfer.2007.11.051Search in Google Scholar
43 V.Kathare, F. A.Kulacki, J. H.Davidson: Buoyant convection in superposed metal foam and water layers, Journal of Heat Transfer132 (2010), pp. 014503-1–014503-410.1115/1.3194767Search in Google Scholar
44 A. M.Matz, D. W.Müller, N.Jost, Morphological and thermal characterization of Al-based open-pore cellular structures, Proc. of Cellular Materials (CellMat2012), Jena (2012), Art. G48, pp. 1–6 (on CD-ROM)Search in Google Scholar
45 B. H.Vos: Measurements of thermal conductivity by a non-steady-state method, Applied Scientific Research, Section A5 (1956), pp. 425–43810.1007/BF03184603Search in Google Scholar
46 G.Woelk: Inturbide Temperaturfelder, Wärme75 (1969), pp. 124–129Search in Google Scholar
47 C. Y.Ho, R. W.Powell, P. E.Liley: Thermal conductivity of the elements: A comprehensive review, Journal of Physical and Chemical Reference Data3 (1975), pp. 756–79610.1021/es00107a726Search in Google Scholar
48 Y. S.Touloukian, R. K.Kirby, R. E.Taylor, P. D.Desai: Thermophysical Properties of Matter: The TPRC Data Series, Vol. 12, Thermal Expansion Metallic Elements and Alloys, IFI/Plenum, New York, USA (1975)10.1007/978-1-4757-1622-1_6Search in Google Scholar
49 L. C.Wang, F.Wang: Preparation of the open-pore aluminum foams using investment casting process, Acta Metallurgica Sinica14 (2001), pp. 27–32Search in Google Scholar
50 Y.Yamada, K.Shimojima, Y.Sakaguchi, M.Mabuchi, M.Nakamura, T.Asahina: Processing of an open-cellular AZ91 magnesium alloy with a low density of 0.05 g/cm3, Journal of Materials Science Letters18 (1999), pp. 1477–148010.1023/A:1006677930532Search in Google Scholar
51 A. M.Matz, B. S.Mocker, D. W.Müller, N.Jost, G.Eggeler: Mesostructural design and manufacturing of open-pore metal foams by investment casting, Advances in Materials Science and Engineering2014 (2014), Art.Nr. 421729, pp. 1–910.1155/2014/421729Search in Google Scholar
52 B. S.Mocker, A. M.Matz, N.Jost, P.Krug: Microstructural characterization of open-pore metal foams of pure metals, Practical Metallography52 (2015), Art. 421729, pp. 83–10710.3139/147.110324Search in Google Scholar
53 K.Kadoya, N.Matsunaga, A.Nagashima: Viscosity and thermal conductivity of dry air in the gaseous phase, Journal of Physical and Chemical Reference Data14 (1985), pp. 947–97010.1063/1.555744Search in Google Scholar
54 J. V.Sengers, J. T. R.Watson: Improved formulations for the viscosity and thermal conductivity of water substance, Journal of Physical and Chemical Reference Data15 (1986), pp. 1291–131410.1063/1.555763Search in Google Scholar
55 T.Vlačić: Ein instationäres Verfahren zur Bestimmung der Temperatur- und Wärmeleitfähigkeit von festen Stoffen, PhD Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen (1976)Search in Google Scholar
56 G.Woelk: Ein Näherungsverfahren zur numerischen Berechnung instationärer Temperaturfelder, Habilitation Thesis, RWTH/TU Aachen (1965)10.1007/978-3-663-07064-1Search in Google Scholar
57 G.Woelk: Verbesserung von Differenzenverfahren durch Teilgebietslösungen, Wärme und Stoffübertragung7 (1974), pp. 208–21410.1007/BF01445308Search in Google Scholar
58 H. R.Shanks, A. H.Klein, G. C.Danielson: Thermal properties of Armco iron, Journal of Applied Physics38 (1967), pp. 2885–289210.1063/1.1710018Search in Google Scholar
59 DIN IEC 60584: Thermocouples – Part 1: E.M.F. Specifications and Tolerances, Beuth, Berlin, Germany (2010)Search in Google Scholar
60 J. R.Taylor: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd Ed., University Science Books, Sausalito, USA (1997)Search in Google Scholar
© 2014, Carl Hanser Verlag, München
