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Home Search Collections Journals About Contact us My IOPscience Thermal conductivity and contact resistance of metal foams This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 J. Phys. D: Appl. Phys. 44 125406 (http://iopscience.iop.org/0022-3727/44/12/125406) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 142.58.187.169 The article was downloaded on 10/03/2011 at 18:32 P
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  Thermal conductivity and contact resistance of metal foams This article has been downloaded from IOPscience. Please scroll down to see the full text article.2011 J. Phys. D: Appl. Phys. 44 125406(http://iopscience.iop.org/0022-3727/44/12/125406)Download details:IP Address: 142.58.187.169The article was downloaded on 10/03/2011 at 18:32Please note that terms and conditions apply.View the table of contents for this issue, or go to the  journal homepage for more HomeSearchCollectionsJournalsAboutContact usMy IOPscience  IOP P UBLISHING  J OURNAL OF  P HYSICS  D: A PPLIED  P HYSICS J. Phys. D: Appl. Phys.  44  (2011) 125406 (7pp) doi:10.1088/0022-3727/44/12/125406 Thermal conductivity and contactresistance of metal foams E Sadeghi 1 , 2 , 3 , S Hsieh 2 and M Bahrami 2 1 Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada 2 Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey,BC, V3T 0A3, CanadaE-mail: ehsans@uvic.ca Received 15 September 2010, in final form 20 January 2011Published 10 March 2011Online at stacks.iop.org/JPhysD/44/125406 Abstract Accurate information on heat transfer and temperature distribution in metal foams is necessaryfor design and modelling of thermal-hydraulic systems incorporating metal foams. Theanalysis of heat transfer requires determination of the effective thermal conductivity as well asthe thermal contact resistance (TCR) associated with the interface between the metal foam andthe adjacent surfaces/layers. In this study, a test bed that allows the separation of effectivethermal conductivity and TCR in metal foams is described. Measurements are performed in avacuum under varying compressive loads using ERG Duocel aluminium foam samples withdifferent porosities and pore densities. Also, a graphical method associated with a computercode is developed to demonstrate the distribution of contact spots and estimate the real contactarea at the interface. Our results show that the porosity and the effective thermal conductivityremain unchanged with the variation of compression in the range 0–2MPa; but TCR decreasessignificantly with pressure due to an increase in the real contact area at the interface.Moreover, the ratio of real to nominal contact area varies between 0 and 0.013, dependingupon the compressive force, porosity, pore density and surface characteristics.(Some figures in this article are in colour only in the electronic version) 1. Introduction Transport phenomena in porous media have been the focusof many industrial and academic investigations [1–4]. The majority of the studies reported in the literature deal withlow porosity media such as granular materials and packedbeds [1,2]. Over the last decade, high porosity micro- structures such as open-cell metal foams have received moreattention. Interest in these media stems from their relativelylow cost, ultra-low density, high surface area to volume ratioand their ability to mix the passing fluid. These features arehighly desirable for a wide variety of applications includingmicroelectronics cooling, aerospace technology, filtration andcompact heat exchangers [3–7]. In the majority of these applications, thereisaninterfacebetweenthefoamandasolidsurface which gives rise to an important phenomenon calledthermal contact resistance (TCR) acting against heat transfer 3 Author to whom any correspondence should be addressed. in metal foams. Due to high porosity and irregularities of the free surface of metal foams, the actual contact area at theinterface with a solid surface is very small; this emphasizesthe significance of TCR at metal foam–solid surface interface.In some applications, metal foams are brazed to a metalsheet which may create a perfect contact, but because of highporosity of the medium, TCR still exists due to constrictionandspreadingoftheheatflowpassingthroughthemetalsheet–foam interface.A review of the literature indicates that in all previousstudies related to heat transfer in metal foams, e.g. [8–15], the TCR was either neglected due to attachment of a metalsheet to the foam or ‘bundled up’ with the effective thermalconductivity and only the effective thermal conductivity valuewas reported. One fundamental issue with combining thetwo is that TCR is an  interfacial phenomenon  which isa function of mechanical load, surface characteristics andthermal conductivity of both interfacing surfaces, whereasthermal conductivity is a transport coefficient characterizing 0022-3727/11/125406+07$33.00  1  © 2011 IOP Publishing Ltd Printed in the UK & the USA  J. Phys. D: Appl. Phys.  44  (2011) 125406 E Sadeghi  et al the  bulk   medium. Thermal conductivity and TCR shouldtherefore be distinguished. Furthermore, the effect of compression on thermal conductivity and TCR has not beenthoroughly investigated.The objective of this study is to measure the thermalconductivity and contact resistance of metal foams andestimate the size and distribution of contact spots (realcontact area) at the interface. The experimental techniquedeveloped in this study allows the deconvolution of TCRand thermal conductivity and was used to perform acomprehensive experimental study to determine the effectivethermal conductivity and TCR at different compressiveloads.A custom-made test bed was designed and built thatenables the measurements of thermal conductivity and TCRof porous media under a vacuum. The test bed was equippedwithaloadingmechanismthatallowstheapplicationofvariouscompressive loads on the samples. ERG Duocel aluminiumfoamswithvariousporositiesandporedensitiesareusedintheexperiments. The tests are performed under a vacuum, wherethe test column was surrounded by an aluminium radiationshield to limit the radiation heat losses. The effective thermalconductivity and TCR are deduced from the total thermalresistancemeasurementsbyperformingaseriesofexperimentswith aluminium foam samples of various thicknesses andsimilarmicro-structures,i.e.porosityandporedensity. Effectsof compression, porosity and pore density are studied on theeffective thermal conductivity and TCR.To estimate the real contact area at the metal foam–solid interface, a pressure sensitive carbon paper is placedbetween the foam and the solid surface to print the contactspots at different compressive loads. A computer code is thendevelopedusingMATLABtoanalysetheproducedimagesandcalculate the size of contact spots. 2. Thermal conductivity and TCR measurements Aschematicofthetestbedforthermalmeasurementsisshownin figure 1. The test chamber consists of a stainless-steel base plate and a bell jar enclosing the test column. The test columnconsists of, from top to bottom, the loading mechanism, thesteel ball, the heater block, the upper fluxmeter, the sample,the lower fluxmeter, the heat sink (cold plate), the load celland the polymethyl methacrylate (PMMA) layer. The heaterblock consists of circular flat copper in which a cylindricalpencil-type electrical heater is installed. The designed coldplate consists of a hollow copper cylinder, 1.9cm high and15cm diameter. Cooling is accomplished using a closed loopwater-glycol bath in which the coolant temperature can be set.The cold plate is connected to the chiller unit which adjuststhe cold water temperature. A 1000lbs load cell is used tomeasure the applied load to the sample. The fluxmeters weremade of a standard electrolyte iron material. In this study, thecold plate temperature and the power of the electrical heaterwere set on 0 ◦ C and 12W, respectively.To measure temperatures, six T-type thermocouples wereattached to each fluxmeter at specific locations shown infigure 1. The thermocouples were located 5mm apart with 12.5 101054512.5 1010545 thermocouplesthermocouplesupper fluxmeterlower fluxmetersamplecold plate(heat sink)load cellelectricalheatersteel ballapplied loadbase plateAll dimensions are in (mm) PMMAinsulation layer Figure 1.  Schematic of the test bed for thermal measurement. Table 1.  Properties of the studied Al foam samples.Sample number #1 #2 #3 #4Porosity 0.903 0.906 0.945 0.953Pore density (PPI) 10 20 10 20Thickness (mm) 13.93 13.90 13.92 13.9317.89 17.91 17.95 17.96 the first one 10mm from the contact surface. The thermalconductivity of the iron fluxmeter was known and used tomeasure the heat flow rate transferred through the contactinterface. The samples used in this study are open-cellaluminium foams. These Duocel foams were producedthrough a proprietary process developed by ERG in which theresulting foam has the identical chemical composition of thebase alloy used. The foams were made of aluminium alloys of 6101 and cut in cylindrical shapes with the diameter of 25mmand then were polished. Aluminium foam samples with theporosity range 90–96% and pore density of 10 and 20 PPI areused in this study; see table 1 for more details. 2.1. Test procedure To study heat conduction only through the solid ligamentsand contact surfaces, experiments were conducted under avacuum. A vacuum level of 10 − 5 mbar was achieved underthe test chamber using a vacuum machine. Temperaturesand pressure were recorded at various compressive loadswhen steady-state conditions were achieved; to reach thermal2  J. Phys. D: Appl. Phys.  44  (2011) 125406 E Sadeghi  et al Table 2.  Uncertainty of involving parameters in the analysis. δQQδT T δt t δAAδP  c P  c δφ s φ s 3.2% 1.7% 0.5% 0.8% 2.5% 2.2% equilibriumalltheexperiment’sparameterswerekeptconstantand carefully monitored for approximately 4–5h for each datapoint. The effects of compression were investigated over therange 0.3–2MPa.The temperature gradient between the hot and cold platesresultsinessentiallyone-dimensionalheattransferfromthetoptothebottomofthetestcolumn. Potentialcontributionofradi-ationheattransferintheexperimentalsetupcanbedividedinto:(1) Radiation inside the micro-structure: our measurementsshow that the maximum temperature difference betweentwo neighbouring pores in the sample is 8.3 ◦ C andtemperature level inside the foam is less than 100 ◦ C.After some calculations, we found that the contribution of radiation compared with conduction heat transfer insidethe foam is less than 1%.(2) Interfacialradiation: thisradiationmayoccurbetweenthefluxmeters and the metal foam surfaces at the interface.The temperature drops at the interface as a result of contact resistance. Our measurements show that thistemperature drop is between 4 and 28 ◦ C, dependingon the compressive load. The maximum contributionof interfacial radiation compared with conduction isestimated to be less than 0.5%.As a result, one can conclude the heat transfer in the presentexperiments is mostly due to conduction. The heat transferthroughthefluxmeterscanbedeterminedusingFourier’sequa-tion: Q =− kA d T  d z,  (1)where d T   /d z  is the temperature gradient along the test col-umn,  k  is the thermal conductivity of the fluxmeters and  A  isthe cross-sectional area of the samples/fluxmeters. The tem-peratures at the top and bottom contact surfaces can be ex-trapolated through the measured heat flux. The measured totalthermal resistance at each pressure,  R tot , includes the sample(bulk) thermal resistance and the TCR (at the top and bottominterfaces) and can be expressed as R tot  = R MF  + TCR = T  ul Q,  (2)where  T  ul  is the temperature difference between the upperand the lower contact surfaces.  R MF  and TCR are the metalfoam resistance and the total contact resistance (summation of contactresistanceatthetopandbottomsurfaces),respectively.To deconvolute thermal conductivity and TCR, twoexperiments were performed with samples of differentthicknesses; but with identical micro-structural parameters,e.g. porosity and pore density. Due to identical micro-structure and similar surface characteristics at the top andbottom interfaces, contact resistances for both samples can beconsidered equal at the same pressure. Applying equation (2)tobothmeasurementsandsubtractingthemyieldstheeffectivethermal conductivity: k eff   = t  1 R MF1 A = t  2 R MF2 A,  (3) k eff   = t  1 − t  2 (R tot1 − R tot2 )A,  (4)where  t  1  and  t  2  are the two different thicknesses of the Alfoam sample at a specific applied pressure and  A  is the cross-sectional area of the sample. To investigate the effect of compression on the sample thickness, Al foam samples withdifferent porosities (0 . 9  < ε <  0 . 96 )  and pore densities werecompressed step by step using a standard tensile-compressionmachine. Thickness variation was measured for all samples atdifferent pressures from 0 to 2MPa using a Mitutoyo digitalmicrometer with the accuracy of 1 µ m. The results show thatthe maximum thickness variation is less than 1.5% and maybe neglected. Equation (4) can be used to find the effective thermal conductivity; the TCR can then be calculated byequation (2). 2.2. Uncertainty analysis Considering the relationships for evaluating the effectivethermal conductivity and the TCR, i.e. equations (4), (2), the relevant parameters in the analysis can be expressed as R tot  = f(Q,T,t,A,P  c ,φ s ).  (5)The main uncertainty in these experiments is due to errorsin determining the heat flux through the sample which leadsto a maximum error of 3.2%. The maximum uncertaintiesfor the thermocouples and the data acquisition readings are ± 1 ◦ C which introduces a maximum error of 1.7% betweenthe interfaces of the sample and the fluxmeters. The relativedensity of the similar samples with two different thicknesseswas measured and the difference was used as a representativeof the morphological uncertainty. This uncertainty as wellas those associated with the load cell, thickness and cross-sectional area measurements are listed in table 2. The maximumuncertaintyforthethermalresistancemeasurementscan be calculated from [16] δR tot R tot =  δQQ  2 +  δT T   2 +  δt t   2 +  δAA  2 +  δP  c P  c  2 +  δφ s φ s  2  1 / 2 .  (6)For this study, the maximum uncertainty is estimated tobe ± 5%. 3. Morphology of contact spots To find the size and distribution of contact spots, a sheetof carbon copy paper along with a white paper was placedon the top and bottom of the samples. The assembly wascompressed in a standard tensile-compression machine andthe contact spots were printed on the white paper. Theprinted images were captured with a high resolution camera.3
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