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Applied Thermal Engineering 66 (2014) 266e273

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Applied Thermal Engineering

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Performance evaluation of single tubular aluminium foam heatexchangers

A. Chumpia*, K. HoomanQueensland Geothermal Energy Centre of Excellence (QGECE), School of Mechanical and Mining Engineering, University of Queensland, Brisbane,Queensland 4072, Australia

h i g h l i g h t s

� Five aluminium foam wrapped heat exchangers, with different foam height and bonding methods, are tested.� A steel finned tube is used as a benchmark for comparison.� Thermal performance of foamed heat exchangers improves with increased foam thickness.� With the same dimensions and pressure drop, heat transfer from metal foam surface is higher than finned ones.� We present correlations to predict pressure drop and thermal resistance of specimens with different foam height and air speed.

a r t i c l e i n f o

Article history:Received 19 November 2012Accepted 30 January 2014Available online 18 February 2014

Keywords:Metal foam heat exchangersHeat exchanger bundlesThermo-hydraulic performanceCross flow measurementsAir-cooled condensersDry cooling towers

* Corresponding author.E-mail address: a.chumpia@uq.edu.au (A. Chumpi

http://dx.doi.org/10.1016/j.applthermaleng.2014.01.071359-4311/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Five samples of aluminium foam-wrapped tubular heat exchanger are being tested for heat transferperformance and pressure drop characteristics. The foam layer has thickness (or height) varied from5 mm to 20 mm. The tests are carried out on each heat exchanger, installed horizontally in a cross-flowarrangement inside an open circuit wind tunnel, one at a time with air velocity varying between 0.5 and5 m/s. Heat transfer rate from 75 �C hot liquid, circulating through the core tube, to external air isevaluated. These results, together with temperature differential between the ambient air and the foamsurface, allow evaluation of the overall thermal resistance. Pressure drops across each sample arerecorded. The performance of the foam heat exchangers is assessed by comparing their thermo-hydraulicresults against those of a conventional finned tube with similar dimensions and tested under the sameconditions. The results show that, within the designated air velocity range, the foam heat exchangerswith thicker foam layer perform better than those with thinner foam layer. However, the heat transferadvantage does not increase linearly with foam thickness e signifying the existence of an optimumthickness when an increase in pressure drop at increased air velocity is taken into account. Finally, thecorrelations to predict the overall thermal resistance and pressure drop are presented.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Metal foams are highly porous materials consisting of mostlyinterconnected and randomly distributed voids called ‘cells’. Typi-cally, a cell approximate shape and form is a near-spherical poly-hedron having 14 faces. Each cell face forms an open passage called‘pore’ to adjacent surrounding cells in all directions. The porousstructure as described therefore makes metal foam permeable, andprovides very well-mixed patterns, to fluid flows in macroscopicscale. In addition, the solid backbone micro-features maintaining

a).

1

the existence of all cells and pores e termed ‘struts’ (or ‘ligaments’,or ‘fibres’) and nodes (where struts join) e have a combined effectresulting in a very high interfacial surface area between the voidand its solid backbone. T’Joen et al. [25] reported approximate fig-ures for this area to be in a range from 500 m2/m3 to 10,000 m2/m3.

Due to their other unique properties of high strength, high ab-sorption to impact, lowweight, excellent noise attenuation, etc. [2],metal foams offer new possibilities in emerging industries wherethese combined properties are sought. Nevertheless, one distinctapplicationwhich can take a maximum advantage of all metal foamfeatures and properties mentioned above is that involving highefficiency heat exchange. Three niche technological areas that fitwithin this broad application are; thermal processes demandinghigh rate of simultaneous chemical reactions [5,26], fast rate heat

Nomenclature

A area, [m2]cp specific heat capacity at constant pressure, [J/kg K]df strut diameter, [m]di core tube internal diameter, [m]do core tube external diameter, [m]Di foam or fin annulus internal diameter ¼ do, [m]Do foam or fin annulus external diameter, [m]Dr diameter ratio ¼ Do/do, [e]H dimensional height, [m]h convective heat transfer coefficient, [W/m2 K]k thermal conductivity, [W/m K]L dimensional length, [m]_m mass flow rate, [kg/s]Nu Nusselt number, [e]P pressure, [Pa]_Q total heat transfer, [W]R thermal resistance, [K/W]R0 thermal resistance, [e]Re Reynolds numberS sum of residual square, [e]t foam thickness or fin height, [m]tf fin thickness, [m]tp fin pitch, [m]tw wall thickness of the core tube, [m]T temperature, [K]U air velocity, [m/s]W dimensional width, [m]Y dependent variable representing DP or Rt, [Pa or K/W]

AbbreviationsHTC convective heat transfer coefficient, [W/m2 K]ISA interfacial surface area, [m2]LSM least squares methodPID proportional e integral e derivative feedback controlPIV particle image velocimetryPPI number of pores per inch, [technically in�1, treated as

e]RTD resistance temperature detectorTCR thermal contact resistance, [K/W]

Greek symbolsD differential ofa,b,j empirical constantsn kinematic viscosity, [m2/s]r density, [kg/m3]s0 surface-to-volume ratio, [m�1]f porosity, [e]U* efficiency function of foam, [e]

Subscriptsa air sidec of a contact between fin or foam and the core tubeh relating to convective heat transfer of air or liquid sidek relating to conductive heat transfer of the core tube

wallliq of the liquid sides of a surfacet overall, totalN of the free air stream

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273 267

removal from high power electronic components, and highly effi-cient heat rejection in power cycles [9] operating at low tempera-ture differentials. It is therefore not surprising that a largerpercentage of open literature on metal foam studies in the pastdecade has been centred around high performance heat exchangersof some forms [4,12,17,19,24]. It is also notable that a large numberof these studies either concern fundamental investigations of thematerials themselves or practical applications dealing with rela-tively small metal foam volume. Compact heat sinks for high den-sity and high power electronic components are obvious examples[3,4,12,23].

Prior research of interest to this present study are thoseinvolving heat exchangers of tubular design. Lu et al. [18] analyti-cally studied forced convection of a round tube fully filled with ahigh porosity metal foam. Uniform heat input was applied at thetube external surface along its total length and the coolant such asair or water flowed inside to remove heat via the foam structure.The Brinkman-extended Darcy momentum model and two-equation heat transfer model based on the work of Calmidi andMahajan [6] for porous media were employed for the solutions oftemperature and velocity distributions of the flow field. Subse-quently, pressure drop of a single-phase flow and heat transferwere evaluated. The results showed the pressure drop as a functionof permeability and that it varied exponentially with the foam PPI.Heat transfer depended on four dimensionless parameters, viz., theratio of the tube radius to the foam pore size (geometry parameter),f Re, with tube diameter as its characteristic length, and fluidesolidthermal conductivity ratio. They concluded that metal-foam filledtubes could significantly enhance the heat transfer, up to fortytimes that of the plain tubes of comparable dimensions.

In parallel to Lu et al. [18], researchers from the same group Zhaoet al. [27] extended their study further on a double tube

construction. They wrapped a layer of metal foam on the outersurface of the tube then wrapped the non-conductive solid wall asthe outermost layer. This was essentially to form a concentric, tube-in-tube structure fully filled with the metal foam which allowedthem to analyze counter flow thermal exchange. The governingmodel are the same as that in Ref. [18] and the analysis was set onthe hotter fluid flowing inside the inner tube while the cooler fluidflowed in the annular section in the opposite direction. Theoutermost wall was assumed to be a perfect insulator, hence noheat exchange between the tube and the surroundings. Zhao et al.[27] parametrically set the test conditions by varying the radius ofthe inner tube and filling the two fluid passages with differentfoams. Heat transfer performance was compared with those of twoother concentric tube-in-tube designs; one with radial fins e andthe other with spiral fins, fixed on the outer surface of the innertube. They reported a significant improvement of heat transfer inthe foam-filled tube comparing with both versions of the finned/foam design. It was also shown that, on both sides of the inner wallseparating the two fluid streams, heat transfer performance of themetal-foam filled heat exchanger is a function of the ratio of theflow cross-sectional area and relative pore density of the metalfoam filling the respective area. Unfortunately, pressure dropanalysis was not discussed.

Mahjoob and Vafai [19] performed an extensive survey onexisting heat transfer coefficient and pressure drop correlations offoam heat exchangers from the literature. The results were groupedinto three main categories with the first describing correlationsbased on micro-structural properties of the metal foams. In thesecond category, the correlations were specific to metal foam tubeheat exchangers. In the third category, correlations were specific tometal foam channel heat exchangers. Correlations listed in thesecond category are those proposed by Refs. [18,27] which,

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273268

together, can predict thermo-hydraulic performance of concentrictube heat exchangers in three possible cases, i.e. the case where theinner tube of the heat exchanger is filled by a metal foam; the casewhere the inner tube is surrounded by a metal foam; and the casewhere the inner tube is filled and surrounded by metal foams.Mahjoob and Vafai [19] chose the first case to demonstrate thisprediction in a counter flow setting. The two working fluids theyselected were cold water flowing through the inner tube and hotexhaust gas flowing in the annular section. The porosity, perme-ability, pore density and mean pore diameter of the foam to fill theinner tube were 0.9272, 0.61 � 10�7 m2, 23 PPI, and 2.02 mm,respectively. The results showed a considerable increase in the heattransfer rate (8e13 times) comparing with that of the same testingconditions but with the metal foam removed from the inner tube.For pressure drop, the authors did not explicitly give the compar-ison between the with-foam and without-foam conditions. Theymerely reported that if the foam was filling the inner tube, varyingthe tube diameter while maintaining the fully filled foam did notaffect the pressure change significantly. Their reason being that thepressure drop is mainly affected by foam micro-structural proper-ties and not by the tube wall. Therefore, changing its diameterwould not create a considerable effect on the pressure drop.

Jamin and Mohamad [14] studied tubular heat exchangerpartially and fully covered by low porosity carbon foam, f ¼ 0.61.The first form consisted of two size annular foams withDi ¼ 15.9 mm, Do ¼ 22.1 mm and 26.1 mm. Each foam annulus was5 mm thick and was press-fit onto two core tubes of do 15.9 mm at5.5 mm apart. There were a total of 15 foam annuli on each tube.Similarly, the fully covered foam tubes were made by press-fittingtwo sizes of foam sleeve (Di 15.9 mm, Do ¼ 22.1 and 26.1 mm)onto their core tube do ¼ 15.9 mm, 152.2 mm in length. The studymeasured heat transfer rate and pressure drop from each sampleand a bare tube, all mounted vertically, in forced convection. Theresults were compared with those of aluminium finned tube withthe specifications: Di 15.9 mm, D0 38.1 mm, tf 0.38 mm, tp 2.52 mm,and number of fin¼ 52. The largest increase in Nusselt number wasachieved by aluminium fins (note the Do of finned tube), which wasabout three times greater than the best carbon foam case. Thelargest pressure drop was created by the 26.1 mm full foam tubewhich the authors regarded its presence as a blunt object. Targetapplication of Jamin and Mohamad’s study [14] was power co-generation and their conclusion was, given the forced convectionexperimental results obtained, aluminium fins were the mostsuitable medium for use in cross-flow heat exchangers.

A metal foam tube bundle based on a single row of aluminiumfoam heat exchangers was studied by T’Joen et al. [25], with the aimto achieve a low pressure drop on the air side. Their heat ex-changers were manufactured in-house using thin layers (4e8 mm)of four different foams (f ¼ 0.913, 0.932, 0.937, 0.951, respectively).Two foam samples had 10 PPI density while the other two had20 PPI. The cores were aluminium tubes with do and di measuring12 mm and 10 mm, respectively. Thermal glue was employed as ameans of contact bonding. Through wind tunnel testings theimpact of various parameters on the thermo-hydraulic perfor-mance was considered, including the Reynolds number, the tubespacing, the foam thickness, bonding material, and the type offoam. The results showed that, providing a good bonding betweenthe foam and the tubes can be achieved, metal foam covered tubeswith a small tube spacing, thin foam layer, and made of foamwith ahigh specific surface area potentially offer strong benefits at higherair velocities (>4 m/s), compared to helically finned tubes. It wasalso reported that the air only penetrates the foam to a certaindepth, resulting in a decreasing performance as the foam heightincreases. Finally the authors concluded that thermal glue contactbonding was found to have a devastating effects on the heat

exchanger performance. They noted that more research is requiredto develop a cost-effective and efficient brazing process to attachmetal foams to the tube cores.

In forming a foam based heat exchanger, different techniquesare employed to attached the foam materials to its tubular core orflat substrate. De Jaeger et al. [8] identified four possible methods;brazing, co-casting, thermal glue bonding, and mechanical press-fitting. Their main objective was to assess TCR associated witheach bonding method. They found brazing to be the best techniquewhile press-fitting being the worst. TCR is an important factor indesigning heat exchange hardware as emphasized by Fiedler et al.[10] and minimizing it can improve heat conduction performanceof composite materials significantly as De Jaeger et al. [8] shows.

The main objective of the present study is to evaluate thermo-hydraulic performances of single tubular aluminium foam heatexchangers. Focus is given to assessing their heat transfer andpressure drop characteristics resulting from different foam mate-rials, heights, and bonding methods between the foam and the wallof solid core cylinder. This work forms a small part of a projectaimed at identifying best design of a single tube, and furtherevaluating their performance in bundle configurations, takingeconomic factors into consideration. The target application of heatexchangers studied in the next stage, in their best configuredbundle form, is an air-cooled condenser in a typical low tempera-ture turbine cycle for geothermal power plants. Geothermal energyis a potentially feasible option in Australia for a base load powergeneration. However, geothermal resources are located in remotelocations with limited cooling water availability. To overcome thisbarrier and remain viable economically, it is envisaged thatrejecting waste heat from geothermal power plants in this contextmust rely heavily on a dry cooling system.

2. Specimen descriptions

The finned heat exchanger was manufactured in-house at theQGECE mechanical workshop. An aluminium solid bar of a length580 mmwas machined to form the finned external structure. Thereare 89 annular fins spread across the total length of 440 mm, eachwith the thickness of 0.6 mm (tf) and sits apart from one another (tp)at 4.24 mm. The core external diameter (do) along the tube coveringwith fins, i.e. the middle 440mm length, measures 30mmwhile thebare sections at either end have do ¼ 32 mm. The tube has the in-ternal diameter (di) 25.8 mm. Essentially, for the most part, the tubewall where heat transfer takes place has a thickness (tw) of 2 mm.

There are five samples of foam covered heat exchanger all usingfoam layer having 20 PPI pore density. Among them, four samplesare made of the same foam type but with a different thickness; viz.,5 mm, 12 mm, 15 mm, and 20 mm. The core tube of each sample inthis set is an aluminium cylinder with external diameter do, mea-sures 32.0 mm and internal diameter, di, 28.5 mm. The foam ma-terial which covers the tube in all four samples, having porosity of0.901, is of the same alloy as the core cylinder. Except for the 15mmsample which has its foam layer pressed-fit to the core, the otherthree have the foam cover and the core tube bonded together byhigh-temperature brazing. The last heat exchanger sample has thefoam thickness of 5 mm bonded with thermal glue to its stainlesssteel core tube. The porosity of the foam layer is 0.937. The core hasthe same do as those of the other four samples but with a smaller di(28.3 mm), resulting in a slightly higher wall thickness.

All foam wrapped heat exchangers, shown in Fig. 1, are readymade commercial products. The first four were supplied by thesame manufacturer. The last sample was supplied by anothervendor and has the core tube and its foam layer bonded togetherdifferently. Table 1 summarizes physical properties of the speci-mens shown in Fig. 1.

Fig. 1. Specimens used in the study. Based on either foam or fin height from left toright: foam-2 (5 mm), foam-1 (5 mm), foam-1 (12 mm), fin (15 mm), foam-1 (15 mm),and foam-1 (20 mm).

Fig. 2. The wind tunnel facility being used in the experiments.

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273 269

3. Experimental set-up and data collection procedure

The test facility is an open circuit wind tunnel shown in Figs. 2and 3. The air is drawn into the tunnel from the right-hand sidethrough a dust filter, a honeycomb separator, and 4 sets ofsmoothing screen. It then passes through the settling section, theconstriction plenum of 5.5:1 ratio (4) into the test section (3). In thetest section, the air mass flows over the hot surface of the testspecimen, takes up heat, and flows into the downstream stabilisingchamber (1).

The hot air exits the tunnel through an elbow bend which di-verts the air stream out of the system via the ceiling (8). Just beforethe elbow, the suction blower is installed in-line and the drivingshaft extends out to the prime driver which is a large 17 kW DCmotor. The constriction section (4) has one pressure ring at its inlet,immediately after the flow settler, and another at the exit where itjoins the test section. The pressure differentials of the two rings areinput to a transducer which generates a signal to drive the controlunit of the blower motor. The air velocity is controlled by a PIDclosed-loop control strategy implemented using LabVIEW softwaresuite. Before the test, the chosen range of air velocity from 0.5 m/sto 5.0m/s is verified by a Particle Image Velocimetry (PIV) (6) underthe empty chamber condition. PIV is an accurate, non-intrusivetechnique for determining the air velocity and its application inthis work is described in a separate study by Khashehchi et al. [15].

The test section has its cross-sectional areas measured454mm� 454mm at the inlet and 462mm� 462mm at the exit. Itis 1220mm long and divided into three compartments horizontallyby two sets of flexi-glass baffle (see Fig. 5). The middle

Table 1Summary of all six heat exchanger specimens.

Surface type Do [mm] t [mm] Materialssurface/core

k [W/m K] Bondingmethod

Fin, reference 62 15 Aluminium 210 CoherentFoam-type 1 42 5 A6101/A6061 5.8 BrazingFoam-type 1 56 12 A6101/A6061 5.8 BrazingFoam-type 1 62 15 A6101/A6061 5.8 Press-fitFoam-type 1 72 20 A6101/A6061 5.8 BrazingFoam-type 2 42 5 A1050/SS316 6.0 Thermal glue

compartment has the cross-sectional area of 454 mm(W) � 210 mm (H) at its inlet. During the experiments, the heatexchanger specimen is installed in the centre line of the middlesection. A pair of pitot tube are installed either side of, and at thesame level to, the specimenwhose pressure drop is to bemeasured.The upstream pitot tube, the specimen, and the downstream pitottube, are located 193 mm, 455 mm, and 810 mm, respectively fromthe test section inlet. The pressure drop is measured by a high ac-curacy pressure differential transducer with an accuracy of�0.06 Pa for a maximum measurement range up to 50 Pa. A pair ofPT-100 RTD probes are installed in the bottom compartment nearthe test section inlet to measure the air inlet temperature. Exittemperature was measured by an XY traversing system (2) wherefour PT-100 probes are mounted and can scan the designated exitarea of the three compartments at the grid size of 10 mm � 10 mm,using similar movement to dot matrix printers. All PT-100 probeshave accuracy of �0.03� C.

On the liquid side, a hot liquid mixture, made of 1 partglycol þ2 parts water by volume, is heated and maintained at75 �C by a heater unit (5). The hot liquid is circulated around aclosed-circuit through the core tube of the heat exchanger by anin-line pump installed in series with an accurate volumetric flowmeter. Liquid inlet and exit temperatures are measured byinstalling two K-Type thermocouples, each on the inlet and exitmetal fittings with the tip of the probe sitting at the centre of theliquid stream. They are calibrated against a FLUKE-9142 FieldMetrology Well to an accuracy of 0.001 �C. Data logging andcontrol of different parts of the system such as air velocity and exitair temperature scanning are co-ordinated by a host computer.The data file logs air inlet and exit temperatures, hot liquid inletand exit temperatures, liquid flow rate, and pressure drop acrossthe test specimen. Before testing the foam-wrapped specimens, aplain aluminium cylinder (do 30 mm di 26 mm), is installed for areference run. The Nusselt numbers according to Hilpert andZukauskas as described by [13] are verified and found to beagreeable with that from the measurement. This ensures the val-idity of the test rig.

For each specimen under test, The air flow is set to 0.5 m/s andthe liquid temperature at heat exchanger inlet is monitored until itis settled within 75 � 0.75 C, all relevant data are logged everysecond for 10 min. The air flow is then increased to the next step of0.5 m/s increment and when the liquid temperature re-settles, theprocess is repeated until air flow reaches 5.0 m/s.

Fig. 3. Side view schematic of the wind tunnel (not drawn to scale). The test section (3) shows staggered row pattern of 8 tube bundle mounting plate (7) but the tests described inthis study use one position in the first row to mount a single tube e the one filling with the black dot.

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273270

4. Analysis

Thermal energy exchange analysis follows theoretical formula-tion of related parameters for forced convection around a cylinderin a cross flow. As the hot liquid mixture enters the heat exchangercore and flows to the exit, it loses heat to the cooler air streamflowing past the heat exchanger external surface. The air is forcedto flow at varying velocity by the suction fan. Only the exchange ofthermal energy occurring inside the test section is taken into ac-count as the heat loss outside the test section is found negligiblysmall.

4.1. Total heat transfer

Total heat transfer, _Q [W], is evaluated from:

_Q ¼ _Q liq ¼ _mliqcpDT (1)

DT is the temperature differential of the hot liquid at the inletand exit of the heat exchanger ¼ Tliq,in � Tliq,out [K].

This present report adopts a concept taken by the authors suchas Cavallini et al. [7] and Moffat et al. [23], among others, inassessing each sample performance. In these studies, the authorsattributed the ability of foam surface in augmenting heat transfer toa qualitative intrinsic property which is lumped together with thefoam convective heat transfer coefficient (HTC). For example, Cav-allini, et al. [7] used HTC.U* to denote this combined parameter intheir analysis.

4.2. Overall thermal resistance between two fluid streams

The effect of net radiation heat transfer between the heat ex-changers and their surroundings inside the test section is insig-nificant and therefore not included in the calculation. With thisassumption, the overall thermal resistance Rt [K/W] is defined as:

RthðTs � TNÞ

_Q(2)

where Ts is internal surface temperature of the heat exchanger [K]taken as the average of liquid inlet and exit temperatures(Tliq,in þ Tliq,out)/2, TN is the free-stream temperature of the bulk air[K], and _Q [W] is as calculated by Equation (1).

All heat exchangers used are new specimens and resistance dueto fouling both on the liquid side and air side can be excluded. Withthis assumption, Rt can be taken as the sum of internal surfaceconvective resistance, conductive resistance through the tube wall,contact resistance at the interface of the tube and the foam layer,and external surface convective resistance. In equation form andthe order as listed, this can be written:

Rt ¼ 1hliq2priL

þ ln rori

2pkLþ Rc þ 1

hahsAs(3)

where hliq is the convective heat transfer coefficient on the liquidside [W/m2 K], ri is the tube internal radius [m], and L is the lengthof the tube section covering with foam (or fins) which is approxi-mately equal to the test section width [m]. On the conductive term,ro is the external radius of the tube; not including the foam andbonding adhesive [m], and k is thermal conductivity of the coretube material [W/m K]. The third term Rc, is the TCR of bondingadhesive.

The last term of Equation (3) needs a special consideration. Toavoid impractical dealing with the foam interfacial surface area (i.e.that in contact with air), the product hahs is interpreted in the samemanner as HTC.U* treated in Cavallini et al. [7]. Using this approach,As can then be taken simply as the external surface area of the coretube under the foam cover. It should be noted that this approachcan be applied equally to the finned surface.

Heat transfer performance of all specimens in this study is re-ported in terms of individual overall thermal resistance, Rt.

5. Results and discussion

5.1. Thermal resistance

The plot of thermal resistance against air velocity is shown byFig. 4. It is apparent that the heat exchangers with smaller foamlayer thickness is less efficient in rejecting heat, i.e. has morethermal resistance, at the same range of air velocity. This is as ex-pected in all cases of the specimens. Another notable result is thatthe two samples with the same foam thickness (5 mm) have asignificant difference in their thermal resistances. The 5 mm-SS(s316 stainless steel core tube, Table 1) performs poorer. This can beattributed to three possible reasons. Firstly, The 5 mm-SS sampleuses thermal glue bonding method between its foam layer and the

Fig. 5. The test section showing the method of pressure drop measurement.Fig. 4. Overall thermal resistance of all six specimens plotted against air velocity.

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core tube. The authors have previously examined thermal contactresistance (TCR) in a separate study. Depending on air velocity, itwas found that thermal glue bonding had TCR between 10% and19%, (corresponding to air velocity 1.5 m/s to 5.0 m/s) of the totalthermal resistance if brazing method TCR is treated to be small andcan be disregarded. Secondly, the 5 mm-SS has a higher porositycompared to the 5 mm-Al (0.937 and 0.901). Higher porosity isassociatedwith less interfacial surface area and it is usually the casethat the heat transfer is decreased. This effect is consistent with thefindings of previous works such as those of Angirasa [1], andMancin et al. [21]. Thirdly, sample 5 mm-SS has stainless steel coretube with higher wall thickness and lower k value than those of thecore tube of 5 mm-Al sample.

The effect of different surface types on heat transfer can beassessed by comparing the results of Fin-15 mm and Foam-15 mm.In this comparison, the finned tube has no TCR between all its 89annular fins and the core tube because the heat exchanger wasmade as a single piece from a solid aluminium round bar. Incontrast the Foam-15 mm sample has the maximum TCR becausethe foam layer and the core tube were press-fit together. Press-fitting gives the highest TCR according to De Jaeger et al. [8].Despite the double disadvantage, the Foam-15 mm still performsconsiderably better than the same thickness Fin-15 mm. If thepressure drop data being discussed in the next section is also takeninto account, it can be concluded that the overall performance offoam surface is undoubtedly more favourable.

Fig. 6. Pressure drop of all six specimens plotted against air velocity.

5.2. Pressure drop

Pressure drop data are purelymeasured values at two imaginaryplanes perpendicular to the direction of the air flow. The planeupstream locates at 200 mm away from the centre line of the testsample, and the one downstream locates 420 mm away from thesame reference. At each plane, a pitot tube was installed from thetop panel to the depth horizontally aligned with the centrelines ofthe test section and the heat exchanger tube being tested. Thedifference in total pressure between the two pitot tubes is taken asthe pressure drop across the sample.

Fig. 5 shows the general setting of the two pitot tubes forpressure dropmeasurement. This arrangement is necessary to keepthe closed-loop air velocity control functioning the way it wascalibrated.

The foam materials covering all foam samples are of similaralloy (kw 220e235W/m K) and having the same PPI density. If twoheat exchangers are wrapped with the same thickness, the expec-tation on pressure drop characteristics should likewise be similar.The pressure drop for all specimens under test, plotted against theair velocity, is shown by Fig. 6.

Following the argument and expectation outlined above, pres-sure drop comparison of the two 5 mm foam tubes is wellconfirmed. The pressure drop is known to be affected by tangible,macroscopic properties of the specimens [19]. Because the two5 mm foam heat exchangers have very similar physical dimensionsand foam specifications, their pressure drop results are thereforepredictively similar. The thin layer of thermal conductive glue beingadded on the external surface of 5 mm-SS tube core to bond itsfoam matrix doesn’t manifest a different effect to the results.

Over the whole range of designated air velocity, the generaltrend of foam thickness toward pressure drop it generates is asexpected for all test samples. The sample with the highest add-onthickness generates the maximum pressure drop while thosewith the lowest thickness generate the minimum pressure drop.The curves diverge toward the maximum air velocity.

The effect of different modified surface structure of the samethickness or height, i.e. foam 15 mm vs. finned 15 mm, to pressuredrop is not significant e with the finned tends to cause less pres-sure drop especially toward the higher air velocities. For all sam-ples, their pressure drop up to the air velocity of 3.5 m/s are notvaried greatly apart.

5.3. Effect of surface type on heat transfer and pressure drop

To visualize the combined effectiveness of the foam heat ex-changers, thermo-hydraulic data of 15 mm foam are plotted incomparison with those of the 15 mm finned-tube. This is as shownin Fig. 7.

It should be noted, from the earlier discussion, that this plotrepresents the worst case performance of the foam tube and the

Fig. 7. Performance comparison of aluminium foam and finned tube of the same Do

and identical core dimension.

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273272

best case for the finned counterpart. This is due to the foam tubehaving the maximum TCR and the finned tube having none.Nevertheless, it is seen here that the trends of the two curvesdiverge as the pressure drop increases. This shows that while theincrease in rate of heat transfer _Q for the finned tube slows down, _Qof the foam tube continues to rise with the increase of pressuredrop (i.e. corresponding to the increase of air velocity or the Rey-nolds number Red, of the air flow). Put it differently, over the rangeof the Reynolds number under this test conditions, the foam tubeexhibits a better heat transfer performance at the same pressuredrop. For example, at about 25 Pa (corresponding to Red¼ 10590, orU ¼ 5 m/s e see Fig. 6) _Q(foam) w 1450 W and _Q(fin) w 1060 W, a37% enhancement.

Followingmethodology presented byMoffat [22], the root-sum-square is used to combine an error due to instrument bias and astatistical error evaluation. Propagation of errors to derived variablefollows themethod present by Kirkup [16]. All propagated errors on_Q are less than 10%.

5.4. Thermal resistance and pressure drop correlations

Following the approach used by Hooman and Merrikh [11], twocorrelations of the form Y ¼ j$Do

do

a$Ub are proposed to assist in the

prediction of overall thermal resistance (Rt) and pressure drop (DP)of the foam heat exchanger tubes. Y is the target parameter beingpredicted which can be either Rt or DP, Do/do is foam to core tubeexternal diameter ratio, U is air velocity, and j,a,b are empiricalcoefficients specific to the two cases, i.e. Rt or DP. The Least SquaresMethod (LSM) and an iteration technique are used to determine thebest fit correlations taking U as the independent quantity, Y as thedependent quantity in the (Ui, Yi) data set where i ¼ 1 to 10(U1 ¼ 0.5, U2 ¼ 1.0, U3 ¼ 1.5, ., U10 ¼ 5.0).

From all ten (Ui, Yi) data pairs the residual DYi, defined asYi,observed � Yi,calculated, are squared and summed to form the sum ofresidual square; S¼ (DY1)2þ (DY2)2þ.þ (DY10)2. According to theLSM, the best values for j,a, and b are found by minimizing S. TheLSM is a well-established procedure [11] so its treatment won’t berepeated here. Full details and its theory can be consulted in sta-tistical or data interpretation references such as [16]. The finalcorrelations are as shown in Equations (4) and (5).

DP ¼ 0:807$�Do

do

�0:859

$U1:828 (4)

Rt ¼ 0:289$�Do

do

��1:617

$U�0:595 (5)

These correlations fit the general experimental data well withthe pressure drop yielding a more accurate prediction. Themaximum DP errors from the thickest foam tube to the thinnestone (i.e. 20 mm, 15 mm, 12 mm, 5 mm) are 17.1%, 17.9%, 10.9%, and10.8% respectively. These errors represent extreme outliers whichoccur at air velocity below 1 m/s because, at low velocity, the de-nominators involve in fraction calculation are small numbers. Ifthese outliers are excluded, all errors of the four thicknessescovering all velocity range are lower than 8%. For Rt, the maximumerrors for the same order of foam thickness are 5.6%, 10.1%, 39.4%,and 24.4%, respectively.

Correlations in thermo-fluids are usually presented in non-dimensional forms. To adhere to this practice, DP can beexpressed as a dimensionless friction factor, f, by a familiarquadratic relation:

DP ¼ f $ra$U2 (6)

where DP is as calculated by Equation (4). By replacing the diameterratio Do/do with a simpler notation Dr and converting the velocityterm to Reynolds number with do as its characteristic length, f canbe written as:

f ¼ 2:675Dr0:859$Re�0:172do

(7)

Equation 7 exhibits its form and magnitude similar to F inrelation to Re as reported by Mancin et al. [20] in their study of airflow through full channel occupied by aluminium foams. Accordingto this study (ref. Eq. 15) F w Re�0.1014.

For thermal resistance, since Rt has the dimension of K/W, itfollows that multiplying it by ka.do will produce dimensionlessthermal resistance, R0. Hence, in a similar fashion, Equation (5) canbe expressed in its dimensionless form as:

R0 ¼ Rt$ka$do ¼ 0:024Dr�1:617$Re�0:595 (8)

6. Conclusions

In this study five foam wrapped heat exchangers of tubulardesign are tested for their thermo-hydraulic performance using afinned tube of comparable dimensions as a benchmark sample.Available foam specimens allow the study of foam thickness effecton heat transfer and pressure drop. In addition, three differentbonding methods applicable among six specimens in this study aidin interpreting data associated with respective specimens. The re-sults show that, for thermal efficiency, overall thermal resistancedecreases with the increase of foam layer thickness. However, thisthermal advantage comes at the expense of increasing pressuredrop. Depending on target applications, as a single tube, theresulting pressure drop may be acceptable as it does not differsignificantly from that of current heat exchanger design. The foamwrapped heat exchanger with suitable foam thickness is seen togive heat transfer benefit while keeping the pressure drop at thesame level as that causes by the finned tube. Experimental resultsare also helpful in developing correlations to predict relevant var-iables of interest. This study defines two correlations to predictpressure drop and thermal resistance using the same set of inputparameters. Non-dimensional forms of these two variables are alsopresented.

Acknowledgements

The authors are grateful to the Queensland Geothermal EnergyCentre of Excellence (QGECE) for providing financial support to this

A. Chumpia, K. Hooman / Applied Thermal Engineering 66 (2014) 266e273 273

study. They also express their gratitude to the following in-dividuals: Professor Thomas Rösgen, Institut Für Fluiddynamik,ETH-Zurich for his work in setting up the PIV facility and its concepttutorial, Mostafa Odabaee for his help in ordering and importingtest specimens, Dr Morteza Khashehchi, QGECE, who helped runand process PIV data for velocity check, Joy Wang and PeterBleakley, EAIT Instrumentation Workshop, for helping with Lab-VIEW data logging, Douglas Malcolm for helping with wind tunneloperation and air velocity PID control program and lastly Berto DiPasquale, EAIT Mechanical Workshop for general fabrication of in-house parts and accessories.

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