metal foam heat exchanger

puli

titute

ETH Center, ML J 36, 8092 Zurich, Switzerlandb ABB Corporate Research Ltd., Segelhof, 5405 Baden-Daattwil, Switzerland

pressure drop across a porous medium as a linear

function of the ow velocity and material perme-

ability. Since then, a series of improvements have

(1918). The addition of a quadratic term in the

linear Darcy Law was rst proposed by Dupuit

(1863), although many mistakenly credit Forch-heimer with the addition of the quadratic term as a

result of his extensive review of other porous me-

dia studies (Forchheimer, 1901). A thorough re-

Mechanics of Materials 35 (20

ARTICLE IN PRESS* Corresponding author. Tel.: +41-1-632-2738; fax: +41-1-Keywords: Metal foam; Porous media; Heat transfer; Open-cell aluminum foam

1. Introduction

Flow through porous media has been studied in

detail ever since Darcys publication in 1856(Darcy, 1856). His work described the uid ow

been made to describe the pressure drop behavior

in better detail, one of which was accounting for

temperature variations in the uid by Hazen

(1893). These temperature variations were later

linked to the viscosity of the uid by KruugerReceived 1 June 2002; received in revised form 30 January 2003

Abstract

Open-cell metal foams with an average cell diameter of 2.3 mm were manufactured from 6101-T6 aluminum alloy

and were compressed and fashioned into compact heat exchangers measuring 40.0 mm 40.0 mm 2.0 mm high,possessing a surface area to volume ratio on the order of 10,000 m2/m3. They were placed into a forced convection

arrangement using water as the coolant. Heat uxes measured from the heater-foam interface ranged up to 688 kWm2,which corresponded to Nusselt numbers up to 134 when calculated based on the heater-foam interface area of 1600

mm2 and a Darcian coolant ow velocity of approximately 1.4 m/s. These experiments performed with water were

scaled to estimate the heat exchangers performance when used with a 50% waterethylene glycol solution, and werethen compared to the performance of commercially available heat exchangers which were designed for the same heat

transfer application. The heat exchangers were compared on the basis of required pumping power versus thermal re-

sistance. The compressed open-cell aluminum foam heat exchangers generated thermal resistances that were two to

three times lower than the best commercially available heat exchanger tested, while requiring the same pumping

power.

2003 Elsevier Ltd. All rights reserved.Metal foams as compact high

K. Boomsma a, D. Poa Laboratory of Thermodynamics in Emerging Technologies, Ins632-1176.

E-mail address: [email protected] (D. Poulikakos).

0167-6636/$ - see front matter 2003 Elsevier Ltd. All rights reservdoi:10.1016/j.mechmat.2003.02.001erformance heat exchangers

kakos a,*, F. Zwick b

of Energy Technology, Swiss Federal Institute of Technology,

03) 11611176

www.elsevier.com/locate/mechmatview of the history of the study of uid dynamics

through porous media can be found in a review by

ed.

of M

ARTICLE IN PRESSNomenclature

A area [m2]C form coecient [m1]CTE coecient of thermal expansion

[mm1 K1]D diameter [m]FS Full scale

K permeability [m2]L length [m]M compression factor []Nu Nusselt number (dened in Eq. (12)) []P pressure [bar]Q volumetric ow rate [m3 s1]R thermal resistance (dened in Eq. (12))

[KW1]

1162 K. Boomsma et al. / MechanicsLage (1998). An end result of the nearly 150 year-old work in porous media is the widely accepted

equation (Eq. (1)) which governs the pressure drop

of a uid passing through a porous medium.

DPL lKV qCV 2 1

The term DP is the pressure drop across the me-dium, L is the length of the medium in the owdirection, l is the dynamic viscosity of the uid, Kis the permeability of the medium, V is the clear-channel (Darcian) velocity of the uid, q is thedensity of the uid, and C is the form coecient ofthe medium.

The extension of the uid dynamic work in

porous media in a channel to include simultaneous

convective heat transfer can be traced back as far

as Koh and Colony (1974); Koh and Stevens

Re Reynolds number (dened in Eq. (4)) []

T temperature [C, K]V velocity [m s1]_WW pumping power [W]c specic heat [kJ kg1 K1]f friction factor []h convection coecient [Wm2 K1]j Colburn factor (dened in Eq. (10)) []k thermal conductivity [Wm1 K1]_mm mass ow rate [kg s1]q heat rate [W]w absolute error []

Greek symbols

D dierence []a thermal diusivity [m2 s1]e porosity fraction (range 100P e > 0) [%]l dynamic viscosity [kgm1 s1]m kinematic viscosity [m2 s1]q density [kgm3]

Subscripts

c coolant

con convection

aterials 35 (2003) 11611176(1975). Their analysis considered a simple slugow velocity prole through the porous medium,

but the cooling eects generated by the presence of

a porous medium were shown. In the course of

developing better analytical models for channel

convection, Kaviany (1985) presented an analyti-

cal solution of the transport equations based on

the quadratic-extended Darcy ow model (Eq.

(1)). Advancements continued in numerical workon forced convection through packed beds of

spheres which included the notable numerical

work performed by Poulikakos and Renken (1987)

and the corresponding experimental investigation

(Renken and Poulikakos, 1988). Many other

models have been proposed to account for other

variables, such as wall eects (Kaviany, 1985;

Mehta and Hawley, 1969), variable porosity(Amiri and Vafai, 1994; Nield et al., 1999), and

cs cross-sectional

e eective

f uid

hyd hydraulic

inlet inlet

outlet outlet

p perimeterpl plates solid

th thermal

kos, 2002). However, in the case of open-cell metal

K. Boomsma et al. / Mechanics of M

ARTICLE IN PRESSeven non-Newtonian uids (Chen and Hadim,

1998, 1999). The great majority of these studies

that are covered by Kaviany (1995) consider

spherical media, which possess porosities in the

range e 0:30:6. This conguration is known asa bed of packed spheres, which models uid owthrough sediment and other granular systems.

The question arises how far these concepts

based on spherical media can be taken to include

other types of porous media. One type of a non-

spherical porous medium is open-cell metal foam.

The structure of open-cell metal foams (Fig. 1)

opens itself to a wide variety of possible applica-

tions which include, but are not limited to, lightweight high strength structural applications,

mechanical energy absorbers, lters, pneumatic

silencers, containment matrices and burn rate

enhancers for solid propellants, ow straighteners,

catalytic reactors, and more recently, heat ex-

changers. The open-cell metal foam structure has

the desirable qualities of a well designed heat ex-

changer, i.e. a high specic soliduid interfacesurface area, good thermally conducting solid

phase, and a tortuous coolant ow path to pro-

mote mixing. Depending on the particular open-

cell metal foam conguration, its specic surface

area varies between approximately 500 to over

10,000 m2/m3 in compressed form (ERG, 1999).

The metal matrix can be manufactured from a

high thermally conducting solid such as aluminum(ks 200 Wm1 K1) or copper (ks 400Wm1 K1), which, merely by its presence in astatic uid, dramatically increases the overall ef-

fective thermal conductivity of the uid-system

(Calmidi and Mahajan, 1999). The overall eective

thermal conductivity of the soliduid system (keff )can be most generally described by the porosity (e)and the conductivities of the uid and solid phasesby kf and ks, respectively (Kaviany, 1995).

keff ekf 1 eks 2This increase in overall eective thermal conduc-

tivity of the soliduid system to a level above that

predicted by Eq. (2) was shown in the 2-D con-duction model by Calmidi and Mahajan (1999).

Noting the inuence of the structure on the ther-

mal conductivity of the metal foam matrix,Boomsma and Poulikakos (2001) developed anfoams, the numerical models have had limited

success, and the experimentation to verify these

models is restricted, particularly to the coolant,

which is typically air. In cooling electronics which

generate a large amount of excess heat, a liquid

coolant is generally preferred over air because of

the greater thermal conductivity and specic heat

capacitance. In view of these requirements, exper-iments using a forced liquid coolant are needed not

only to investigate the feasibility of using open-cell

metal foams as heat exchangers, but also to provide

a basis against which numerical models can be

compared. The goal of this investigation is to

provide an experimental study of the performance

of open-cell aluminum foam heat exchangers in a

forced convection ow arrangement using a liquidcoolant, which is deionized, degassed water.

Comparisons with existing heat exchanger systems

for the application of cooling of electronics are also

provided.

2. Experiment

2.1. Apparatus

The goal of the experiment was to measure the

hydraulic and thermal performance of the open-

cell aluminum foams when used as heat exchang-

ers in a forced convection ow arrangement. The

concept was to direct the coolant ow through a

rectangular channel in which the aluminum foamheat exchanger is placed, occupying the entire

cross-section of the channel. A heater was attachedimproved analytical heat conduction model based

on the idealized 3-D unit cell of an open-cell metal

foam.

There currently exist analytical (du Plessis et al.,

1994; Diedericks and du Plessis, 1997; Smit and duPlessis, 1999; Lu et al., 1998) and numerical models

(Calmidi and Mahajan, 2000; Lage et al., 1996) for

the uid ow and heat transfer in packed beds of

spheres and extensive databanks of uid ow and

heat transfer experiments used as verication of

these models (Antohe et al., 1997; Lage et al., 1997;

Lage and Antohe, 2000; Boomsma and Poulika-

aterials 35 (2003) 11611176 1163to the aluminum foam via the heat spreader plate,

Fig. 1. (a) Open-cell aluminum foam (T-6106 alloy) in its as-manufactured state with a porosity of e 92% and approximately 6 mmdiameter pores (ks 200 Wm1 K1). (b) Close-up view on an individual cell of the aluminum foam depicted in (a). (c) Open-cell metalfoam similar to that shown in (a), but after compression by a factor of four. (d) Close-up view of the compressed foam depicted in (c).

Note the altered form of the individual cells that had originally resembled the cell in (b).

1164 K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176

ARTICLE IN PRESS

through which the heat was conducted and even-

tually convected into the coolant stream. The

characterization of the open-cell metal foam heat

exchangers included measuring the temperature of

the heater block, the temperature of the heat

spreader plate, the coolant temperature at severallocations in the coolant ow, the power delivered

to the heating device, and the pressure drop across

the heat exchangers for various coolant ow rates.

A general overview of the experimental apparatus

is shown in Fig. 2. The channel assembly is shown

in detail in two separate views in Fig. 3.

Eight pressure taps measuring 0.2 mm in di-

ameter were bored into the housing at variouslocations to measure the static pressure, as seen in

Fig. 3(b). The outermost ports were used for the

pressure drop calculations to avoid the static

pressure variations generated by the acceleration

and deceleration of the uid as it enters and leaves

the metal foam. The other six ports were used as a

symmetry check of the ow. During the experi-

ments, the pressure variation between the left and

right ports did not uctuate more than 3% and was

therefore neglected.

The metal foam heat exchanger housing was

manufactured from Ryton R4, which has a lowthermal conductivity (0.3 Wm1 K1) and a rea-sonable CTE (22 106 m/m C). The static pres-sure drop of the coolant across the metal foam

heat exchanger was measured by two dierent

dierential pressure transducers corresponding to

their individual pressure ranges. A Huba dieren-

tial pressure transducer was used for measuring

the pressure in the lower pressure range, from 0 to0.20 bar, with an accuracy of 0.5% FS (0.001

bar). For the pressure range from 0.20 to 3.45 bar,

an Omega (PX81DO-050DT) dierential pres-

sure transducer was employed with an accuracy

of 0.25% FS (0.009 bar). E-type thermocou-

ples (chromel/constantan) of 0.15 mm diameter

a Acqu

Data Acquisition PC

Coo

Heate

Power Supply Oscilloscope

re th

K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176 1165

ARTICLE IN PRESSRotameter

Dat

Coolant Chiller/Recirculator

Pressure RegulatingValve Thermocouples

20.0

Metal Foam

Fig. 2. Schematic view of the experimental setup used to measuminum foam heat exchangers.Foam Housing

Pressure Transducer

USB isition Device

Valve Array

lant Flow Direction

r Assembly

e thermal and hydraulic characteristics of the compressed alu-

Mshows

foam

foam

of M

ARTICLE IN PRESSmeasured the temperatures at various locations of

the experimental apparatus. The thermocouples

were calibrated in a thermal bath to within 0.5 Cand were inserted through the 0.2 mm diameter

pressure taps that were located in the bottom of

the channel to measure the temperature of the

coolant ow (Fig. 3(b)). The pressure drop mea-surements were performed both with and without

the thermocouples inserted through the pressure

taps to determine if their presence altered the

pressure readings. No eects were observed.

The data from the thermocouples and the

pressure transducers were measured by a USB

data acquisition device manufactured by IOTech.

This device enabled the real-time measurement,recording, and display of the temperature and

pressure drop data on the attached personal

METAL FOA

FLOWINLET

FLOWOUTLET

PRESSURE PORTS

(a)

HEATER ASSEMBLY

Fig. 3. (a) Cross-sectional view of the foam test housing which

assembly, and the path of the coolant ow. (b) Top view of the

placement of the foam component of the assembled compressed

1166 K. Boomsma et al. / Mechanicscomputer.

The coolant was pumped through the experi-

mental apparatus by a Neslab chiller. It provided a

maximum coolant ow rate of approximately

10 l/min, could dissipate a total of 1600 W, and

regulated the coolant inlet temperature to within0.3 C.

The coolant ow rate was measured using two

dierent rotameters. The lower ow rate range

varied from 0 to 1.0 l/min, which corresponded to

a ow velocity of 00.21 m/s for a channel cross-

section of 40.0 mm 2.0 mm. For this lower range,a Voogtlin rotameter with 1% FS (0.01 l/min) ac-curacy was utilized. The higher ow rate rangetested varied from 1.00 to 5.00 l/min, corre-

sponding to a ow velocity range of 0.211.04 m/sfor a channel cross-section of 40.0 mm 2.0 mm.In the higher ow rate range, a Wisag 2000 ro-

tameter was employed with an accuracy of 1% FS

(0.11 l/min).

The heating system consisted of a blockmachined

from oxygen-free copper (ks 400 Wm1 K1)measuring 40.0 mm 44.0 mm 20.0 mm high. Fiveholes measuring 6.35 mm in diameter were bored

through the block to hold ve 220 W cartridge

heaters in place. The voltage and current delivered to

the ve cartridge heaters were monitored by an os-

cilloscope. The maximum power delivered to the

heater block was 1100 W. Smaller holes measur-

ing 0.2 mm in diameter were drilled into the top

and base of the copper heater block, perpendicu-lar to the coolant ow direction. This allowed the

insertion of small diameter thermocouples to mea-

FLOWOUTLET

FLOWINLET

4cm7cm

(b)

the location of the aluminum foam heat exchanger, the heater

test housing depicted in (a) with the lid removed to show the

heat exchanger.

aterials 35 (2003) 11611176sure the temperature dierence across the heater

block.

2.2. Aluminum foam heat exchangers

One of the desirable qualities of the open-cellmetal foam in a heat exchanger application is the

large specic surface area, which ranges from ap-

proximately 500 to over 3000 m2/m3. Compressing

the foam further increases this already large sur-

face area to volume ratio. To generate an array of

open-cell metal foam heat exchangers, 6101-T6

aluminum alloy (ks 218 Wm1 K1) was castinto foam form at two dierent porosities ofe 92% and 95% with an average cell diameter of2.3 mm. This foam is listed as 40 PPI by the

phys

76.0 82.5

52.0 66.9

Specic surface area [m2/m3] Measured porosity [%]

2700 92.8

50

60

70

80

90

100

0 2 4 6 8 10

Expected Porosity (95%)Effective Porosity (95%)Expected Porosity (92%)Effective Porosity (92%)

M

[%]

of M

ARTICLE IN PRESSmanufacturer (ERG, 1999). The PPI acronym

designates pores per linear inch, but due to the

ambiguity of this label, the pore diameters of the

uncompressed 40 PPI foam were visually measured

by hand using a microscope and a scale calibrated

to one-tenth of a millimeter and were tabulated in

Table 1.The specic surface area of these foams was

further increased by compressing them by a factor

of M , which signies the ratio of the pre-com-pression to post-compression height of the foam

block. In the one-dimensional compression pro-

cess, the lateral sides of the metal foam are not

Table 1

Compressed foam physical data (Panel A), uncompressed foam

Foam Compression Name

Panel A

5% 2 95-02

4 95-04

6 95-06

8 95-08

8% 2 92-02

3 92-03

6 92-06

Panel B

Foam Pore diameter [mm]

40 PPI 2.3

K. Boomsma et al. / Mechanicsrestrained. This is done to prevent any mass ac-

cumulation in the foam caused by lateral materialmovements during the compression process.

However, any material which ows to the out-

side of the compression device is lost in the ma-

chining of the foam to its nal overall dimensions,

thus the resulting porosity of the foam may be

higher than what would be predicted by Eq. (3).

ecompressed 1M1 euncompressed 3The porosities of the aluminum foams were cal-

culated by weighing them and comparing the

density to that of solid 6101-T6 aluminum alloy.

The corresponding expected porosities were also

calculated by Eq. (3), using the manufacturersstated initial, uncompressed porosity of euncompressedand the given nominal compression factor, M .Table 1 lists both the measured and expected po-ical data (Panel B)

Expected porosity [%] Measured porosity [%]

90.0 88.2

80.0 80.5

70.0 68.9

60.0 60.8

84.0 87.4

aterials 35 (2003) 11611176 1167rosities, and Fig. 4 shows their relationship

graphically. The various congurations of alumi-

num foams are named using two pairs of digits.

The rst pair is pre-compression porosity; the

number 92 designates euncompressed 92%. The sec-ond pair of digits designates the compression fac-

tor, M . The foam 92-04, for example, was 92%porous in its uncompressed state and then com-pressed by a factor of four. In Fig. 4, the porosities

of the 95% pre-compression foam samples that

Fig. 4. Plot of the porosity of the raw foam material which was

used in the aluminum foam heat exchangers. The lines denote

the porosity predicted by the manufacturers stated initial po-rosity (e) and compression factor (M) based on Eq. (3), whilethe individual points are the measured values for the raw foam

material.

given in length normalized units of [barm1] based

of M

ARTICLE IN PRESSwere measured closely follow the relationship as

predicted by Eq. (3). However, the porosities of

the 92% pre-compression foam remained higher

than those predicted by Eq. (3) and the manufac-

turers given data. By the consistency of the errorof the porosity data points from the predicted line

for the 92% initial porosity foam, it can be as-

sumed that this discrepancy is due to an inaccurate

estimate of the initial porosity given by the foam

manufacturer.

The open-cell aluminum foams measured 40.0

mm 40.0 mm 2.0 mm after the nal machiningprocess. To make them functional heat exchang-ers, each foam piece was brazed in a central posi-

tion to an adjoining heat spreader plate which

enabled a copper heating block to be mounted

on the opposing side. Each heat spreader plate

consisted of 6092 aluminum alloy with 18% SiC

particles to increase the thermal conductivity to

approximately 250 Wm1 K1 and measured 58.0mm 58.0 mm 1.9 mm thick.

2.3. Experimental procedure

Each open-cell aluminum foam heat exchanger

was tested three times following the identical

procedure. The heat exchanger was mounted into

the test housing. The coolant was then pumped

through the foam at the maximum attainable owrate, which varied according to the overall ow

resistance of the individual heat exchanger. The

inlet temperature of the coolant was held at 220.3

C. After the 20 min stabilization period, fullpower to the heater cartridges was turned on, and

the entire experimental apparatus was allowed to

reach steady-state. Starting from the maximum

ow rate, the temperatures at various locationswere measured and recorded in real-time via the

USB data acquisition device and PC, which also

recorded the pressure drop reading from the

pressure transducer. The maximum coolant tem-

perature allowed during operation was 100 C, atwhich the coolant began to vaporize.

The ow rate was read from the rotameter.

After the data were taken, the ow rate was re-duced, and the apparatus was given 5 min to reach

steady-state for the next data point measurement.

1168 K. Boomsma et al. / MechanicsAs noted in the work by Boomsma and Poulikakoson the 40.0 mm length of the heat exchangers, and

the right-hand ordinate is the actual pressure drop

measured in the experiments, and is given in the

units of [bar]. As expected, those foams which

possess the highest solid fraction (lowest e) as seenin Table 1 generated the largest pressure drop.(2002) and Antohe et al. (1997), the direction in

which the ow rate is adjusted does not have an

eect on the calculated permeability and form

coecient needed to describe the ow resistance of

a porous medium.

3. Results and discussion

3.1. Pressure drop

The amount of work required to pump the

coolant through a heat exchanger is a critical heat

exchanger design parameter. In the work byBoomsma and Poulikakos (2002), the open-cell

metal foams which comprised the in-ow compo-

nent of the heat exchangers in this study were

tested for their hydraulic characteristics. The pa-

rameters used to describe the pressure drop char-

acteristics of the foam heat exchangers are the

permeability (K) and the form coecient (C)which are dened in Eq. (1). The metal foamcongurations used in this heat transfer study were

produced under conditions identical to those used

for the foams in the hydraulic characterization

study of open-cell metal foams conducted by

Boomsma and Poulikakos (2002). However, in

assembling the heat exchangers, some of the alu-

minum brazing material which attaches the foam

to the heat spreader plate partially lled the poresat the interface which reduced the eective ow

cross-sectional area of the heat exchanger and in-

creased the ow resistance of the metal foam heat

exchangers when compared to the results of the

similar, unbrazed foams in Boomsma and Pouli-

kakos (2002).

The assembled heat exchangers were tested

anew for their hydraulic characteristics and theresults of the pressure drop tests were plotted

graphically in Fig. 5. The left-hand ordinate is

aterials 35 (2003) 11611176These were led by the two most compressed foams,

brazed counterpart due to the presence of the

brazing material in the pores of the open-cell metal

foam at the brazing interface. Foams 95-08 and

92-06 showed a slight decrease in the ow resis-

tance when compared to their unbrazed counter-

parts. This change in behavior by the two mosthighly compressed brazed foams can be attributed

to warpage and distortion in the foam from the

brazing process, thereby allowing ow bypass.

With the remaining ve aluminum foam heat ex-

changers, the amount of the increase of the ow

resistance was not consistent. The change in the

0

10

20

30

40

50

60

70

80

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

0.0 0.5 1.0 1.5 2.0

95-0295-0495-0695-0892-0292-0392-06

P/L[barm-1] P[bar]

V [ms-1]


ARTICLE IN PRESS95-06 and 95-08, with foam 92-06 generating

nearly the same pressure drop. The foam which

produced the lowest pressure drop was foam 95-02, which was also the most porous of the samples.

The hydraulic characteristics of the brazed

foams were calculated by using a least squares

curve tting approach as described in Antohe et al.

(1997) and Boomsma and Poulikakos (2002) to

solve for the K and C in Eq. (1). These perme-ability and form coecient values were compared

to the values obtained in Boomsma and Poulika-kos (2002), which used the same aluminum foam

congurations, but without any brazing material.

Table 2 compares the permeability and form co-

ecients between the assembled heat exchangers

Fig. 5. Pressure-drop curves for the metal foam heat ex-

changers plotted on a length-normalized (DPL1) and actualpressure scale (DP ) against the Darcian ow velocity (V ).and the unbrazed foam blocks, along with the

corresponding uncertainty percentages. Almost

every assembled heat exchanger showed an in-

crease in the ow resistance compared to its un-

Table 2

Flow resistance comparison

Foam Unbrazeda

K [1010 m2] C [m1] K [1010 m

95-02 44.4 1168 34.4

95-04 19.7 2707 6.87

95-06 5.25 4728 3.16

95-08 2.46 8701 2.52

92-02 36.7 1142 30.8

92-03 23.0 1785 8.26

92-06 3.88 5518 3.95

aResults reported in Boomsma and Poulikakos (2002).ow restriction depends upon the non-standard

individual production process of each heat ex-changer.

For a more general base of comparison, the

hydraulic characteristics of the heat exchangers

can be viewed using non-dimensional ow factors.

One of which is the Reynolds number (Re) as de-ned for porous media in Kaviany (1995). For a

degree of uniformity in the eld of porous media,

the characteristic length used in the Re is replacedby the square root of the permeability (K) asshown in Eq. (4), where q is the density of theuid, V is the Darcian ow velocity, and l is thedynamic viscosity of the uid.

Re qVK

p

l4

The other commonly used non-dimensional

ow describing factor is the Fanning friction fac-

tor (f ) which is given in Eq. (5). This providesinformation concerning the required pressure drop

(DP ) across a heat exchanger and comes into use

Brazed heat exchanger

2] rk [%] C [m1] rC [%]

13.4 1276 2.9

7.0 2957 3.2

8.7 5066 9.8

7.4 4731 5.6

10.2 1472 5.0

9.1 2820 3.9

6.7 3399 5.4

of Materials 35 (2003) 11611176

ARTICLE IN PRESSwhen the heat transfer performance-to-cost ratio is

considered.

f DP4 LDhyd

qV 2

2

5In Eq. (5), the hydraulic diameter (Dhyd) is de-scribed by Eq. (6)

D 4Acs 6

Re

f

1

10

100

0 20 40 60 80 100 120 140

95-0295-0495-0695-0892-0292-0392-06

Fig. 6. The calculated friction factor (f ) of the aluminum foamheat exchangers based on Eq. (5) plotted against the Re as de-ned in Eq. (4).

1170 K. Boomsma et al. / Mechanicshyd Lp

with Acs being the cross-sectional area of the owchannel (80.0 mm2), and Lp being the wetted pe-rimeter of the ow channel (84.0 mm). Fig. 6 plotsthe friction factor (f ) of Eq. (5) against the Re, ascalculated in Eq. (4). The plot of the friction factor

levels o after a permeability based Re of ap-proximately 20. In this range, the pressure drop

over the foam is dominated by the form coecient

of Eq. (1). This is in agreement with the published

results on the pressure drop of the ow through

both uncompressed and compressed metal foamsin Boomsma and Poulikakos (2002).

3.2. Heat exchanger performance

A practical measure of the performance of a

heat exchanging device is the dimensionless Nus-

selt number (Nu) (Bejan, 1995) as given in Eq. (7).Nu hDhydkc

qAconDT

Dhydkc

7

The coecient h is the convection heat transfercoecient which characterizes the heat transfer

between a solid and a uid. The thermal conduc-

tivity of the coolant is given as kc, and the ow ofheat driven by a temperature dierence of DT isrepresented as q. Dhyd is the hydraulic diameter asgiven in Eq. (6). For uniformity in comparingthese results to the those from other investigations,

the convection surface area, Acon, was consideredto be the interface area between the open-cell

aluminum foam and the heat spreader plate (1600

mm2).

The temperature reference in Eq. (7) is an ar-

bitrary variable, because the location of the refer-

ence temperature positions is subjective. It was notpossible to reliably measure the temperature of the

aluminum foam directly, so two small holes were

drilled 1 mm deep into the top surface of the 1.9

mm thick heat spreader plate on opposing sides of

the copper heating block at central location, giving

a temperature reference (Tpl) that was independentof the quality of the soldering between the heating

element and the heat exchanger. It gave a goodmeasure of the average plate temperature when

compared to the temperature dierence across the

copper heater block, which experienced a maxi-

mum temperature dierence from approximately

18 C at the lower coolant ow speed range to lessthan 1 C at the upper end of the coolant owspeed range (V > 1:0 m/s). The other referencetemperature (Tc;inlet) was the temperature of thecoolant at the channel entrance. It was set to 295

K and did not vary more than 0.3 K during the

experimentation. The following is the nal relation

for DT used in Eq. (7)

DT Tpl Tc;inlet 8

where Tpl is the temperature of the AlSiC heatspreader plate and Tc;inlet is the temperature of thecoolant at the inlet of the metal foam heat ex-

changer. The heat transfer rate to the coolant (q) isdened by the following energy balanceq _mmcTc;outlet Tc;inlet 9

where _mm is the mass ow rate of the coolantpassing through the heat exchanger, c is the spe-cic heat of the incompressible coolant, and Tc;outletis the coolant temperature at the metal heat ex-

changer outlet. The inlet and outlet coolant tem-peratures Tc;inlet; Tc;outlet were measured at 1.5 cmbefore and after the heat exchanger at the middle

of the 2 mm channel height to accurately measure

the mean temperature of the stream. The heat

transfer rate which was evaluated with Eq. (9) was

then back checked against the measurement of the

power deliver to the heater cartridges to ensure

that the mean temperature of the coolant streamwas being measured. With the substitution of Eqs.

(8) and (9) into Eq. (7), the Nu was calculated bythe following expression from the experimental

K. Boomsma et al. / Mechanics of M

ARTICLE IN PRESSdata.

Nu qAconTpl Tc;inlet

Dhydkc

_mmcTc;outlet Tc;inletAconTpl Tc;inlet

Dhydkc

10

The Nusselt numbers for the open-cell aluminum

foam heat exchangers were calculated at various

coolant ow rates and plotted against the coolant

ow speed in Fig. 7. The bare AlSiC heat spreader

plate is also included in this comparison, and is

labeled as plate.All Nusselt numbers began at zero for a zero

coolant ow velocity and increased monotonically

0

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0

95-0295-0495-0695-0892-0292-0392-06plate

V [m/s]

Nu[-]

Fig. 7. The heat convection quantifying Nu as calculated in Eq.

(7) plotted against the Darcian ow velocity (V ).with increasing coolant velocity. In the lower

coolant ow velocity range, up to 0.729 m/s, the

aluminum foam heat exchanger 92-06 achieved the

largest Nu values. At the coolant ow velocityvalue of 0.729 m/s, the Nu of foam 95-04 surpassedthat of foam 92-06, and then continued for amaximum Nu of 134.6 at a coolant ow velocity of1.33 m/s. The foams with the lowest Nu valueswere the two most porous foams, 92-02 and 95-02,

as seen by the comparison between Fig. 7 and

Table 1, in which the porosities of the raw metal

foam used for the heat exchangers are given. The

Nu values of the remaining three aluminum foamheat exchangers, 92-03, 95-06, and 95-08, werenearly identical, except in the coolant velocity

range under 0.50 m/s, where foam 95-08 had

consistently a lower Nu value than the other twofoams, 92-03 and 95-06.

Heat exchangers are commonly characterized

by the Colburn j factor, which gives a heat transferperformance estimate comparing the convection

coecient to the required ow rate of a heat ex-changer. This relationship is closely related to the

friction factor in Fig. 6. The Colburn j factor isbased on the measured convection coecient (h),the necessary velocity of the coolant in order to

achieve the corresponding convection coecient

(V ), and the uids mechanical and thermal prop-erties, as described by the density (q), specic heat(c), kinematic viscosity (m l q1), and the uidthermal diusivity (a k q1 c1). The Colburnj factor is given in Eq. (11).

j hqcV

va

2=311

Fig. 8 plots the Colburn j factor against the Re,as dened in Eq. (4) and done in the work by

Kays and London (1984), which has become one

of the standard methods for reporting the per-

formance of heat exchanging devices. Note that

the bare plate is not included on this graph be-

cause the Re in a clear channel is calculated in acompletely dierent manner from the metal foam

experiments. The characteristic length in the Reof a clear channel is based on the hydraulic dia-

meter (Dhyd), while in a porous medium, thecharacteristic length is derived from the perme-

aterials 35 (2003) 11611176 1171ability (K).

01

2

3

4

5

0 5 10 15 20

95-0295-0495-0695-0892-0292-0392-06

W[W]

(b)

[K .kW 1]RthFig. 9. (a) Plot of the required pumping power ( _WW ) dened inEq. (12) against the corresponding thermal resistances (R ) as

of M

ARTICLE IN PRESS3.3. Pumping power considerations

In any heat exchanger design, the heat convec-

tion performance of the heat exchanger must beweighed against the energy required to operate the

system, which is the pumping power in this con-

guration. The required pumping power was cal-

culated for the aluminum foam heat exchangers at

various coolant ow velocities according to Eq.

(12).

Re

j

0.00

0.05

0.10

0.15

0.20

0.25

0 20 40 60 80 100 120 140

95-0295-0495-0695-0892-0292-0392-06

Fig. 8. The commonly used heat exchanger characterization

parameter, the Colburn j factor of Eq. (11) plotted against theRe as dened in Eq. (4).

1172 K. Boomsma et al. / Mechanics_WW DPQ 12In Eq. (12), _WW is the pumping power, DP is thepressure drop across the aluminum foam heat ex-

changer, and Q is the volumetric ow rate of thecoolant passing through the heat exchanger.

In addition to the Nu and the Colburn j factor,a common means to measure the heat convectioneectiveness is the thermal resistance. Lower

thermal resistance facilitates the heat ow through

the heat exchanger. Eq. (13) gives the common

denition (Rth) for the thermal resistance in a heatconvection arrangement.

Rth DTq Tpl Tc;inlet

_mmcTc;outlet Tc;inlet 13

The measured value of the power delivered to the

heating cartridges via the oscilloscope was used as

a back check for reasonable gures obtained by

measuring the temperature dierence of the cool-0.001

0.01

0.1

1

10

100

0 50 100 150 200

95-0295-0495-0695-0892-0292-0392-06plate

[K .kW 1]Rth

W[W]

(a)

aterials 35 (2003) 11611176ant across the heat exchanger. During the experi-

ments, the power losses to the environment did not

exceed 10%.

The thermal resistances were calculated for the

aluminum foam heat exchangers and the bare

plate at various coolant ow velocities and were

plotted in Fig. 9 against the required pumping

power as dened in Eq. (12). Fig. 9(a) is a conve-nient log plot of the data for a general overview. In

the corresponding plot of the same data in Fig.

9(b) on a linear scale, the optimal design is that

which minimizes the distance from the point to the

origin of the plot. This point was obtained by

foam 92-06, with a thermal resistance of 8.00

th

calculated in Eq. (13). (b) Close-up view of the pumping power

versus thermal resistance plot of (a) showing foam 92-06 best

approaching the ideal zero-approaching value for both the

pumping power and thermal resistance.

KkW1 and a required pumping power of 1.29 Wat a coolant ow velocity of 0.356 m/s. The two

other foams which also rated well in this perfor-

mance to eciency comparison were foams 95-04

and 92-03. The worst performance by a metal

foam heat exchanger was generated by 95-08,

eight individual heat exchangers. Therefore, the

pumping power and thermal resistance results re-

ported in Fig. 9 had to be further adjusted to es-

timate the performance of a heat exchanger array

consisting of eight individual metal foam heat ex-

changers. To make these coolant and congura-

al co

[Wm


ARTICLE IN PRESSwhich did not even t into the scale of Fig. 9(b). Its

relatively poor performance can be attributed to

the brazing process which also caused the unusu-

ally low ow resistance for such a compressed

foam (Fig. 5). The bare plate had the overall

highest average thermal resistance. Comparing the

bare plate against two foams at a relatively high

thermal resistance of 50 KkW1, namely foams95-02 and 92-02, the plate required a pumping

power which was 10 times greater than that re-

quired by the two aforementioned foams.

3.4. Heat exchanger comparison

To evaluate their practicality as heat exchangers

in industrial applications, the results of the heattransfer experiments performed on the aluminum

foam heat exchangers were compared to test re-

sults from an internal investigation performed by

Asea Brown Boveri (Tute, 1998) on various heat

exchangers. This evaluation was carried out by

comparing the required coolant pumping power

against the thermal resistance. However, since

these readily available heat exchanger congura-tions were tested with a 50% waterethylene glycol

solution, the aluminum foam heat exchanger ex-

periments had to be scaled to account for the

higher viscosity and lower thermal capacitance of

the 50% waterethylene glycol solution. The rele-

vant physical properties of water (Incropera and

De Witt, 1990) and the 50% ethylene glycolwater

coolant (Tute, 1998) are listed in Table 3.The experiments reported in Tute (1998) were

conducted on a cooling system which consisted of

Table 3

Coolant properties at 300 K

Property coolant Density

q [kgm3]Therm

k 103Water 997 61350% waterethylene glycol 1034 420tion adjustments, an approach based on the

following assumptions was used to scale the per-

formance of aluminum foam heat exchangers as if

they were tested with a 50% waterethylene glycol

solution in an array of eight individual heat ex-

changers.

1. The heat rate (q) for all varying ow conditionsremained unchanged from the water experi-

ments to the 50% waterethylene glycol experi-

ments.

2. The operating temperatures measured in the

water experiments remained unchanged.

3. The volumetric ow rate of 50% waterethylene

glycol solution was adjusted in proportion to its

lower heat capacitance value and its higher den-sity to maintain the same heat transfer rate

achieved in the experiments conducted with wa-

ter. This adjustment required a 31% greater vol-

umetric ow rate of the 50% waterethylene

glycol mixture to achieve the same cooling ca-

pacity under the rst assumption.

4. To estimate the pressure drop across the alumi-

num foam heat exchangers using the 50%waterethylene glycol solution, the permeability

(K) and form coecient (C) obtained from thepressure drop experimentation were used in

Eq. (1).

5. The required pumping power for a cooling unit

of eight heat exchangers is obtained by multi-

plying the required pumping power of an indi-

vidual heat exchanger by a factor of eight.6. The thermal resistance of a cooling unit consisting

of eight individual metal foam heat exchangers

nductivity1 K1]

Dynamic viscosity

l 103 [N sm2]Specic heat

c [J kg1 K1]

0.86 41793.19 3302

turbulence enhancers, and a simple at plate with

a 0.2 mm channel height. In the experiments done

by ABB (Tute, 1998), each individual heat ex-

changer had a convection surface area in contact

with the coolant measuring 34 mm in the length of

the ow stream and 45 mm across, which providedan overall convective area of 1530 mm2. This is

compared to the conguration for the experiments

completed on the compressed aluminum foam heat20.1

1

10

100

100095-0295-0495-0695-0892-0292-0392-06plate

W[W]

Heat exch. with protrusions

0.2 mm Gap


ARTICLE IN PRESSwas estimated by dividing the thermal resistance

of a single 1600 mm2 metal foam heat exchangerby a factor of eight.

Fig. 10 plots the required pumping power (Eq.

0.010 2 4 6 8 10 12

][ 1.kWKRth

Brand name heat exch.

Fig. 10. Plot of the predicted pumping power ( _WW ) versusthermal resistance (Rth) for the compressed aluminum foamheat exchangers when using a 50% waterethylene glycol

coolant. These results are compared to the results of test on

three commercially available heat exchanger congurations as

reported in Tute (1998).(12)) against the thermal resistance dened in Eq.

(13) for various compressed aluminum foam heat

exchangers and the bare AlSiC plate as they would

perform in an array of eight individual heat ex-

changers using a 50% waterethylene glycol solu-tion. These results are overlayed onto the test

results by ABB (Tute, 1998), in which three dif-

ferent heat exchanger congurations were consid-

ered. These tested heat exchangers consisted of a

brand name heat exchanger, a generic at plate

heat exchanger with small protrusions to act as

Table 4

Average uncertainty of coecients (%)

Foam q Nu ReK

95-02 17.9 19.3 11.8

95-04 13.1 14.5 9.6

95-06 14.5 25.8 11.9

95-08 13.6 14.3 11.5

92-02 16.3 16.9 13.2

92-03 13.7 14.7 10.3

92-06 12.6 15.1 10.3exchangers, which was 1600 mm , or 4.6% larger.

The thermal resistances of the commercially

available heat exchanger congurations in Tute

(1998) were calculated in a manner identical to Eq.

(13).Several observations can be made by scaling the

water experiments to using the 50% waterethyl-

ene glycol solution. Comparing the compressed

aluminum foam heat exchangers in Fig. 10, it is

clear that they generated an Rth that was lowerthan the best heat exchanger tested by ABB (Tute,

1998) by a factor of nearly two. Another relevant

observation is the preservation of the order of thepumping power curves of the various compressed

aluminum foam heat exchangers. This means that

the relative performance of the heat exchangers

with the 50% waterethylene glycol solution can be

well evaluated by using water. The only exception

was the at AlSiC plate. Due to its high perme-

ability (K) and correspondingly low form coe-cient (C), the pumping power requirement for theAlSiC plate increased by a disproportionately

smaller factor than the compressed aluminum

foam heat exchangers, and in Fig. 10, the perfor-

mance of the AlSiC plate surpassed that of the

worst performing compressed aluminum foam

heat exchanger, 95-08, due to its relatively high

thermal resistance.

f j _WW

16.5 21.6 17.1

16.5 17.3 8.8

20.6 28.6 7.8

20.6 18.0 8.5

13.5 19.1 15.7

16.5 17.5 9.918.3 18.2 7.9

of f , labeled as wf , which is a function of V and Pis as follows:

signicant improvement in the eciency over


ARTICLE IN PRESSseveral commercially available heat exchangers

which operate under nearly identical conditions.The metal foam heat exchangers decreased the

thermal resistance by nearly half when compared

to currently used heat exchangers designed for the

same application.

Acknowledgements

It is gratefully acknowledged that this research

was supported jointly by the Swiss Commission

for Technology and Innovation (CTI) through

project no. 4150.2 and by the ABB Corporatewf ofoV

wV

2 of

oPwP

2s14

The average percentage values of these coecients

are tabulated in Table 4.

4. Conclusion

Open-cell aluminum foams were compressed byvarious factors and then fashioned into heat ex-

changers intended for electronic cooling applica-

tions which dissipate large amounts of heat.

Various common heat exchanger evaluation

methods were applied to the data assembled from

the extensive heat transfer experiments, which in-

cluded the hydraulic characterization, the heat

transfer performance, and an eciency study todetermine the most ecient metal foam heat ex-

changer conguration for a particular heat trans-

fer conguration. It was seen that the compressed

aluminum foams performed well not only in the

heat transfer enhancement, but they also made a3.5. Uncertainty analysis

The coecients plotted in Figs. 510 were an-

alyzed for their associated uncertainties following

the standard procedure outlined in Taylor (1997).An example to nd the absolute uncertainty valueResearch Center, Baden-Daattwil, Switzerland.References

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ARTICLE IN PRESS

Metal foams as compact high performance heat exchangersIntroductionExperimentApparatusAluminum foam heat exchangersExperimental procedure

Results and discussionPressure dropHeat exchanger performancePumping power considerationsHeat exchanger comparisonUncertainty analysis

ConclusionAcknowledgementsReferences

metal foam heat exchanger

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