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]
K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176 1169
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
K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176 1173
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
1174 K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176
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
K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176 1175
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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1176 K. Boomsma et al. / Mechanics of Materials 35 (2003) 11611176
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