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Mechanics of Materials 35 (2003) 1161–1176
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Metal foams as compact high performance heat exchangers
K. Boomsma a, D. Poulikakos
a
a,*
, F. Zwick
b
Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology, Swiss Federal Institute of Technology,
ETH Center, ML J 36, 8092 Zurich, Switzerland
b
ABB Corporate Research Ltd., Segelhof, 5405 Baden-D€attwil, Switzerland
Received 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 fluxes measured from the heater-foam interface ranged up to 688 kW m2 ,
which corresponded to Nusselt numbers up to 134 when calculated based on the heater-foam interface area of 1600
mm2 and a Darcian coolant flow velocity of approximately 1.4 m/s. These experiments performed with water were
scaled to estimate the heat exchangersÕ performance when used with a 50% water–ethylene glycol solution, and were
then 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 resistance. 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.
Keywords: Metal foam; Porous media; Heat transfer; Open-cell aluminum foam
1. Introduction
Flow through porous media has been studied in
detail ever since DarcyÕs publication in 1856
(Darcy, 1856). His work described the fluid flow
pressure drop across a porous medium as a linear
function of the flow velocity and material permeability. Since then, a series of improvements have
*
Corresponding author. Tel.: +41-1-632-2738; fax: +41-1632-1176.
E-mail address: [email protected] (D. Poulikakos).
been made to describe the pressure drop behavior
in better detail, one of which was accounting for
temperature variations in the fluid by Hazen
(1893). These temperature variations were later
linked to the viscosity of the fluid by Kr€
uger
(1918). The addition of a quadratic term in the
linear Darcy Law was first proposed by Dupuit
(1863), although many mistakenly credit Forchheimer with the addition of the quadratic term as a
result of his extensive review of other porous media studies (Forchheimer, 1901). A thorough review of the history of the study of fluid dynamics
through porous media can be found in a review by
0167-6636/$ - see front matter 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.mechmat.2003.02.001
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Nomenclature
A
C
CTE
D
FS
K
L
M
Nu
P
Q
R
Re
T
V
W_
c
f
h
j
k
area [m2 ]
form coefficient [m1 ]
coefficient of thermal expansion
[m m1 K1 ]
diameter [m]
Full scale
permeability [m2 ]
length [m]
compression factor [–]
Nusselt number (defined in Eq. (12)) [–]
pressure [bar]
volumetric flow rate [m3 s1 ]
thermal resistance (defined in Eq. (12))
[K W1 ]
Reynolds number (defined in Eq. (4)) [–
]
temperature [C, K]
velocity [m s1 ]
pumping power [W]
specific heat [kJ kg1 K1 ]
friction factor [–]
convection coefficient [W m2 K1 ]
Colburn factor (defined in Eq. (10)) [–]
thermal conductivity [W m1 K1 ]
Lage (1998). An end result of the nearly 150 yearold work in porous media is the widely accepted
equation (Eq. (1)) which governs the pressure drop
of a fluid passing through a porous medium.
DP
l
¼ V þ qCV 2
L
K
ð1Þ
The term DP is the pressure drop across the medium, L is the length of the medium in the flow
direction, l is the dynamic viscosity of the fluid, K
is the permeability of the medium, V is the clearchannel (Darcian) velocity of the fluid, q is the
density of the fluid, and C is the form coefficient of
the medium.
The extension of the fluid 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
m_
q
w
mass flow rate [kg s1 ]
heat rate [W]
absolute error [–]
Greek symbols
D
difference [–]
a
thermal diffusivity [m2 s1 ]
e
porosity fraction (range 100 P e > 0) [%]
l
dynamic viscosity [kg m1 s1 ]
m
kinematic viscosity [m2 s1 ]
q
density [kg m3 ]
Subscripts
c
coolant
con
convection
cs
cross-sectional
eff
effective
f
fluid
hyd
hydraulic
inlet
inlet
outlet outlet
p
perimeter
pl
plate
s
solid
th
thermal
(1975). Their analysis considered a simple slug
flow velocity profile through the porous medium,
but the cooling effects 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 analytical solution of the transport equations based on
the quadratic-extended Darcy flow model (Eq.
(1)). Advancements continued in numerical work
on 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 effects (Kaviany, 1985;
Mehta and Hawley, 1969), variable porosity
(Amiri and Vafai, 1994; Nield et al., 1999), and
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even non-Newtonian fluids (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 0:3–0:6. This configuration is known as
a bed of packed spheres, which models fluid flow
through 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 nonspherical porous medium is open-cell metal foam.
The structure of open-cell metal foams (Fig. 1)
opens itself to a wide variety of possible applications which include, but are not limited to, light
weight high strength structural applications,
mechanical energy absorbers, filters, pneumatic
silencers, containment matrices and burn rate
enhancers for solid propellants, flow straighteners,
catalytic reactors, and more recently, heat exchangers. The open-cell metal foam structure has
the desirable qualities of a well designed heat exchanger, i.e. a high specific solid–fluid interface
surface area, good thermally conducting solid
phase, and a tortuous coolant flow path to promote mixing. Depending on the particular opencell metal foam configuration, its specific 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 W m1 K1 ) or copper (ks 400
W m1 K1 ), which, merely by its presence in a
static fluid, dramatically increases the overall effective thermal conductivity of the fluid-system
(Calmidi and Mahajan, 1999). The overall effective
thermal conductivity of the solid–fluid system (keff )
can be most generally described by the porosity (e)
and the conductivities of the fluid and solid phases
by kf and ks , respectively (Kaviany, 1995).
improved 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 du
Plessis, 1999; Lu et al., 1998) and numerical models
(Calmidi and Mahajan, 2000; Lage et al., 1996) for
the fluid flow and heat transfer in packed beds of
spheres and extensive databanks of fluid flow and
heat transfer experiments used as verification of
these models (Antohe et al., 1997; Lage et al., 1997;
Lage and Antohe, 2000; Boomsma and Poulikakos, 2002). However, in the case of open-cell metal
foams, 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 specific heat
capacitance. In view of these requirements, experiments 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 flow arrangement using a liquid
coolant, which is deionized, degassed water.
Comparisons with existing heat exchanger systems
for the application of cooling of electronics are also
provided.
keff ¼ ekf þ ð1 eÞks
The goal of the experiment was to measure the
hydraulic and thermal performance of the opencell aluminum foams when used as heat exchangers in a forced convection flow arrangement. The
concept was to direct the coolant flow through a
rectangular channel in which the aluminum foam
heat exchanger is placed, occupying the entire
cross-section of the channel. A heater was attached
to the aluminum foam via the heat spreader plate,
ð2Þ
This increase in overall effective thermal conductivity of the solid–fluid system to a level above that
predicted by Eq. (2) was shown in the 2-D conduction model by Calmidi and Mahajan (1999).
Noting the influence of the structure on the thermal conductivity of the metal foam matrix,
Boomsma and Poulikakos (2001) developed an
2. Experiment
2.1. Apparatus
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Fig. 1. (a) Open-cell aluminum foam (T-6106 alloy) in its as-manufactured state with a porosity of e ¼ 92% and approximately 6 mm
diameter pores (ks 200 W m1 K1 ). (b) Close-up view on an individual cell of the aluminum foam depicted in (a). (c) Open-cell metal
foam 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).
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through which the heat was conducted and eventually 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 several
locations in the coolant flow, the power delivered
to the heating device, and the pressure drop across
the heat exchangers for various coolant flow 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 diameter were bored into the housing at various
locations 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 fluid as it enters and leaves
the metal foam. The other six ports were used as a
Power Supply
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symmetry check of the flow. During the experiments, the pressure variation between the left and
right ports did not fluctuate more than 3% and was
therefore neglected.
The metal foam heat exchanger housing was
manufactured from Ryton R4, which has a low
thermal conductivity (0.3 W m1 K1 ) and a reasonable CTE (22 · 106 m/m C). The static pressure drop of the coolant across the metal foam
heat exchanger was measured by two different
differential pressure transducers corresponding to
their individual pressure ranges. A Huba differential pressure transducer was used for measuring
the pressure in the lower pressure range, from 0 to
0.20 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) differential pressure transducer was employed with an accuracy
of 0.25% FS (±0.009 bar). E-type thermocouples (chromel/constantan) of 0.15 mm diameter
Oscilloscope
Data Acquisition PC
Metal Foam Heater Assembly
Foam Housing
Rotameter
Pressure Transducer
Pressure
Regulating
Valve
Thermocouples
20.0
Valve Array
USB
Data Acquisition Device
Coolant Chiller/
Recirculator
Coolant Flow Direction
Fig. 2. Schematic view of the experimental setup used to measure the thermal and hydraulic characteristics of the compressed aluminum foam heat exchangers.
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HEATER ASSEMBLY
METAL FOAM
PRESSURE PORTS
FLOW
INLET
FLOW
OUTLET
(a)
FLOW
INLET
4cm
7cm
FLOW
OUTLET
(b)
Fig. 3. (a) Cross-sectional view of the foam test housing which shows the location of the aluminum foam heat exchanger, the heater
assembly, and the path of the coolant flow. (b) Top view of the foam test housing depicted in (a) with the lid removed to show the
placement of the foam component of the assembled compressed foam heat exchanger.
measured the temperatures at various locations of
the experimental apparatus. The thermocouples
were calibrated in a thermal bath to within 0.5 C
and 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 flow (Fig. 3(b)). The pressure drop measurements were performed both with and without
the thermocouples inserted through the pressure
taps to determine if their presence altered the
pressure readings. No effects 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
computer.
The coolant was pumped through the experimental apparatus by a Neslab chiller. It provided a
maximum coolant flow rate of approximately
10 l/min, could dissipate a total of 1600 W, and
regulated the coolant inlet temperature to within
0.3 C.
The coolant flow rate was measured using two
different rotameters. The lower flow rate range
varied from 0 to 1.0 l/min, which corresponded to
a flow velocity of 0–0.21 m/s for a channel crosssection of 40.0 mm · 2.0 mm. For this lower range,
a V€
ogtlin rotameter with 1% FS (±0.01 l/min) accuracy was utilized. The higher flow rate range
tested varied from 1.00 to 5.00 l/min, corresponding to a flow velocity range of 0.21–1.04 m/s
for a channel cross-section of 40.0 mm · 2.0 mm.
In the higher flow rate range, a Wisag 2000 rotameter was employed with an accuracy of 1% FS
(±0.11 l/min).
The heating system consisted of a block machined
from oxygen-free copper (ks 400 W m1 K1 )
measuring 40.0 mm · 44.0 mm · 20.0 mm high. Five
holes measuring 6.35 mm in diameter were bored
through the block to hold five 220 W cartridge
heaters in place. The voltage and current delivered to
the five cartridge heaters were monitored by an oscilloscope. The maximum power delivered to the
heater block was 1100 W. Smaller holes measuring 0.2 mm in diameter were drilled into the top
and base of the copper heater block, perpendicular to the coolant flow direction. This allowed the
insertion of small diameter thermocouples to measure the temperature difference across the heater
block.
2.2. Aluminum foam heat exchangers
One of the desirable qualities of the open-cell
metal foam in a heat exchanger application is the
large specific surface area, which ranges from approximately 500 to over 3000 m2 /m3 . Compressing
the foam further increases this already large surface area to volume ratio. To generate an array of
open-cell metal foam heat exchangers, 6101-T6
aluminum alloy (ks ¼ 218 W m1 K1 ) was cast
into foam form at two different porosities of
e ¼ 92% and 95% with an average cell diameter of
2.3 mm. This foam is listed as 40 PPI by the
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Table 1
Compressed foam physical data (Panel A), uncompressed foam physical data (Panel B)
Foam
Panel A
5%
8%
Compression
Name
Expected porosity [%]
Measured porosity [%]
2
4
6
8
95-02
95-04
95-06
95-08
90.0
80.0
70.0
60.0
88.2
80.5
68.9
60.8
2
3
6
92-02
92-03
92-06
84.0
76.0
52.0
87.4
82.5
66.9
Panel B
Foam
Pore diameter [mm]
Specific surface area [m2 /m3 ]
Measured porosity [%]
40 PPI
2.3
2700
92.8
manufacturer (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 specific surface area of these foams was
further increased by compressing them by a factor
of M, which signifies the ratio of the pre-compression to post-compression height of the foam
block. In the one-dimensional compression process, the lateral sides of the metal foam are not
restrained. This is done to prevent any mass accumulation in the foam caused by lateral material
movements during the compression process.
However, any material which ‘‘flows’’ to the outside of the compression device is lost in the machining of the foam to its final overall dimensions,
thus the resulting porosity of the foam may be
higher than what would be predicted by Eq. (3).
ecompressed ¼ 1 Mð1 euncompressed Þ
ð3Þ
The porosities of the aluminum foams were calculated 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 manufacturerÕs
stated initial, uncompressed porosity of euncompressed
and the given nominal compression factor, M.
Table 1 lists both the measured and expected po-
100
Expected Porosity (95%)
Effective Porosity (95%)
Expected Porosity (92%)
Effective Porosity (92%)
90
80
ε
[%] 70
60
50
0
2
4
6
8
10
M
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 manufacturerÕs stated initial porosity (e) and compression factor (M) based on Eq. (3), while
the individual points are the measured values for the raw foam
material.
rosities, and Fig. 4 shows their relationship
graphically. The various configurations of aluminum foams are named using two pairs of digits.
The first pair is pre-compression porosity; the
number 92 designates euncompressed ¼ 92%. The second pair of digits designates the compression factor, M. The foam 92-04, for example, was 92%
porous in its uncompressed state and then compressed by a factor of four. In Fig. 4, the porosities
of the 95% pre-compression foam samples that
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K. Boomsma et al. / Mechanics of Materials 35 (2003) 1161–1176
were 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 manufacturerÕs given data. By the consistency of the error
of the porosity data points from the predicted line
for the 92% initial porosity foam, it can be assumed 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 final machining
process. To make them functional heat exchangers, each foam piece was brazed in a central position 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 W m1 K1 and measured 58.0
mm · 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 flow
rate, which varied according to the overall flow
resistance of the individual heat exchanger. The
inlet temperature of the coolant was held at 22±0.3
C. After the 20 min stabilization period, full
power to the heater cartridges was turned on, and
the entire experimental apparatus was allowed to
reach steady-state. Starting from the maximum
flow rate, the temperatures at various locations
were 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 temperature allowed during operation was 100 C, at
which the coolant began to vaporize.
The flow rate was read from the rotameter.
After the data were taken, the flow rate was reduced, and the apparatus was given 5 min to reach
steady-state for the next data point measurement.
As noted in the work by Boomsma and Poulikakos
(2002) and Antohe et al. (1997), the direction in
which the flow rate is adjusted does not have an
effect on the calculated permeability and form
coefficient needed to describe the flow 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 by
Boomsma and Poulikakos (2002), the open-cell
metal foams which comprised the in-flow component of the heat exchangers in this study were
tested for their hydraulic characteristics. The parameters used to describe the pressure drop characteristics of the foam heat exchangers are the
permeability (K) and the form coefficient (C)
which are defined in Eq. (1). The metal foam
configurations 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 aluminum brazing material which attaches the foam
to the heat spreader plate partially filled the pores
at the interface which reduced the effective flow
cross-sectional area of the heat exchanger and increased the flow resistance of the metal foam heat
exchangers when compared to the results of the
similar, unbrazed foams in Boomsma and Poulikakos (2002).
The assembled heat exchangers were tested
anew for their hydraulic characteristics and the
results of the pressure drop tests were plotted
graphically in Fig. 5. The left-hand ordinate is
given in length normalized units of [bar m1 ] based
on 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 seen
in Table 1 generated the largest pressure drop.
These were led by the two most compressed foams,
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3.2
80
95-02
95-04
95-06
95-08
92-02
92-03
92-06
70
60
50
∆P/L
40
[bar·m-1]
2.8
2.4
2.0
1.6
30
1.2
20
0.8
10
0.4
0
0.0
0.5
1.0
V
1.5
∆P
[bar]
0.0
2.0
[m·s-1]
Fig. 5. Pressure-drop curves for the metal foam heat exchangers plotted on a length-normalized (DPL1 ) and actual
pressure scale (DP ) against the Darcian flow velocity (V ).
95-06 and 95-08, with foam 92-06 generating
nearly the same pressure drop. The foam which
produced the lowest pressure drop was foam 9502, which was also the most porous of the samples.
The hydraulic characteristics of the brazed
foams were calculated by using a least squares
curve fitting approach as described in Antohe et al.
(1997) and Boomsma and Poulikakos (2002) to
solve for the K and C in Eq. (1). These permeability and form coefficient values were compared
to the values obtained in Boomsma and Poulikakos (2002), which used the same aluminum foam
configurations, but without any brazing material.
Table 2 compares the permeability and form coefficients between the assembled heat exchangers
and the unbrazed foam blocks, along with the
corresponding uncertainty percentages. Almost
every assembled heat exchanger showed an increase in the flow resistance compared to its un-
1169
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 flow resistance when compared to their unbrazed counterparts. This change in behavior by the two most
highly compressed brazed foams can be attributed
to warpage and distortion in the foam from the
brazing process, thereby allowing flow bypass.
With the remaining five aluminum foam heat exchangers, the amount of the increase of the flow
resistance was not consistent. The change in the
flow restriction depends upon the non-standard
individual production process of each heat exchanger.
For a more general base of comparison, the
hydraulic characteristics of the heat exchangers
can be viewed using non-dimensional flow factors.
One of which is the Reynolds number (Re) as defined for porous media in Kaviany (1995). For a
degree of uniformity in the field of porous media,
the characteristic length used in the Re is replaced
by the square root of the permeability (K) as
shown in Eq. (4), where q is the density of the
fluid, V is the Darcian flow velocity, and l is the
dynamic viscosity of the fluid.
pffiffiffiffi
qV K
Re ¼
ð4Þ
l
The other commonly used non-dimensional
flow describing factor is the Fanning friction factor (f ) which is given in Eq. (5). This provides
information concerning the required pressure drop
(DP ) across a heat exchanger and comes into use
Table 2
Flow resistance comparison
Foam
95-02
95-04
95-06
95-08
92-02
92-03
92-06
a
Unbrazeda
Brazed heat exchanger
K [1010 m2 ]
C [m1 ]
K [1010 m2 ]
rk [%]
C [m1 ]
rC [%]
44.4
19.7
5.25
2.46
36.7
23.0
3.88
1168
2707
4728
8701
1142
1785
5518
34.4
6.87
3.16
2.52
30.8
8.26
3.95
13.4
7.0
8.7
7.4
10.2
9.1
6.7
1276
2957
5066
4731
1472
2820
3399
2.9
3.2
9.8
5.6
5.0
3.9
5.4
Results reported in Boomsma and Poulikakos (2002).
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100
Nu ¼
95-02
95-04
95-06
95-08
92-02
92-03
92-06
f 10
1
0
20
40
60
80
100
120
140
Re
Fig. 6. The calculated friction factor (f ) of the aluminum foam
heat exchangers based on Eq. (5) plotted against the Re as defined in Eq. (4).
when the heat transfer performance-to-cost ratio is
considered.
DP
2 f ¼ qV
L
4 Dhyd
2
ð5Þ
In Eq. (5), the hydraulic diameter (Dhyd ) is described by Eq. (6)
Dhyd ¼
4Acs
Lp
ð6Þ
with Acs being the cross-sectional area of the flow
channel (80.0 mm2 ), and Lp being the wetted perimeter of the flow channel (84.0 mm). Fig. 6 plots
the friction factor (f ) of Eq. (5) against the Re, as
calculated in Eq. (4). The plot of the friction factor
levels off after a permeability based Re of approximately 20. In this range, the pressure drop
over the foam is dominated by the form coefficient
of Eq. (1). This is in agreement with the published
results on the pressure drop of the flow through
both uncompressed and compressed metal foams
in Boomsma and Poulikakos (2002).
3.2. Heat exchanger performance
A practical measure of the performance of a
heat exchanging device is the dimensionless Nusselt number (Nu) (Bejan, 1995) as given in Eq. (7).
hDhyd
q
Dhyd
¼
Acon DT kc
kc
ð7Þ
The coefficient h is the convection heat transfer
coefficient which characterizes the heat transfer
between a solid and a fluid. The thermal conductivity of the coolant is given as kc , and the flow of
heat driven by a temperature difference of DT is
represented as q. Dhyd is the hydraulic diameter as
given in Eq. (6). For uniformity in comparing
these results to the those from other investigations,
the convection surface area, Acon , was considered
to 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 arbitrary variable, because the location of the reference temperature positions is subjective. It was not
possible 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 independent
of the quality of the soldering between the heating
element and the heat exchanger. It gave a good
measure of the average plate temperature when
compared to the temperature difference across the
copper heater block, which experienced a maximum temperature difference from approximately
18 C at the lower coolant flow speed range to less
than 1 C at the upper end of the coolant flow
speed range (V > 1:0 m/s). The other reference
temperature (Tc;inlet ) was the temperature of the
coolant 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 final relation
for DT used in Eq. (7)
DT ¼ Tpl Tc;inlet
ð8Þ
where Tpl is the temperature of the AlSiC heat
spreader plate and Tc;inlet is the temperature of the
coolant at the inlet of the metal foam heat exchanger. The heat transfer rate to the coolant (q) is
defined by the following energy balance
q ¼ m_ cðTc;outlet Tc;inlet Þ
ð9Þ
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K. Boomsma et al. / Mechanics of Materials 35 (2003) 1161–1176
where m_ is the mass flow rate of the coolant
passing through the heat exchanger, c is the specific heat of the incompressible coolant, and Tc;outlet
is the coolant temperature at the metal heat exchanger outlet. The inlet and outlet coolant temperatures ðTc;inlet ; Tc;outlet Þ were measured at 1.5 cm
before 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 stream
was being measured. With the substitution of Eqs.
(8) and (9) into Eq. (7), the Nu was calculated by
the following expression from the experimental
data.
Nu ¼
¼
q
Dhyd
Acon ðTpl Tc;inlet Þ kc
m_ cðTc;outlet Tc;inlet Þ Dhyd
Acon ðTpl Tc;inlet Þ kc
ð10Þ
The Nusselt numbers for the open-cell aluminum
foam heat exchangers were calculated at various
coolant flow rates and plotted against the coolant
flow 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 flow velocity and increased monotonically
140
120
100
80
95-02
95-04
95-06
95-08
92-02
92-03
92-06
plate
Nu
[-] 60
40
20
0
0.0
0.5
1.0
1.5
2.0
V [m/s]
Fig. 7. The heat convection quantifying Nu as calculated in Eq.
(7) plotted against the Darcian flow velocity (V ).
1171
with increasing coolant velocity. In the lower
coolant flow velocity range, up to 0.729 m/s, the
aluminum foam heat exchanger 92-06 achieved the
largest Nu values. At the coolant flow velocity
value of 0.729 m/s, the Nu of foam 95-04 surpassed
that of foam 92-06, and then continued for a
maximum Nu of 134.6 at a coolant flow velocity of
1.33 m/s. The foams with the lowest Nu values
were 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 foam
heat exchangers, 92-03, 95-06, and 95-08, were
nearly 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 two
foams, 92-03 and 95-06.
Heat exchangers are commonly characterized
by the Colburn j factor, which gives a heat transfer
performance estimate comparing the convection
coefficient to the required flow rate of a heat exchanger. This relationship is closely related to the
friction factor in Fig. 6. The Colburn j factor is
based on the measured convection coefficient (h),
the necessary velocity of the coolant in order to
achieve the corresponding convection coefficient
(V ), and the fluidÕs mechanical and thermal properties, as described by the density (q), specific heat
(c), kinematic viscosity (m ¼ l q1 ), and the fluid
thermal diffusivity (a ¼ k q1 c1 ). The Colburn
j factor is given in Eq. (11).
h v 2=3
j¼
ð11Þ
qcV a
Fig. 8 plots the Colburn j factor against the Re,
as defined in Eq. (4) and done in the work by
Kays and London (1984), which has become one
of the standard methods for reporting the performance of heat exchanging devices. Note that
the bare plate is not included on this graph because the Re in a clear channel is calculated in a
completely different manner from the metal foam
experiments. The characteristic length in the Re
of a clear channel is based on the hydraulic diameter (Dhyd ), while in a porous medium, the
characteristic length is derived from the permeability (K).
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K. Boomsma et al. / Mechanics of Materials 35 (2003) 1161–1176
0.25
100
95-02
95-04
95-06
95-08
92-02
92-03
92-06
0.20
0.15
95-02
95-04
95-06
95-08
92-02
92-03
92-06
plate
10
W
[W]
j
1
0.10
0.1
0.05
0.01
0.00
0.001
(a)
0
20
40
60
80
100
120
0
140
50
Re
Fig. 8. The commonly used heat exchanger characterization
parameter, the Colburn j factor of Eq. (11) plotted against the
Re as defined in Eq. (4).
W_ ¼ DPQ
ð12Þ
In Eq. (12), W_ is the pumping power, DP is the
pressure drop across the aluminum foam heat exchanger, and Q is the volumetric flow rate of the
coolant passing through the heat exchanger.
In addition to the Nu and the Colburn j factor,
a common means to measure the heat convection
effectiveness is the thermal resistance. Lower
thermal resistance facilitates the heat flow through
the heat exchanger. Eq. (13) gives the common
definition (Rth ) for the thermal resistance in a heat
convection arrangement.
Rth ¼
DT
Tpl Tc;inlet
¼
q
m_ cðTc;outlet Tc;inlet Þ
ð13Þ
The measured value of the power delivered to the
heating cartridges via the oscilloscope was used as
a back check for reasonable figures obtained by
measuring the temperature difference of the cool-
200
10
15
20
95-02
95-04
95-06
95-08
92-02
92-03
92-06
3
In any heat exchanger design, the heat convection performance of the heat exchanger must be
weighed against the energy required to operate the
system, which is the pumping power in this configuration. The required pumping power was calculated for the aluminum foam heat exchangers at
various coolant flow velocities according to Eq.
(12).
150
5
4
3.3. Pumping power considerations
100
Rth [K . kW –1]
W
[W]
2
1
(b)
0
0
5
Rth [K . kW –1]
Fig. 9. (a) Plot of the required pumping power (W_ ) defined in
Eq. (12) against the corresponding thermal resistances (Rth ) as
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.
ant across the heat exchanger. During the experiments, 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 flow velocities and were
plotted in Fig. 9 against the required pumping
power as defined in Eq. (12). Fig. 9(a) is a convenient 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
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K. Boomsma et al. / Mechanics of Materials 35 (2003) 1161–1176
K kW1 and a required pumping power of 1.29 W
at a coolant flow velocity of 0.356 m/s. The two
other foams which also rated well in this performance to efficiency comparison were foams 95-04
and 92-03. The worst performance by a metal
foam heat exchanger was generated by 95-08,
which did not even fit into the scale of Fig. 9(b). Its
relatively poor performance can be attributed to
the brazing process which also caused the unusually low flow 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 K kW1 , namely foams
95-02 and 92-02, the plate required a pumping
power which was 10 times greater than that required by the two aforementioned foams.
3.4. Heat exchanger comparison
To evaluate their practicality as heat exchangers
in industrial applications, the results of the heat
transfer experiments performed on the aluminum
foam heat exchangers were compared to test results 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 configurations were tested with a 50% water–ethylene glycol
solution, the aluminum foam heat exchanger experiments had to be scaled to account for the
higher viscosity and lower thermal capacitance of
the 50% water–ethylene glycol solution. The relevant physical properties of water (Incropera and
De Witt, 1990) and the 50% ethylene glycol–water
coolant (Tute, 1998) are listed in Table 3.
The experiments reported in Tute (1998) were
conducted on a cooling system which consisted of
1173
eight individual heat exchangers. Therefore, the
pumping power and thermal resistance results reported in Fig. 9 had to be further adjusted to estimate the performance of a heat exchanger array
consisting of eight individual metal foam heat exchangers. To make these coolant and configuration adjustments, an approach based on the
following assumptions was used to scale the performance of aluminum foam heat exchangers as if
they were tested with a 50% water–ethylene glycol
solution in an array of eight individual heat exchangers.
1. The heat rate (q) for all varying flow conditions
remained unchanged from the water experiments to the 50% water–ethylene glycol experiments.
2. The operating temperatures measured in the
water experiments remained unchanged.
3. The volumetric flow rate of 50% water–ethylene
glycol solution was adjusted in proportion to its
lower heat capacitance value and its higher density to maintain the same heat transfer rate
achieved in the experiments conducted with water. This adjustment required a 31% greater volumetric flow rate of the 50% water–ethylene
glycol mixture to achieve the same cooling capacity under the first assumption.
4. To estimate the pressure drop across the aluminum foam heat exchangers using the 50%
water–ethylene glycol solution, the permeability
(K) and form coefficient (C) obtained from the
pressure drop experimentation were used in
Eq. (1).
5. The required pumping power for a cooling unit
of eight heat exchangers is obtained by multiplying the required pumping power of an individual heat exchanger by a factor of eight.
6. The thermal resistance of a cooling unit consisting
of eight individual metal foam heat exchangers
Table 3
Coolant properties at 300 K
Property coolant
Density
q [kg m3 ]
Thermal conductivity
k 103 [W m1 K1 ]
Dynamic viscosity
l 103 [N s m2 ]
Specific heat
c [J kg1 K1 ]
Water
50% water–ethylene glycol
997
1034
613
420
0.86
3.19
4179
3302
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K. Boomsma et al. / Mechanics of Materials 35 (2003) 1161–1176
1000
95-02
95-04
95-06
95-08
92-02
92-03
92-06
plate
100
10
W
[W]
1
0.2 mm Gap
0.1
Heat exch. with protrusions
Brand name heat exch.
0.01
0
2
4
6
Rth [ K . kW –1]
8
10
12
Fig. 10. Plot of the predicted pumping power (W_ ) versus
thermal resistance (Rth ) for the compressed aluminum foam
heat exchangers when using a 50% water–ethylene glycol
coolant. These results are compared to the results of test on
three commercially available heat exchanger configurations as
reported in Tute (1998).
was estimated by dividing the thermal resistance
of a single 1600 mm2 metal foam heat exchanger
by a factor of eight.
Fig. 10 plots the required pumping power (Eq.
(12)) against the thermal resistance defined 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 exchangers using a 50% water–ethylene glycol solution. These results are overlayed onto the test
results by ABB (Tute, 1998), in which three different heat exchanger configurations were considered. These tested heat exchangers consisted of a
brand name heat exchanger, a generic flat plate
heat exchanger with small protrusions to act as
turbulence enhancers, and a simple flat plate with
a 0.2 mm channel height. In the experiments done
by ABB (Tute, 1998), each individual heat exchanger had a convection surface area in contact
with the coolant measuring 34 mm in the length of
the flow stream and 45 mm across, which provided
an overall convective area of 1530 mm2 . This is
compared to the configuration for the experiments
completed on the compressed aluminum foam heat
exchangers, which was 1600 mm2 , or 4.6% larger.
The thermal resistances of the commercially
available heat exchanger configurations 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% water–ethylene glycol solution. Comparing the compressed
aluminum foam heat exchangers in Fig. 10, it is
clear that they generated an Rth that was lower
than 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 the
pumping power curves of the various compressed
aluminum foam heat exchangers. This means that
the relative performance of the heat exchangers
with the 50% water–ethylene glycol solution can be
well evaluated by using water. The only exception
was the flat AlSiC plate. Due to its high permeability (K) and correspondingly low form coefficient (C), the pumping power requirement for the
AlSiC plate increased by a disproportionately
smaller factor than the compressed aluminum
foam heat exchangers, and in Fig. 10, the performance of the AlSiC plate surpassed that of the
worst performing compressed aluminum foam
heat exchanger, 95-08, due to its relatively high
thermal resistance.
Table 4
Average uncertainty of coefficients (%)
Foam
q
Nu
ReK
f
j
W_
95-02
95-04
95-06
95-08
92-02
92-03
92-06
17.9
13.1
14.5
13.6
16.3
13.7
12.6
19.3
14.5
25.8
14.3
16.9
14.7
15.1
11.8
9.6
11.9
11.5
13.2
10.3
10.3
16.5
16.5
20.6
20.6
13.5
16.5
18.3
21.6
17.3
28.6
18.0
19.1
17.5
18.2
17.1
8.8
7.8
8.5
15.7
9.9
7.9
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3.5. Uncertainty analysis
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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2ffi
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ð14Þ
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þ
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4. Conclusion
Open-cell aluminum foams were compressed by
various factors and then fashioned into heat exchangers intended for electronic cooling applications 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 included the hydraulic characterization, the heat
transfer performance, and an efficiency study to
determine the most efficient metal foam heat exchanger configuration for a particular heat transfer configuration. It was seen that the compressed
aluminum foams performed well not only in the
heat transfer enhancement, but they also made a
significant improvement in the efficiency over
several 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 Corporate
Research Center, Baden-D€
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