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Submitted to the 2000 ASME IMECE:
Undergraduate Research and Design in Heat Transfer
November 5-10, 2000, Orlando, Florida
2-e-2-1
THERMAL CHARACTERISTICS OF A COMPACT, PASSIVE THERMAL
ENERGY STORAGE DEVICE
Candice A. Bauer and R.A. Wirtz
Mechanical Engineering Department
University of Nevada, Reno
Reno, NV 89557
ABSTRACT
A Thermal Energy Storage (TES) system uses a
Phase Change Material (PCM) to store heat during
peak power operation of variable power dissipating
devices via the latent heat effect. The TES composite
developed is a plate-like structure that consists of a
central core of foamed aluminum that is packed with a
PCM. By considering the elements of the composite to
be thermal resistors and constructing a flat-plate
thermal conductivity apparatus, the plate-to-plate
effective thermal conductivity is determined. The
composite effective thermal conductivity is primarily
composed of the thermal conductivity of the
aluminum foam which is reduced by the effect of the
aluminum foam-to-plate bond resistance. Heat flow
through the PCM slightly augments the effective
thermal conductivity. An increase in aluminum foam
metal fraction results in an increase in the effective
thermal conductivity of the composite because only
about 2% of the heat flow is through the PCM, and the
interfacial bond resistance decreases due to increased
contact area. The trade-off is that as there is an
increase in aluminum foam metal fraction, the
volumetric latent heat decreases; thus, the storage time
is reduced.
T
∆T
ε
(1-ε)
Temperature
Change in temperature
Volume Fraction of PCM
Volume Fraction of Aluminum Foam
Subscripts
al
Aluminum
bond
Epoxy Bond between Aluminum Plate and
Foam
foam
Aluminum Foam
PCM
Phase Change Material (PG)
pl
Aluminum Plate
vol
Volume
INTRODUCTION
Multi chip modules (MCM) are variable power
dissipating devices that are commonly found in
microprocessors and similar electronic equipment.
Because power is consumed at different rates, a
conventional MCM cooling system must be designed
for the peak power heat load. Thermal Energy Storage
(TES) systems offer a design alternative. A TESsystem uses a Phase Change Material (PCM) to store
heat during periods of peak power operation via the
latent heat effect. During periods of low-power
operation, this energy is removed from the system.
The incorporation of TES in the temperature control
system of an electronics module having a variable heat
dissipation rate will improve system reliability and
allow for a smaller, less power consuming module
cooler.
Phase Change Materials that undergo “dry” phase
transition (no liquid phase) are attractive TESmaterials since packaging difficulties associated with
solid-liquid PCM’s are avoided [Hale et al., 1971].
NOMENCLATURE
A
Area
h
Latent Heat
k
Thermal Conductivity
keff
Effective Thermal Conductivity
Q
Heat Flow
R
Thermal Resistance
Ri
Interfacial Resistance
t
Thickness
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Copyright © 2000 by ASME
Furthermore, the absence of a liquid phase eliminates
the need for cooling loops, pumps, and other fluid
handling systems. Thus, the TES unit operates
passively and is inherently reliable. Since there is no
fluid phase, the performance of the unit will be
independent of g-loading and system orientation.
“Dry” PCM’s are materials that undergo either
solid-state phase transition or are encapsulations of
solid-liquid PCM’s engineered so that the liquid phase
is not apparent. An example of the first kind of
material is the polyalcohol pentaglycerine (C5H13O3).
Pentaglycerine can be combined with other
polyalcohols to make a material that transitions at
temperatures between 24°C and 86°C. The latent
heats of these materials are comparable to the paraffin
PCM’s currently in use. Zheng and Wirtz [2000] have
recently described the design of a TES-hybrid cooler
that utilizes polyalcohol-based PCM’s.
The second category of “dry” PCM’s
(encapsulations of solid-liquid PCM’s) has been
developed in a variety of formats. Colvin and
Mulligan [1990] experimented with slurries of microencapsulated paraffins. Fossett and co-workers [1998]
used micro-encapsulated PCM powder.
The fabrication methodology and effective thermal
conductivity of a plate-like TES composite that
consists of a central core of foamed aluminum that is
packed with pentaglycerine (PG) is investigated in this
work. Since most electronic applications are compact,
a new-technology TES-system must be incorporated
into the existing structure without increasing space
requirements. This may be achieved by designing
TES-systems that serve two purposes: cooling module
and structural component. The intent of this project is
to develop plate-like TES-composite structural
elements which may be applied in the commercial
electronic equipment industry. For example, the
microprocessor chip set in a laptop computer is a
variable-power MCM.
Space and battery life
considerations dictate that the cooling system size of
the processor be minimized. The current TES concept
could be incorporated into the sheet metal and case of
the unit so that excess heat could be stored without
increasing the size or weight of the computer. This
approach would have the added benefit of stabilizing
the skin temperature of the laptop.
shows a sample of the sandwich-structure loaded with
PG. Leoni and Amon [1997] used foamed aluminum
in this way to design a paraffin-based wearable
electronics unit. Fossett and co-workers [1998]
applied the technique to an avionics cooling
application charged with micro-encapsulated paraffin
beads.
Fig. 1 Thin aluminum plates are bonded
to the foamed aluminum.
Fig. 2 A balsa wood form encompasses a composite
sample which consists of thin aluminum sheets
bonded to foamed aluminum which is impregnated
with a phase change material.
COMPOSITE DESCRIPTION
The TES composite developed is a plate-like
thermally conductive sandwich-structure containing
the solid-state phase change material PG. Thin
aluminum plates are bonded to the PCM-impregnated
aluminum foam to form the plate-like structure.
Figure 1 shows an example of the structure obtained.
Since the thermal conductivity of PG is quite small
(0.17 W/mK), the aluminum foam acts as a thermal
conductivity enhancer for the PG mass while
providing structural rigidity to the sandwich structure.
By combining the two elements (aluminum foam +
PCM), the effective thermal conductivity of the
composite is significantly increased so that it can
readily respond to changes in heat loading. Figure 2
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Copyright © 2000 by ASME
Construction.
As shown in Fig. 2, two 1.0 mm thick aluminum
plates are glued to 12.7 mm thick sheets of aluminum
foam (Duocel, ERG Aerospace) with a thermally
conductive epoxy (OMEGABOND-200, Omega
Engineering). The next step is to fill the aluminum
foam with the PCM. A form made from balsa wood is
fitted to three edges of the plate/foam composite, and
the PCM, in powder-form, is poured and packed into
the void-space of the foam material. Care is taken to
avoid air pockets. A fourth balsa wood edge is then
glued to the composite.
Balsa wood, an insulator, is chosen for the edge
seal so that nearly one dimensional plate-to-plate heat
flow may be obtained. This allows for measurement
of the plate-to-plate effective thermal conductivity of
the composite independent of sample size. Samples
fabricated in this work are 50.8 mm x 101.6 mm (2” x
4”) resulting in a face area, A = 5161 mm2.
Three samples of aluminum foam, having three
different porosities (ε), were considered. Table 1
summarizes the effective thermal conductivity and
effective density of the aluminum foam samples as a
function of volume fraction of metal, (1-ε) [ERG
Aerospace, 1999].
100°C. Solid-solid phase transition should occur at
temperatures well below the melting point of the
materials. The materials must be chemically stable.
The phase transition process must be reversible and
hysteresis-free. Finally, these materials must possess
significant latent heats; at least comparable to the
solid-liquid PCM’s currently in use.
Combinations of the polyalcohols pentaglycerine
[PG] and neopentylglycol [NPG] show promise of
fulfilling these requirements. Binary solid solutions of
these materials can be formulated to obtain materials
with solid-state phase transition temperatures ranging
between 21°C (the eutectic point) and 86°C (pure PG).
Furthermore, the latent heat of the PG/NPG system
will range from about 81 J/gm at the eutectic point up
to about 183 J/gm (pure PG) [Chandra et al., 1988].
This is comparable to paraffin compounds currently in
use. This project utilizes pure PG as the PCM. The
latent heat of PG is 183 J/gm, and transition occurs at
86°C.
HEAT TRANSFER MODEL
The plate-to-plate effective thermal conductivity of
the composite may be determined by considering the
elements of the composite to be thermal resistors.
This is shown in Fig. 3. Heat flows across the
encapsulating plates and in parallel through the
aluminum foam and the PCM. The total thermal
resistance across the sandwich structure is t/keffA
where keff is the plate-to-plate effective thermal
conductivity of the sandwich-structure. The thermal
resistance of the path through the aluminum foam
consists of the foam thermal resistance, (Rfoam +
2Rbond). The thermal resistance of the path through the
PCM is RPCM + 2Ri. Rbond and Ri are the epoxied
foam-to-aluminum sheet and PG-to-aluminum sheet
interfacial resistances, respectively. Zheng and Wirtz
have measured Ri” = Ri A = 4 x 10-4 m2K/W [Zheng
and Wirtz, 2000]. The foam-to-aluminum sheet
thermal resistance, Rfoam, is not known.
Table 1 Properties of aluminum foam samples.
Metal
Fraction
1-ε
0.077
0.084
0.090
Pore Size
[Pores
per inch]
5
20
10
Density
ρfoam
[kg/m3]
207.5
227.3
244.1
Conductivity
kfoam [W/mK]
7.6
8.3
8.9
The PCM used should meet some minimum
requirements. It should be possible to “set” the phase
transition temperature of the PMC to meet system
needs.
In the electronics cooling application,
temperature stabilization requirements will typically
range from near ambient (20°C) up to approximately
Fig. 3 Mathematical model - working thermal circuit. The elements of the system are
presented in terms of thermal resistances.
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Copyright © 2000 by ASME
temperature of the hot side of the gage plate.
Similarly, a thermocouple at 3 measures the hot side
of the composite plate. Additional thermocouples
connecting points 1 - 2 and 3 - 4 measure the
temperature drop across the gage plate and the
composite plate, respectively. An ice point is used to
calibrate the thermocouples. By measuring the
temperature of the plate, the correct slope may be
obtained for interpolating the voltage to temperature
relationship to give the temperature drops across each
sample. Additionally, measuring the voltage change
across the sample plates directly minimizes the
measurement error.
Assuming one-dimensional
steady conduction across the conductivity apparatus
gives an expression for the thermal conductivity of the
unknown sample in terms of the conductivity of the
gage plate as
The thermal resistance across the aluminum
sandwich-plates is small, Rpl ≈.001 °C/watt, so it is
neglected. Similarly, Ri ≈0.08 °C/watt while RPCM ≈
17 °C/watt, so 2Ri relative to RPCM can be neglected.
Analysis of the circuit subject to these simplifications
gives
k eff =
 e⋅k

2⋅e⋅R" ⋅k
PCM
bond PCM (1)
⋅1+
+
2⋅R" ⋅k
 k

(1− e)⋅t
bond foam 
foam

1+
(1− e)⋅t
k foam
Equation (1) shows that the composites effective
thermal conductivity is primarily composed of the
kfoam, reduced by the effect of the aluminum foam-toplate bond resistance, R”bond. This is represented by
the first term on the right hand side of the Eq. (1).
Heat flow through the PCM slightly augments keff.
This is represented by the last two terms on the right
hand side of Eq. (1).
k
FLAT-PLATE
THERMAL
CONDUCTIVITY
APPARATUS
A flat-plate thermal conductivity apparatus was
constructed to measure the effective thermal
conductivity of the composite plates. An exploded
view of the thermal conductivity apparatus is shown in
Fig. 4. The apparatus consists of a 50.8 mm x 101.6
mm (2” x 4”) flat plate heat source and a 50.8 mm x
101.6 mm (2” x 4”) flat cold-plate sandwiching two
50.8 mm x 101.6 mm (2” x 4”) flat-plate samples.
One sample is the measurement sample (unknown
thermal conductivity), and the other is a stainless steel
gage plate that has a thermal conductivity of 14.9
W/mK and a thickness of 8.59 mm.
The heater plate consists of a foil heating element
bonded to a 6.3 mm aluminum plate. The cooling
plate was designed using a simple heat exchanger
concept. A circulator/cooler (Neslab Inc.) pumps
coolant through a zigzag passage milled into the back
of a 12.6 mm thick aluminum plate. The apparatus is
covered with sheets of balsa wood insulation during
testing.
Type-T thermocouples are used to measure the
temperature drops across the sample and the gage
plate. A wire groove is cut into the aluminum
sandwich plates of the sample (see Fig. 2) and the
gage plate. The thermocouple junction beads are
carefully constructed to fit well within the groove.
The thermocouple is then buried into thermal paste
(OMEGATHERM, Omega Engineering) in the groove
to hold the thermocouple in place as well as guarantee
that the thermocouple is measuring the temperature of
the plate.
Temperature drops across the interfaces between
sample plates do not need to be addressed since the
temperature drop across the sample plates is measured
directly. Care is taken to provide a thin layer of
thermal paste to increase surface contact between the
plates. A thermocouple at 1 (see Fig. 4) measures the
eff
t
t
= k gage ⋅
sample
gage
∆T
∆T
⋅
gage
(2)
sample
Fig. 4 Schematic of flat-plate thermal
conductivity apparatus demonstrating
placement of plates and thermocouples.
4
Copyright © 2000 by ASME
RESULTS
Measurement of the composite overall effective
thermal conductivity allows for the determination of
the bond resistance, Rbond using Eq. (1).
An
assessment of the bond resistance per unit contact
area, R”bond, illustrates the uniformity of the epoxy
bonding technique. If there is a uniform value of
R”bond, then Eq. (1) can be used as a predictive
measure of performance.
Figure 5 shows the test apparatus with the
insulation removed. From top to bottom, the heater
plate is placed above the stainless steel gage plate.
This is followed by the sample where the balsa wood
form is in place. The cooling plate at the bottom is
connected to the cooler.
Three sandwich-structures, having three different
foamed-aluminum porosities were constructed and
tested. In each case, the void-volume of the foamedaluminum was packed with PG to a density of
approximately 0.65 gm/cm3.
Some thermal
conductivity tests were repeated to assess the
consistency of the experiment. Successive, separate
experiments on the same sample gave results that are
typically within ±2.7% of each other.
Table 2 Summary of experimental results.
Metal
kfoam
keff,
R”bond
keff , W/mK,
R”bond=5.2EFraction W/mK (measured)
x 105
05 m2K/W
W/mK
m2C/W
(1-ε)
0.077
7.6
4.3
5.4
4.4
0.084
8.3
4.9
4.8
4.7
0.090
8.9
5.0
5.4
5.1
Table 2 summarizes the results. Comparison of kfoam
with measured values of the overall effective thermal
conductivity, keff, shows that the epoxy-bonding
process reduces the plate-to-plate conductance by
approximately 43%. This reduction in performance
could be reduced if an aluminum brazing process
replaced the epoxy bonding process. The brazing
process, however, is more expensive. The value of the
unit contact area bond resistance is quite uniform.
This indicates that the fabrication process is consistent
and reproducible. The average value of the contact
area bond resistance is R”bond = 5.2E-05 m2K/W, and
this value is used in Eq. (1) to predict composite
overall effective thermal conductivity, keff.
Figure 6 is a plot of the epoxy bond resistance
versus the volume fraction of foamed aluminum
Fig. 5 Picture of flat-plate thermal
conductivity apparatus showing heater
plate, gage plate, composite sample, and
cold plate.
RBond =
R"Bond
(1 − ε ) ⋅A
(3)
where (1-ε) A is the foamed aluminum-to-aluminum
plate contact area. The figure shows that the overall
bond thermal resistance decreases with an increase in
volume fraction of foamed aluminum (an increase in
contact area).
UNCERTAINTY ANALYSIS
Based on manufacturers’ specifications and
an assessment of measurement capabilities, tolerances
are placed on the individual variables. The 3σ errors
are then interpreted by a data reduction algorithm.
The dimensional measurements are estimated to have
a 3σ error of ±0.001m.
It is estimated that
temperatures are measured with an accuracy of
±0.1°C. The error of the thermal conductivity of the
gage plate, kgage, is approximated at ±0.0023W/mK.
These error estimates are then submitted to a Monte
Carlo simulation program. The variable that causes
the largest error deviation is kgage. An error analysis
shows that the thermal conductivity of the sandwich
structure can be measured with a 3σ accuracy of
±9.5%. The results represent an interval of confidence
and are shown as error bars in the figures.
Fig 6 Epoxy bond resistance versus the volume
fraction of foamed aluminum.
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Copyright © 2000 by ASME
Figure 7 is a plot of the composite effective thermal
conductivity as a function of volume fraction of
foamed aluminum. The figure shows the expected
increase in keff with increasing metalization of the heat
storage volume.
This is due to two effects: an
increase in the foamed-aluminum effective thermal
conductivity, kfoam, with an increase in metal-fraction,
and a decrease in Rbond due to the increased foam-tosheet aluminum contact. When R”bond is set equal to
zero, keff increases. This shows that the performance
of the system is improved by reducing R”bond.
Another important observation is that when kfoam is
plotted, it is lower than keff when R”bond = 0. Since
2.5% of the heat flows through the PCM path, the
PCM in the foam does increase keff as compared to the
empty aluminum foam.
Additionally, the line
representing R”bond = 0 will intersect with the empty
foam line when ε = 1 since the volume fraction metal
is a function of ε, (1-ε).
The volumetric latent heat of PG packed to a
density of ρ = 0.65 gm/cm3 is ρPCMhPCM=27.95
joule/cm3.
The volumetric latent heat of the
composite (PG in aluminum foam) is
hvol = ε ⋅ρ PCM ⋅hPCM
Fig. 7 Composite effective thermal conductivity as
a function of volume fraction of foamed aluminum.
(4)
Figure 8 plots the composite effective latent heat as a
function of metal fraction. As expected, the thermal
capacity decreases with an increase in metalization of
the storage volume.
Figures 7 and 8 demonstrate that there is a trade-off
in the design of these TES-composites. An increase in
aluminum foam metal fraction results in an increase in
keff. This will result in a reduction in temperature drop
across the sandwich structure for given heat input.
However, this same increase in aluminum foam metal
fraction will result in a reduction in heat storage
capacity of the system.
Figure 9 demonstrates the TES-effect by
comparing the temperature versus time plots of the
empty aluminum foam to the composite.
The
experiment consists of insulating a sample and the
heater plate. The heater plate supplies approximately
58.5 W of power to the system; it is estimated that
10% of the heat is lost to the environment.
Temperature readings are taken every 10 seconds.
When the aluminum foam is empty, the temperature
climbs at a continuous rate. When the foam is filled
with the PG, the temperature levels off as the PG
undergoes its phase change (approximately 86oC).
The graph shows a slightly higher temperature, which
is expected since there are direct paths of aluminum
throughout the composite. The calculated time for the
material to change phases, in other words, its storage
time, is 66.8 seconds. The graph shows a storage
time of 74 seconds. As expected, the experimental
value is higher than the calculated value because about
10% of the heat applied to the system is lost to the
environment.
Fig. 8 Composite effective latent heat as a function
of metal fraction.
Fig. 9 Latent heat effect demonstrated by comparing
the temperature versus time plots for the empty
foamed aluminum and of the composite.
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Copyright © 2000 by ASME
ACKNOWLEDGEMENTS
Special appreciation goes to the Nevada
Department of Energy (DOE) Experimental Program
to Stimulate Competitive Research (EPSCoR) and the
University of Nevada, Reno for their continued
support and financial contributions.
CONCLUSION
A Thermal Energy Storage system (TES) uses a
phase change material to store heat during peak power
operation of variable power dissipating devices via the
latent heat effect. Phase Change Materials (PCM) that
undergo “dry” phase transition (no liquid phase) are
attractive TES-materials since packaging difficulties
associated with solid-liquid PCM’s are avoided.
The TES composite developed is a plate-like
thermally conductive sandwich-structure containing
the solid-state phase change material pentaglycerine
(PG). Thin aluminum plates are bonded to the PCMimpregnated aluminum foam to form the plate
-like
structure.
A flat-plate thermal conductivity apparatus was
constructed to measure the effective thermal
conductivity of the composite plates. Measurement of
the composite overall effective thermal conductivity
allows for the determination of the bond resistance.
By considering the elements of the composite to be
thermal resistors, the plate-to-plate effective thermal
conductivity is determined. Heat flows across the
encapsulating plates and in parallel through the
aluminum foam and the PCM. The composites
effective thermal conductively is primarily composed
of the thermal conductivity of the aluminum foam,
reduced by the effect of the aluminum foam-to-plate
bond resistance. Heat flow through the PCM slightly
augments the effective thermal conductivity.
An increase in aluminum foam metal fraction
results in an increase in the effective thermal
conductivity because only about 2% of the heat flow is
through the PCM, and the interfacial bond resistance
decreases due to increased contact area. The trade-off
is that the volumetric latent heat decreases with an
increase in metalization; thus, the storage time is
reduced.
REFERENCES
Colvin, D.P. and Mulligan, J.C. (1990) “Method of
using a PCM Slurry to Enhance Heat Transfer in
Liquids”, U.S. Patent 4911232.
Chandra, D., Barrett, C. S., and Benson, D. K. (1988)
“X-Ray Diffraction Studies of Solid Solutions of
Pentaglycerine-Neopentylglycol”, Advances in X-ray
Analyses, Vol. 32, pp.609-616.
ERG Aerospace. Duocel Aluminum Foam Product
Literature (1999).
Fossett, A. J., Maguire, M. T., Kudirka, A.A., Mills,
F. E., and Brown, D. A. (1998) “Avionics Passive
Cooling With Microencapsulated Phase Change
Materials”, Journal of Electronic Packaging, Vol. 120,
No. 3, pp.238-242.
Hale, D. V., Hoover, M. J., and O’Neill, M. J. (1971)
“Phase Change Materials Handbook”, NASA
technical report 72N19956.
Leoni, N. and Amon, C. (1997) “Transient Thermal
Design of Wearable Computers with Embedded
Electronics Using Phase Change Materials”, ASME
HTD-Vol. 343, pp. 49–56.
Zheng, N. and Wirtz, R. A. (2000) “Methodology for
Designing A Hybrid Thermal Energy Storage Heat
Sink”, to appear, ASME International Mechanical
Engineering Congress & Exposition, Orlando, FL.
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Copyright © 2000 by ASME