Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
THERMAL MANAGEMENT USING “DRY” PHASE CHANGE MATERIALS
R.A. Wirtz, Ning Zheng and Dhanesh Chandra
University of Nevada, Reno
Reno, NV 89557
ABSTRACT
I. INTRODUCTION
The thermal response characteristic of a hybrid
cooler that is charged with a “dry” solid-solid phase
change compound is evaluated. A mathematical model
that simulates the performance of a cooler/heat storage
unit is formulated. A prototype heat sink that
incorporates heat storage using a “dry” PCM is tested,
and used to benchmark the simulation model. Different
heating and cooling strategies are evaluated and a
figure of merit, characteristic of the cooler/PCM under
development is introduced.
Incorporation of a heat storage capability in the
temperature control system of an electronic module
having a variable heat dissipation rate will allow for a
smaller, less-power-consuming module cooler.
Materials formulated to undergo phase transition at key
temperatures can provide this load-leveling capability
via the latent heat effect.
NOMENCLATURE
As
b
c
cal
cpcm
C”
D
htr
H
Hpcm
kal
kpcm
mi
nf
q
s
t
T
Ttr
U
W
δTtr
∆x
Heat exchange volume surface area
Heat sink base thickness
PCM effective heat capacity
Specific heat of aluminum
Specific heat of PCM
PCM unit conductance
Heat sink depth
Heat of transition
Fin height
PCM mass depth
Thermal conductivity of aluminum
Thermal conductivity of PCM
Element mass
Number of fins
Input power
Fin spacing
Fin thickness
Temperature
Transition temperature
Heat exchanger heat transfer coefficient
Hybrid cooler width
Transition temperature interval
Element length
Phase transformations in materials have been
employed in a variety of temperature stabilization
applications, including thermal control of electronics.
Organic-based, solid-to-liquid phase change materials,
and in particular paraffin-based PCM’s such as those
recently discussed by Leoni and Amon [1997], have the
advantage of being inexpensive and widely available.
Their solid-liquid transition temperatures can be
controlled by material selection. However, the liquid
phase presents fluid containment problems both due to
the presence of the liquid, and due to volume expansion
during transition to the liquid phase. This results in
increased complexity and cost.
Other solid-to-liquid phase transition materials
having appropriate transition temperatures and latent
heats include the salt hydrates and certain metallic
alloys. Salt hydrates are generally corrosive, they
absorb and loose water during phase transition, and
they tend to form partially hydrated crystals, effecting
performance. Metallic alloys have been employed in
some high-performance military systems [Antohe et al,
1996]. On a unit volume basis, their latent heats are
generally superior to those of the hydrocarbons. They
also exhibit relatively high thermal conductivity.
However, mass densities that are an order of magnitude
greater than the hydrocarbons result in relatively heavy
packages.
There are some very attractive “dry” material
systems where the difficulties described above are
avoided. These include micro-encapsulated solid-liquid
phase change composites and solid-solid organic phase
change compounds.
74
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
Table 1. Comparison of some "dry" PCM's with typical paraffin-based, salt hydrates and metallic-alloy PCM’s [Lane,
1983].
Transition
Temp. range
o
C
Latent Heat
Joule/cc
Density
gm/cc
Solid – Solid Organic Compounds (TCC)
S-S (dry)
21 – 100
144 - 212
~ 1.1
Micro-encap. Paraffin (Thermosorb)
S-L (dry)
6 - 101
95 - 186
~ 0.9
Paraffin (Eicosane, Docosane, etc.)
S-L (wet)
-12 – 71
128 – 197
0.75 – 0.88
Non-Paraffin Organics (Beeswax)
S-L (wet)
-13 - 187
131 - 438
0.85 – 1.54
Salt Hydrates (MgSO4-7H2O)
S-L (wet)
28 - 137
270 - 650
1.5 – 2.2
Metallics (Eutectic Bi-Cd-In)
S-L (wet)
30 - 125
200 - 800
6 – 10
Material type
A. Micro-Encapsulated Phase Change Composites
These composites, in powder form, consist of tiny
beads that contain the phase change material inside thin
polymer shells [Fossett et al, 1998]. Individual capsules
range from ten microns to one mm in diameter with
impermeable, semi-rigid shell walls of typically less
than one micron thickness. The core phase change
material, which is usually a blend of paraffin
compounds, comprises 80% – 85% of the composite
mass. Core PCM’s are blended to establish the phase
transition temperature. Because the core material is a
blend of materials, transition actually occurs over a
relatively wide temperature interval, typically about
10oC.
B. Solid-Solid Organic Phase Change Compounds
These are materials that undergo reversible solidstate crystal structure transitions at temperatures
ranging from the ambient up to about 100oC. These
materials have significant heats of transition,
comparable to and exceeding the paraffin-based
PCM’s. Transition temperatures can be selected by
forming solid solutions of different organic compounds.
Transition can occur over a fairly limited temperature
interval.
Table 1 compares some important characteristics
of the “dry” PCM’s (solid-solid organic phase change
compounds and micro-encapsulated paraffins) with
representative solid-liquid PCM’s. It can be seen that
the dry PCM’s are generally comparable to the paraffin
compounds. The metallics and salt hydrates have
generally higher volume-based latent heats.
In this paper, we evaluate the thermal response
characteristics of a hybrid cooler that is charged with a
solid-solid phase change compound. A mathematical
model that simulates the performance of a cooler/heat
storage unit is formulated and used to evaluate different
electronics cooling strategies. A prototype heat sink that
incorporates heat storage is tested, and used to
benchmark the simulation model. Different heating and
cooling strategies are evaluated and a figure of merit,
characteristic of the cooler/PCM under development is
introduced.
II. HYBRID COOLER DESIGN
CONCEPTS
The storage capacity and transient response
characteristics of an electronics module cooler
employing PCM will be proportional to:
• the characteristics of the heat load and duty cycle
applied to the cooler,
• the amount of phase change material present in the
cooler and its thermophysical properties,
particularly the heat of transition and transition
temperature interval, and
• the specific design configuration of the cooler (heat
sink plus phase change material).
The use of dry phase change materials will allow
us to consider fairly simple design concepts. Figure 1
shows the general concept where the overall cooler
volume is divided into three separate sub-volumes.
Volumes A and C are metallized phase change volumes.
C
B
A
Heat
Source
COOLANT
Fig. 1 Hybrid cooler design concept.
75
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
Table 2. Properties of a solid-solid dry PCM.
Density
ρpcm
gm/cc
1.1 (approx.)
Sp. Heat
cpcm
joule/gm K
2 (approx)
Latent Heat
htr
joule/cc
212
They each contain both phase change material and a
metal conducting path that is in thermal contact with
the PCM. Volume B is the volume occupied by the heat
sink where convection to the coolant (air) takes place.
Heat flow is from a source that is thermally attached to
one of the exposed faces of volume A, through storage
volume A to volume B. Since the heat transfer surface
of volume B is at an elevated temperature, heat also
flows into storage volume C. The UAs product of
volume B (the heat exchanger capacity, watt/oC) is
sized to accommodate the steady heat loading of the
source so that volumes A and C operate at some steady
temperatures that are below the start-of-phasetransition-temperature, Ttr.
As heat loading is
increased, temperatures in volumes A, and subsequently
C, will increase, initiating phase transition, energy
storage, and temperature stabilization. Upon reduction
of the heat loading from the die, temperatures will
decrease and reverse phase transition will release stored
energy to volume B and the coolant.
Conducting paths in the storage volumes might
consist of discrete elements such as parallel pins or
plates, metal foam or a metallic binder. If plates or pins
are used to metalize volumes A and C, then it seems
logical that the heat transfer surface in volume B would
be an extension of these forms.
The effect on performance of the relative volume
fractions of volumes A and C will have to be
considered in addition to overall cooler size,
thermophysical characteristics of candidate PCM’s, and
peak power and duty cycle characteristics of the heat
load. It may be that for a given heat loading and duty
cycle, the best performance will be obtained with either
volume A or C absent.
We envision that a relatively simple fabrication
methodology will be possible with this design concept,
with the dry PCM cast into an overall metal
conduction/convection structure. For example, if the
metal structure consists of a series of thin parallel rods
or plates, the dry PCM would be introduced between
the rods/plates. If global encapsulation is necessary, we
envision coating appropriate surfaces of exposed PCM
with an elastomer.
Trans. Temp.
Ttr
o
C
81
Trans. T-interval
∆Ttr
o
C
1
Th. Conductivity
kpcm
watt/m K
0.2 (approx.)
s
H
Hpcm
D
b
W
Fig. 2 Diagram of Hybrid Cooler
III. PROTOTYPE HYBRID COOLER
Figure 2 shows the hybrid cooler that is evaluated
in this work. It is a simple modification of a
commercially available aluminum plate-fin heat sink
where the lower portion of the space between fins is
filled with the phase change material. An elastomer
coating is used to globally encapsulate the PCM. The
heat source is bonded to the underside of the base plate.
The unit has the following dimensions: H = 50.8mm, W
= 54.3mm, D = 50.2mm, t (fin thickness) = 0.81mm.
The unit has 15 fins so that s = 3mm.
In the context of Fig. 1, the lower portion of the
fin-volume is the metalized phase change volume
(volume A in Fig. 1), and the upper portion acts as the
heat exchange surface (volume B in Fig. 1). For
convenience in our prototype testing, we use natural
convection cooling. Addition of a small axial-flow fan
to the top of the unit would boost overall performance
considerably.
The dry phase change material used is a solidsolid organic phase change compound having the
properties tabulated in Table 2. This material, called a
Temperature Control Compound (TCC), is one of a
class of organic solid solutions being developed for this
76
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
application.1 The material is a waxy granulate that is
plastic in its high temperature phase. Particle size
ranges from 0.1mm to 1.0mm. Solid solutions can be
formulated to undergo transition at temperatures
ranging from about 24oC up to 89oC. The heat of
transition ranges from 144 - 212 joule/cc, and the
transition temperature interval ranges up to about 4oC.
The volume expansion at transition ranges to
approximately 4%. The material is a dielectric having
an electrical resistivity of approximately 108Ωcm.
Melting occurs at 80 oC to 100 oC above the solid-solid
transition. Furthermore, these materials burn slowly,
similar to paraffin. Their ignition temperatures are
estimated to be in the 300 oC to 400 oC range.
fins, then there are 2nf – 2 half-fins that can store
energy in the PCM. The heat entering a given half-fin
is qn(t) = q(t)/(2nf-2), and the rate leaving is UAs,n
[T(Hpcm) – Tamb], where As,n = As/(2nf-2) is the surface
area of the half-fin, U is the exchanger heat transfer
coefficient.
The lower part of Fig. 3 is the thermal circuit for a
simple, 7-element heat transfer model. The circuit
shows seven lumped masses interconnected by thermal
resistances. We divide the storage volume of each halffin into six elements: three PCM-elements, and three
aluminum-plate-elements. Since sk pcm << tkal , we
can neglect axial conduction between the PCMelements. We also assume that the temperature in the
base-element, To is uniform. The element masses and
interconnecting thermal resistances are tabulated in
Table 3 where mempty is the mass of the heat sink
without PCM, mPCM is the mass of PCM added to the
heat sink, and nele is the number of mass elements of the
model.
IV. SEMI-EMPIRICAL HEAT
TRANSFER MODEL
Due to the symmetry of the plate-fin design, a
mathematical model of a “half-fin” segment of the
hybrid cooler can be formulated. The half-fin geometry
is shown in Fig. 3. Let “x” be a coordinate system,
parallel to the fin-plate with origin at its base. The halffin consists of a base-volume (-b < x < 0), a metallized
heat storage-volume (PCM + aluminum plate, 0 < x <
Hpcm), and a heat exchanger volume (aluminum finplate in thermal contact with the ambient, Hpcm < x <
H). Heat enters the control volume at the base, and
leaves it through the exchanger volume. If there are nf
The quantity C’’ is the unit conductance between
the heat storage volume metallization and PCM mass
(see R1-4, R2-5, R3-6 of Table 3). The conductance is
proportional to the effective thermal conductivity of the
PCM, kpcm(eff) and inversely proportional to the contact
resistance at the metalization-PCM interface, R”i [oC
m2/watt].
(UAs)n [T – Tamb]
qn(t)
s/2
∆x
b
t/2
Hpcm
H
0
qn(t)
m0
x
m4
m5
m6
m1
m2
m3
Tam
Fig. 3 Half-fin hybrid cooler heat transfer model.
1
Materials are being developed by Sierra-Nevada Research and
Development, Inc., Incline Village, Nevada, (775) 784-6714.
77
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
Table 3 Model element masses and thermal resistances.
Element Mass
m1 , m2 , m3
m0
mempty − (m1 + m2 + m3 )
R0-1
∆x / 2
t
k al D
2
C''=
m4,m5,m6
t
ρ al ∆xD
2
m PCM
2(n f − 1)nele
Thermal Resistance
R1-2, R2-3
R3-amb
∆x
t
k al D
2
4k pcm (eff ) / s
1 + 4k pcm (eff ) Ri ' ' / s
R1-4, R2-5, R3-6
1
UAs ,n
(1)
Since the PCM mass is in granular form, its
effective thermal conductivity is less than the thermal
conductivity of the base material. The amount of
reduction depends on the packing arrangement of the
particles, particle shape, and particle contact areas.
Typically, kpcm(eff) is 10% - 25% of the particle thermal
conductivity [Kaviany, 1995].
1
C " ∆xD
Energy balance equations are written for each
element mass, and the resulting seven ordinary
differential equations are solved as an initial-value
problem for the element temperature response using a
Runge-Kutta solver. The initial condition for the
solution is the steady operating temperature of the unit
with an initial input power, qn(0)=qinit/(2nf-2).
2( H pcm − x) 

1
T (0, x) − Tamb = q n (0) 
+

k al tD 

U (0) As ,n

(3)
The metallization-to-PCM contact resistance, R i”
is difficult to estimate. Contact resistances for hardmaterial to soft-material interfaces can range from
where U(0) is the initial unit surface conductance of the
heat exchanger volume.
10 − 4 m 2 C o / watt to 10 − 2 m 2 C o / watt .
Numerical Accuracy and Convergence. We typically
complete the numerical integration of the ODE-system
using a time step size of 0.6 second. Recalculation of
selected results using one-third of this time step size
gives essentially the same result. We have also repeated
selected simulations using a 9-element model. The
results are virtually the same as obtained using the 7element model. Run times are typically less than 2
minutes on a desk-top pc equipped with a400Mhz
microprocessor.
If we assume k pcm (eff ) = .15k pcm = 0.03
watt/m°C, then C’’ can range from about
4watt / m 2 C to 40watt / m 2 C . Given this wide
range, we will empiricize the model, and use
experimental measurements to establish the value of C”
for a given hybrid cooler.
The internal energy of each element mass is
characterized by its heat capacity and a single
temperature, Ti. For the PCM mass elements, we
incorporate the latent heat effect into the specific heat
as follows:
Figure 4 plots eq. (2) for the material described by
Table 2. For a transition temperature interval, δTtr =
1oC, the latent heat effect is manifested as a 100-fold
increase in heat capacity.
8
6
5
4
3
2
c(T) [joule/gm °C]
h

c pcm + tr , Ttr ≤T ≤ (Ttr + δTtr )


δTtr
c(T ) = 
(2)


c pcm , otherwise
1000
100
8
6
5
4
3
δTtr
2
10
8
6
5
4
3
2
1
80
81
82
83
Temperature [°C]
Fig. 4 PCM Property
78
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
V. EXPERIMENTS AND MODEL
CALIBRATION
110
The unit is brought to a steady operating
temperature that is a few degrees below the PCM
transition temperature, and the initial input power, qinit,
and base temperature rise above the ambient
temperature, Το(0)− Τamb, are recorded. This establishes
the initial value of the exchanger-volume unit surface
conductance.
U (0) =
1
T (0) − Tamb 2 H pcm 
−
As ,n  o

k al tD 
 q n (0)
(4)
Since natural convection cooling is employed, the
exchanger conductance will vary with its temperature
level. Therefore, we write the conductance as
0.25
T (t , H pcm ) − Tamb 
U (t ) = U (0) 

T (0, H pcm ) − Tamb 


(5)
Figure 5 shows the response of the hybrid cooler
charged with 36 gm of PCM. The heater power is
initially set at qinit = 8.71 watt, and Tamb = 24oC. The
resulting steady state base temperature, after 68 minutes
of operation, is To(0) = 77 oC. With an initial heat input
per half-fin of 0.32 watt Eq. (4) gives
U (0) As ,n = 0.0062 ⋅watt / o C . The power is then
increased to qfinal = 16.82 watt, and the base temperature
response is recorded. The data (open circles) show the
base temperature rapidly increasing to about 90oC and
then leveling off for about 20 minutes. This is followed
100
Temperature [°C]
Experiments are used to gain experience with dry
PCM’s in this application, and to establish the value of
C’’for a given prototype cooler-PCM combination. The
cooler is instrumented with a thermocouple, with the
junction buried in the geometric center of the base of
the unit. The thermocouple/electronic ice point output is
monitored with a strip-chart recorder. We estimate
temperatures are measured with an accuracy of about
±0.25 oC and a time resolution of ±5 sec. A 25mm x
25mm foil heater is bonded to the base of the unit, and
the bottom of the base and sides of the unit are
insulated with layers of balsa wood. We also estimate
that about 3% of the input power to the heater is lost
through the balsa insulation, and power is measured
with an accuracy of ±5%. The prototype hybrid cooler
is typically charged with 35 - 45gm of PCM, and this
makes Hpcm ≈25mm (see Fig. 2 and 3).
Measured
T0
T3
T4
T6
90
80
-15
-5
5
70
15
25
35
45
Time [min]
Fig. 5 Temperature Profile
by an additional temperature increase after the storage
capacity of the cooler is exceeded.
The figure also shows temperatures calculated by
the semi-empirical model with C” = 20 watt/m2 oC.
This value of C” minimizes the rms error between the
measured and calculated base temperature increase to
less than 1.2oC. The figure plots heat sink temperatures
To and T3, together with PCM temperatures T4 and T6.
The heat sink temperature spread (To-T3) is a measure
of the effectiveness of the storage-volume
metallization. For the present hybrid cooler it is about
4oC. The response of the PCM temperature, particularly
T6, is a measure of the heat storage capacity of the unit
in that when T6 > (Ttr + δ
Ttr ) , the latent heat storage
capacity of the unit is exhausted. The figure shows T4
and T6 rapidly increasing to the start of transition
temperature, Ttr = 81oC and then level off. T4 reaches
82oC (the end of transition temperature) at t = 21min.
T6 reaches this point at t = 27min, signifying complete
transition of the PCM to it’s high-temperature phase.
We have completed the above described
experiment a number of times with 36 gm < mpcm < 42
gm. In each case we find that C” = 20 watt/m2 oC
nearly minimizes the rms difference between calculated
and measured values of To. In all cases the rms
difference is less than 1.3oC. Therefore, we will use this
value of C” to characterize conduction between the
storage-volume metalization and PCM mass in the
following parametric study.
VI. PARAMETRIC ANALYSIS OF
PROTOTYPE COOLER
Assume the 15-fin hybrid cooler, charged with 40
gm of PCM and residing in an ambient at 20oC, is
operated at some initial power level, qinit, such that the
steady state base temperature is To = Ttr = 81oC. The
79
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
q2/qinit = 0.5
100
100
q1/qinit
1.25
1.5
2.0
90
80 0
10
20
30
δts = 43.2 min
40
50
60
70
80
90
100
Temperature [°C]
Temperature [°C]
T0
T4
T6
δts(min)
91.3
43.2
21.6
δtr(min)
38.8
40.0
41.2
90
80 0
20
40
60
80
100
120
140
δtr = 40.0 min
Time [min]
70
70
Time [min]
Fig. 7 Comparison of different q1/qinit
Fig. 6 Parametric analysis results
Define the storage time, δts-, as the time interval
for the storage capacity of the hybrid cooler to be
exhausted. This is the time interval between the time
when To = Ttr and T6 > (Ttr + δ
Ttr ). In a similar
way, define the recovery time, δtr, as the time required
to recover the storage capacity of the PCM mass. This
is the time interval between T6 = (Ttr + δ
Ttr ) and
T4 < Ttr .
Figure 6 shows an example of the above described
numerical experiment for the case where
q1 / qinit = 1.5 and q 2 / qinit = 0.5 . The figure plots
the base temperature (To) and PCM temperatures at the
bottom and top of the storage-volume (T4, T6). At t =
43.2 min, T6 ≥ 82oC, so phase transition of all of the
PCM mass is complete (δts = 43.2 min). At this point in
time, To = 92.5oC. The input power is then reduced to
0.5q init . At t = 83.2 min T4 ≤ 81oC, so all of the PCM
mass has undergone reverse transition. This defines the
recovery time, δtr = 83.2min – 43.2min = 40.0min.
Figure 7 compares the cooler base temperature
response for three ratios of
q1 / qinit with
q 2 / qinit = 0.5 . The figure shows that, as
q1 / qinit increases, the temperature level of the cooler
base during phase transition increases relative to Ttr.
The temperature stabilization time, δts, decreases with
increase in q1 / qinit . On the other hand, the
temperature recovery time is only weakly dependent on
q1 / qinit , showing only a slight increase with
q1 / qinit . This is because q1 / qinit merely establishes
the “initial” temperature distribution for the cool-down
phase, and the temperature gradients in the metalized
parts of the cooler are relatively small.
Figures 8 and 9 look at how variations in the PCM
unit conductance, C”, and transition temperature
interval, δTtr effect the base temperature response.
Figure 8 plots the base temperature response for three
values of C”, and Fig. 9 plots it for two values of
transition temperature interval. Figure 8 shows that an
increase in C” lowers the temperature level of the
cooler relative to Ttr during the transition process. As a
consequence, the heat transfer rate to the coolant is
decreased; and for a given power input, the rate of
energy storage in the PCM mass is increased. The net
result is that δts decreases. Since the cooler is operating
at a lower temperature, the recovery time is also
decreased when C” is increased. The net result is that
coolers having highly conductive storage volumes
(increased metallization) respond more rapidly, and
C'' (watt/m2°C)
10
20
40
100
δts (min) δtr (min)
53.2
49.0
43.2
40.0
37.7
34.9
q1/qinit = 1.5, q2/qinit = 0.5
Temperature [°C]
input power level is stepped to a new value, q1 , and the
temperatures increase until such time that the storage
capacity of the PCM is exhausted. At that point, the
power is reduced to q 2 and temperatures decrease,
with reverse transition occurring in the PCM mass.
90
80 0
20
40
60
80
100
120
Time [min]
70
Fig. 8 Effect of C''
80
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
δTtr (°C)
1
10
100
δts (min)
43.2
61.1
δtr (min)
40.0
36.9
10000
q1/qinit = 1.5, q2/qinit = 0.5
8
6
5
4
3
δts & δtr [min]
Temperature [°C]
2
90
1000
8
6
5
4
3
Eq. (6) and (7)
2
100
80 0
20
40
60
80
100
8
6
5
4
3
120
2
Time [min]
10
0.0
70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(q1/qinit - 1) & (1 - q2/qinit)
Fig. 10 δts and δtr relation vs. q ratio
Fig. 9 Effect of δTtr
of simulations for various values of q1 / qinit shows that
exhibit more precise temperature control.
Figure 9 shows that an increase in transition
dTo
during transition.
dt
temperature interval increases
In the same way as with Fig. 8, the temperature level of
the cooler is increased, leading to an increase in δts.
This increase is, of course, at the expense of a higher
operating temperature of the cooler base, and less
precise control of module temperature.
The temperature stabilization time, δts, should be
inversely proportional to the incremental change in
input power, q1 − qinit . Dimensional analysis implies
that
Figure 10 plots δts-values (open square symbols)
and δtr-values (open circles), determined by the
 q1

q
− 1 or 1 − 2 ,
q init
qinit

numerical simulation, versus 
depending on whether the unit is being heated or
cooled. Eq. (6) and (7) are also plotted in the figure.
All “data” and both equations plot on the same curve.
It is noted that, τs is the stabilization time when
q1 / qinit = 2 , and τr is the recovery time when
q 2 = 0 . As a consequence, the value of τs or τr can
be determined by recourse to one prototype experiment.
−1
 q1


−
1
δt s = τ s 
q

 init

(6)
VII. CONCLUSIONS
where τs is a time that is characteristic of the heating
process. It is a figure of merit for a given hybrid
cooler/PCM combination. Due to the asymptotic nature
of the cool-off process, the temperature recovery time,
δtr, should be inversely proportional to the input power
[
decrement below qinit , i.e. δ
t r ∝ qinit − q 2
]− 1 so that
δtr should be given by a similar expression
−1

q2 
δt r = τ r 
1 − q 

init 

τs = 21 min.
(7)
where τr is a time that is characteristic of the cooling
process. Furthermore, since the heating and cooling
mechanisms of the hybrid cooler are the same, τr = τs.
For the present hybrid cooler, charged with 40 gm of
TCC and with C” = 20 watt/m2 oC, a regression analysis
Hybrid coolers used for temperature stabilization
of electronic modules having time dependent heat
dissipation rates can be modeled as thermally connected
volumes with each volume having a specific
functionality. In the present case, the cooler consists of
a base-volume, heat-storage-volume, and heatexchange-volume. A simple, semi-empirical thermal
response model can be formulated where volumes are
subdivided into mass elements, and energy balance
equations can be written for each element. Because the
thermophysical properties of the PCM incorporated into
the system are generally not well known, the model
must be parameterized by comparison with a prototype
experiment.
A prototype hybrid cooler can be constructed by
charging a commercially available parallel-plate heat
sink with “dry” phase change material. Such a device
has a number of advantages relative to units charged
with solid-to-liquid coolers, the most notable one is
81
Proc. Fifteenth IEEE Semiconductor Thermal Measurement and Management Symposium, March 9-11, 1999, San
Diego CA, IEEE # 99CH36306.
packaging simplicity. The current cooler, charged with
a solid-solid phase transition compound called TCC,
exhibits good thermal control with a PCM conductance
of 20 watt/m2 oC, and a characteristic heating/cooling
time of 21 min.
Numerical simulations show that an efficient
hybrid cooler should have a high PCM conductance and
small transition temperature interval in order to provide
tight thermal control. The PCM conductance can be
maximized by proper incorporation of metallization
into the storage-volume. The simulations also show
that the transient response of a given hybrid cooler can
be characterized by τs. This quantity can be measured
using a single experiment. It should prove to be a
useful figure of merit for evaluating various design
alternatives.
REFERENCES
Antohe, B.V., Lage, J.L., Price, D.C. and Weber, J.L.
(1996) “Thermal Management of High Frequency
Electronic Systems with Mechanically Compressed
Microporous Cold Plates” Thermal Management of
Commercial and Military Electronics, Proc. ASME
National Heat Transfer Conference, pp. 179-186.
Fossett, A.J., Maguire, M.T., Kudirka, A.A., Mills, F.E.
and Brown, D.A. (1998) “Avionics Passive Cooling
with Microencapsulated Phase Change Material”, J.
Electronic Packaging, Vol. 120, pps. 238 – 242.
Kaviany, M. (1995) Principals of Heat Transfer in
Porous Media, 2-nd ed., Springer.
Lane, C.A. (1983) Solar Heat Storage and Latent Heat
of Materials, CRC Press Inc., Boca Raton FL.
Leoni, N. and C. Amon (1997) “Transient Thermal
Design of Wearable Computers with Embedded
Electronics Using Phase Change Materials”, ASME
HTD-Vol. 343, pp. 49 – 56.
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