Latent heat of fusion (hf)*[kJ] 14.9 30.9 17.2 34.5
Heat storage efficiency*
[J/g] 57.0 96.0 72.8 115.2
[J/cm3] 93.0 193.1 107.5 215.6 +Calculated with AL =150W/mK determined via static heating test shown in Figure 4 (d).
*Calculated from material property measured and the measured PCM mass.
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The in-plane temperature difference T2 corresponding thermal diffusion efficiency in the PCM can be roughly
estimated as follows 8.
𝛥𝑇2 =𝑄
𝑁fin{
𝑙𝑛(𝑅0)−𝑙𝑛( 𝑅i)
2𝜋(𝐻−2𝑡skin)𝜆l} (2)
where Q and Nfin are the total heat load and the number of fins. Ri and Ro are the equivalent radii of the fin cross section
and of the region that the fin should cover. Here, Ro is determined by the pitch of fins (p). In this calculation, the
temperature of the fins is assumed to be lengthwise uniform.
The T2 becomes smaller for thinner fins and with a smaller pitch for a fixed area fraction fin; however, a small
fin pitch can be problematic in the powder removal. In addition, the thermal conductivity of the thin fins molded via
AM tends to be smaller than the bulk property. The reason for this discrepancy is considered to be smaller actual
dimensions, imperfect surface layer (e.g., adhered powders), and small thermal conductivity due to the residual stress.
In order to determine the fin pattern, the out-of-plane thermal conductance of various fin layouts were evaluated using
a small test piece (Figure 4(d)). As a result, a vertically aligned columnar fin with the equivalent radius (Ri) of 0.84
mm was selected. The thermal conductivity of the fin was determined to be 150 W/mK based on the dimension of the
CAD data, which is 13% smaller than that given in the material data sheet (173 W/mK , EOS GmbH).
Finally, lateral thermal conductivities x and y of the PCM-fin composite are estimated. As shown in Figure 4(c),
the heat penetrates two layers successively; a no-fin layer with the thickness of (p-afin) and a fin-PCM composite layer
(area ratio: afin / p) with the thickness of afin. The thermal resistance of the former is dominant, since the AL is larger
than l by two orders of magnitude. Thus, by neglecting the latter, the x and y are modeled as follows.
𝜆x = 𝜆y = (𝑝
𝑝−𝑎fin ) 𝜆l (3)
By including the contribution of the exterior skins, the in-plane temperature difference T3 for the partial heating case
is calculated as follows.
∆𝑇3 =𝑄/2
𝜆AL𝑡skin(2𝑤+2𝐻)𝐿ex
⁄ +𝜆x(𝐻−2𝑡skin)(𝑤−2𝑡skin)
𝐿ex⁄
(4)
The first and second items in the denominator are the thermal conductance of the exterior skins and that of the PCM-
fin composite, respectively. The contribution of the latter is less than 5%.
V. Evaluation of Heat Transfer Characteristics
The heat transfer characteristics of the test pieces (Table 4) were evaluated under uniform heating, partial heating,
and uniform cooling. The results were compared with the design (Sec. IV B) and simplified thermal analyses that the
engineer can perform easily in the early design phase by changing the parameters. A detailed, three-dimensional
analysis that demands much effort is beyond the scope of this study. The heat absorption characteristics evaluated via
DSC (0.1 ℃/min, and 13mg for SP30L), the thermal conductivities of PCMs evaluated via hot-wire method, and the
thermal conductivity of the fin evaluated via static heating test were used in the analyses. The whole setups were
Figure 4. Design method for the internal fins. (a) Isolation of problem into three temperature differences
(T1, T2, T3). (b) Estimation of T2. (c) Estimation of lateral thermal conductivity. (d) Static heating test.
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wrapped with foam insulation that is at least 60mm thick in all experiments. Thermal filler paste (1.35 W/mK) was
filled between the heater and test piece and between the test pieces and the cold plate.
A. Evaluation of device-level heat storage capacity
The test pieces were heated from room temperature to
approximately 50 ℃ at the heat flux of q = 0.5 W/cm2 with a thin
aluminum plate bonded with a polyimide sheet heater. The heat
storage capacities were calculated from the total heat input and the
change in the average temperature among the test piece and heater
before and two minutes later than the switching off, and then the
sensible heat was subtracted. The experimental results agree with the
designed value based on the PCM mass and the latent heat evaluated
via DSC. The significant improvement in the heat storage capacity
due to the employment of the salt hydrate (SP30L) has been
successfully demonstrated.
B. Melting Behavior under Uniform Heating
The test setup and thermocouple (T/C) locations are shown in Figure 6 (a, b). A thick aluminum heater block in
which four rod heaters are inserted was attached to the test piece using six PEEK bolts and SUS nuts. The temperature
distribution in the heater block is evaluated by T/Cs inserted into the holes in the vicinity of the thermal interface. The
temperature was the highest at the center, decreasing toward the edge. The difference between the center and the edge
was approximately 1.0 ℃. The temperature difference between the heater block and the top face of the device was
within 1.0 ℃ under the maximum heat flux (q = 1.0 W/cm2). The sheathed T/C inserted in the grooves (T/C #3),
which indicates an intermediate temperature of the heater and the top face of the device, is used in the calculations of
the overall temperature drop Ttot.
An example of temperature evolution is shown in Figure 6 (c). The T/C #22 starts to increase earlier than T/C #21
and T/C #20 due to the enhanced out-of-plane heat conduction through the side skins and embedded pipes. The
temperature difference between T/C #3 and Tm, and that between T/C #20 and Tm are considered to be close to Ttot
and T2 in Sec. IV B, respectively. The T1 was calculated as T1= Ttot - T2.
The time when the PCM completely melts in the experiment was determined from T/C #20 as follows. A thermal
analysis for a fin and the surrounding PCM was performed via Thermal Desktop ® as shown in Figure 7(a-b). The
top and bottom skins of the device were neglected in the analysis. The time when the PCM completely melts
corresponds to the time when the temperature of “PCM_BTM” starts to rise sharply. The first order and the second
order differentials (designated as dT/dt and d2T/dt2, respectively) of the fin temperature at the bottom (FIN_Btm) are
shown in Figure 7(b). The time for the peak of d2T/dt2 is closer to the time for the complete melt of PCM than that of
Figure 5 Heat storage capacity
excluding sensible heat.
0
10
20
30
40
Oct. SP30L Oct. SP30LLate
nt
he
at o
f fu
sio
n [
kJ]
Design
Test
PCM-26 PCM-27
Figure 6. Uniform heating experiment. (a) Setup. (b) Thermocouple locations. (c) An example of
temperature data (PCM-26, SP30L, Q = 80 W (1.0 W/cm2)).
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dT/dt. Thus, in the experiment, the time when d2T/dt2 of T/C #20 peaked was determined as the time for the complete
melt of PCM. The dT/dt and d2T/dt2 calculated with the raw temperature data have a high dispersion due to the small
temperature change around the Tm. Therefore, the moving averages of those were taken in the range of ± 20 s to smooth
the curve.
A comparison of Ttot among the design, analysis, and experiment are shown in Figure 7 (c). The contributions of
T1 and T2 are indicated by color. For the analysis, the differences between FIN_TOP and FIN_BTM and that
between FIN_BTM and PCM_BTM were taken as T1 and T2, respectively. Overall, both of the design and analysis
are confirmed to give good quantitative predictions. PCM-26 (oct), PCM-26 (SP30L), and PCM-27 (SP30L) have
been confirmed to meet the thermal requirement (Ttot < 10 K under q =1.0 W/cm2, Table 1).
The Ttot in the experiment remained in the similar values to those in the analysis, even though the influence of
the side skins and the embedded pipes were neglected in the analysis. In addition, a larger Ttot was observed in the
experiment than the analysis for PCM26 (SP30L). The out-of-plane thermal conductance of the skins and the pipes
are estimated as 3.89 W/K and 2.84 W/K in total, respectively. Those of the PCM-fin composite are estimated as 19.7
W/K (PCM-26) and 11.2 W/K (PCM-27). The PCM around the edge of the device melts earlier, and then the heat
conducts through the bottom skin from the edges to the center. However, the contribution of this in-plane conduction
is not significant compared to the out-of-plane conduction through the fin.
The difference between the two PCMs in the experiment was significantly smaller than expected in the design.
The mechanism can be explained as follows. In the analysis, a part of the heat input branches off from the axial heat
flow to the radial heat flow, resulting in a smaller T1 than the design (Eq. (1)). This effect is more pronounced when
the thermal conductivity of PCM is large. On the other hand, the T2 is underestimated in the design due to the
assumption of temperature uniformity in the height. The PCM at the top melts before the bottom of the fin starts to
heat up. In the late stage, PCM at the upper region has already melted, thus the heat input from the top mostly conducts
through the fin. The radial heat flux from the fin to PCM at the bottom becomes higher than the assumption under the
uniform temperature condition, resulting in a larger T2. This effect is also more pronounced when the thermal
conductivity of PCM is large, since the PCM at the upper region melts earlier. A larger fin radius (Ri) will suppress
this mechanism because the fin temperature becomes more uniform in the height; however, it also expands the fin
pitch (p) given the fixed fin area ratio (fin) leading to larger T2. There is no doubt that the adoption of a PCM with a
larger conductivity will improve the thermal performance of the device; however, improvement of design method is
necessary to use its potential.
C. Melting Behavior Under Partial Heating
The current fin layout is not intended for use under a partial heating condition. However, the footprint area of the
target and the allowable height for the PCM device may not be sufficient to meet the heat storage requirement. In that
case, the thermal engineer will consider a slight extension of the footprint of the PCM device. Another possibility of
partial heating is a very ununiform heat dissipation from the component. Therefore, the thermal modeling of the lateral
heat conduction of the device is also significant.
Figure 7. Thermal analysis for a fin and surrounding PCM with Thermal Desktop ®. (a) Temperature
contour at the time for complete melt. (b) Temperature evolution for PCM-26(oct), Q = 80 W (1.0 W/cm2).
(c) Comparison of the design, analysis, and experiment on Ttot= T1 + T2 for q = 1.0 W/cm2.
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The setup, T/C locations, and an example of the temperature evolution with the heat load Q = 80 W (q = 2.0
W/cm2) are shown in Figure 8(a, b, c), respectively. The temperature at the bottom center (T/C #20) start to increase
earlier than the those at the top edge (T/C #26, T/C #27).
A three-dimensional thermal analysis was performed as shown in Figure 9(a-b). The internal PCM-fin composite
excluding the skins and embedded pipes is modeled as a solid rectangular with an anisotropic thermal conductivity
(x, y, and z listed in Table 3). The density was set at the volume-average of those for the aluminum and the PCM in
a liquid state. The external skins were modeled as surfaces with the thickness of 1.1 mm. The comparison in the Ttot
among the design, 3D analysis, and experiment is shown in Figure 9(c). In the design, it was roughly estimated as
Ttot = T1 / 2 + T3. Overall, both of the design and the analysis are shown to give conservative estimations. The
possible reasons of small Ttot in the experiment are the thicker skin than the current assumption, the existence of
embedded pipes, the uncertainty of the skin thickness due to machining, and determination error of the time for the
complete melt of PCM.
D. Freezing Behavior under Uniform Cooling
The experimental setup and T/C locations are shown in Figure 10 (a, b). The test piece was attached to an aluminum
cold plate with six PEEK bolts. The cold plate was initially maintained at 40℃ via heater control. The fluid (a mixture
of water and Nybrine Z1) began circulating when the valve was opened.
Figure 8. Partial heating experiment. (a) Setup. (b) Thermocouple locations. (c) An example of temperature
data (PCM-26, SP30L, Q = 80 W (q = 2.0 W/cm2 when calculated with contact area).
Figure 9. Thermal Analysis via Thermal Desktop ®. (a) Example of temperature contour map. The location
of the nodes referred in (a) is also shown. (b) Example of temperature evolution, (c) Comparison with the
design and the experimental result on the temperature difference Ttot
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The result for PCM-26 (oct) is shown in Figure 10 (c). The temperatures of both the cold plate and the PCM device
started to increase when those reach 26.5 - 27.0 ℃, which is the sign of solidification. The solidification happened all
over the device within 0.5 min. The solidification point (Ts) agrees with the result of DSC (Figure 3).
The result for PCM-26 (SP30L) is shown in Figure 10 (d). The Ts was 24.5 - 25.0 ℃, which is slightly lower than
the result of 3-layer calorimeter (26.0 ℃). The solidification did not occur simultaneously, even though the in-plane
temperature variation in the cold plate was within ± 0.3 ℃. The solidification propagated from the bottom left to the
top right (based on Figure 10(b)). The temperature increased sharply when the solidification occurred, both in the cold
plate (e.g., #30) and the top skin of the device (e.g., T/C #23). It indicates that the solidification propagates rapidly in
vertical direction. Note that it is not clear whether the solidification at a point influences those in the neighborhood. It
is also possible that solidification is caused simply by the local temperature. The solidification of PCM dissipates a
large amount of heat, which may lead to temperature increase in the neighborhood. The actual phenomenon is
considered to be very complicated.
The solidification behavior is known to be influenced by the sample amount, cooling rate, and mechanical
disturbance, existence of nuclei, and so on. Since SP30L is not the pure material, the composition may be nonuniform
in the device, which may cause spatial variation in the solidification point. The thorough physical discussion is difficult
without knowing the PCM temperature itself. However, it is crucially important to know which temperature the cold
plate should take for solidification of the PCM device and how the solidification propagates, especially when the
Figure 10. Freezing experiment. (a) Setup. (b) Thermocouple locations. (c) Temperature evolution for
PCM-26 (Oct). (d) Temperature evolution for PCM-26 (SP30L). The graphs for the cold plate and the
PCM device in the same experiment are separated to improve visibility in (c) and (d).
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device is used cyclically in a short time period (e.g., observation instrument in an LEO satellite). Partial cooling
behavior should be also understood, since it happens when the device is cooled via a fluid loop or heat pipes.
The thermal analysis for cooling experiment has not been performed since the subcooling followed by a
temperature backlash during solidification cannot be modeled only with a standard function of Thermal Desktop ®.
An elaborated SINDA/Fluint code and a modeling of the thermal response are necessary in the future.
VI. Conclusion
A spacer-type PCM device made by additive manufacturing (AM) was designed, manufactured, and tested. A
highly anisotropic, vertically aligned fin layout was shown to meet a strict requirement for a high heat flux component,
up to 1.0 W/cm2. In addition, high-density lithium nitrate trihydrate-based PCM (SP30L, Rubitherm Technologies
GmbH) was introduced. Its heat absorption/dissipation characteristic was evaluated via DSC and 3-layer calorimeter;
the results were consistent except for solidification point. The device filled with SP30L showed a significantly higher
heat storage capacity than one filled with octadecane. The overall temperature drop Ttot was not significantly reduced
by adopting SP30L despite its large thermal conductivity. The problem is very complicated because the influences of
density and thermal conductivity are not separated. Further experimental and analytical works are necessary to
quantify the influence of each parameter. The solidification point for the device is a few K lower than the material
level. The difference may be crucial in cyclic use in an LEO satellite. Further development and testing of salt hydrates
are necessary, including thermal cycle stability and chemical compatibility.
Acknowledgments
We are grateful to Dr. E. Kieseritzky and Mr. G. Lindenberg in Rubitherm Technologies GmbH for helpful
discussions on the characteristics of salt hydrates and testing methods.
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