Effect of Phase Change Material on Dynamic Thermal Management Performance for Power Electronics Packages

As the market for more fuel efficient and environmentally friendly vehicles grows, the demand for more versatile and capable electric vehicles (EVs) increases. These vehicles will require more electrical power to accommodate a wide variety of uses, from commercial transportation of passengers and goods to military vehicles of varying size and capabilities. Power electronics (PE) are one of the most important components in the EV system. Increasing the PE efficiency, durability and lifespan are crucial in developing more robust and cost-friendly EVs.

In the past, power electronic systems used a silicon insulated-gate bipolar transistor as the main working component [1]. The advent of silicon carbide (SiC)-based power electronic devices has resulted in substantial performance improvements [2]. SiC devices are thinner than Si devices, have a higher thermal conductivity (and therefore a lower thermal resistance), and can operate reliably at much higher temperatures [2]. Si devices typically cannot withstand temperatures higher than 150 °C, whereas SiC devices have been calculated, using first-order simulations, to operate at temperatures up to 600 °C [2,3]. While operating at such high temperatures is theoretically possible, high temperatures reduce device reliability. The package is also made up of a variety of substrate layers that act to both dissipate heat and add stability to the package. Due to the varying coefficients of thermal expansion in the substrate layers, high-temperature fluctuations can degrade package stability over time [4]. Three of the most important factors in PE packaging are performance, reliability, and cost. Reliability of PE packages may be improved by decreasing both the maximum temperature and temperature fluctuations experienced by the package [4]. The cost of the packaging can be reduced by decreasing the number of SiC die that are necessary to divide the heat load experienced by the devices.

Due to its thermal storage properties, utilizing phase change material (PCM) in PE packaging has the potential to aid in thermal management [5]. PCMs absorb heat at a constant temperature during a change in phase [6]. PCM incorporated into PE packaging can effectively store heat dissipated by the devices during its transient operation via phase change from solid to liquid (or in some cases solid to solid) transformations, lowering the peak junction temperature in the device [7]. The latent heat absorption during phase change also reduces dramatic temperature fluctuations experienced by the package [8]. The reduction in temperature fluctuations in the package could help mitigate thermally accelerated failures in the substrate layers of the package, increasing package overall fatigue life [4,9]. While there have been reviews of both PCMs [8] and packages [4] for automotive PE, there have been very few studies that model performance of PCMs under transient conditions. In the only published transient thermal modeling study with SiC, power pulses were investigated to evaluate the viability of PCM as a source of supplemental cooling in PE packages, but only model a single PCM (xylitol) in the study [6].

This paper investigates the effects of incorporating PCM into both single-sided and dual-sided power electronics packages. PCMs with varying material properties are incorporated into the packages. The PCMs' effect on the maximum junction temperature of the SiC die, temperature fluctuations in the package, and the potential for die reduction are analyzed. This analysis used transient heat load models for both urban and interstate travel to predict PE package performance.

Two PE packages, without PCM, were modeled using parapower, an open-source tool developed by the Army Research Lab. parapower uses a matlab-based code that solves a resistor network model of the system using implicit Euler formulation that offers a fast analysis of thermomechanical systems and medium fidelity modeling of PCMs [10,11]. The single-sided package was based on the device used in the 2014 Honda Accord [4,12]. The package is comprised of an aluminum base plate, solder, and direct bonded copper (DBC) on silicon nitride (Si₃N₄) with the power devices (two SiC die) located 6.5 mm from the coolant (Fig. 1). The second package was based off the 2016 Chevrolet Volt device [4,13] and is comprised of the same materials, but with two layers to take advantage of double-sided cooling (Fig. 2).

where the maximum efficiency, η, is 98% and assumed constant [17]. The absolute value of the power is taken to maintain power even during deceleration, to simulate regenerative braking. Figure 4 shows the power and speed used to create the heat load model. This transient heat load was divided by the number of die in the package, with the assumption that the heat rate was divided evenly among the die in the package. The US06 drive cycle (top) was the more aggressive cycle, with power spikes reaching over 80 kW and average power stretches up to 20 kW. The urban drive cycle (bottom) had lower power levels, but longer periods of moderate power levels up to 10 kW.

where ρ is the density, u is the flow speed, and μ is the dynamic viscosity of the fluid. During the simulations, the total mass flow through the channels was 1.14 × 10⁻³ kg/s and yielded a Reynolds number of 754 for the 24 module design, indicating a laminar flow, even if the same amount of flow was directed through ten modules. Thus, the variation in the overall heat transfer coefficient was insignificant and assumed constant throughout during all simulations.

where ρ is the density, H_f is the latent heat of fusion (solid to liquid), and k is the thermal conductivity of the high-temperature (liquid) phase [21].

Erythritol was chosen due to its melting temperature and high heat of fusion though pure erythritol has the disadvantage of poor thermal conductivity (Table 1). A PCM consisting of erythritol impregnated with nickel was also simulated. This PCM was developed and tested by Oya et al. and retained the high heat of fusion of pure erythritol, while increasing its thermal conductivity by a factor of 16 [22]. An erythritol-copper composite was modeled using methods developed by Shamberger and Fisher to simulate the performance and material characteristics of low-k and high-k composite materials [23]. Indium was selected for modeling for its relatively high thermal conductivity during liquid phase and the ongoing interest in metallic PCMs. Due to indium's high melt temperature, a maximum junction temperature of 175 °C had to be considered for this case alone.

Once the PCMs were selected, the packages were modeled with various PCM placement. A single-sided package with phase change material was designed with the PCM in direct contact with the top surface (Fig. 5). Any potential electrical complications due to the introduction of metallic PCMs or PCM-metal composites were ignored for this study. Three different dual-sided packages were investigated with PCM incorporated into different layers of the package (Fig. 6). Multiple configurations of dual-sided packages were modeled to observe the effects of heat spreading on PCM effectiveness. Figure 6(a) shows the PCM inserted into the periphery of the package. Figure 6(b) shows the PCM embedded into the emitter and collector of the package, closest to the SiC die. Figure 6(c) shows the PCM embedded in the layer of DBC nearest to the SiC die.

The amount of each PCM that was incorporated into the single-sided package was determined from parametric simulations. Care must be taken when selecting the PCM thickness as there can yield negative returns (higher junction temperature) when considering low-k PCMs and diminishing returns in PCM thickness with higher-k composite PCMs (Fig. 7). Figure 7(a) shows the negative returns experienced by a package with 24 die and erythritol during the US06 drive cycle. Due to the low-k of erythritol, increasing the PCM thickness beyond the optimum 7 mm increases the maximum temperature experienced by the die as the lower conductivity of the liquid phase begins to have an insulative effect. Figure 7(b) shows the diminishing returns experienced by a package with 24 die and erythritol-copper composite during the US06 drive cycle. Even with a higher-k composite, increasing the thickness of the PCM shows diminishing returns due to the melt temperature and the transient nature of the heat load.

Simulations were run with all four PCMs on top of the single-sided package using their individual optimum thicknesses in packages containing 10, 12, 14, 16, 18, 20, and 24 die. Of the PCMs modeled the erythritol-copper composite allowed for the greatest reduction in the number of die in the single-sided package. Figure 8 shows the junction temperature in the single-sided packages with ten die for each PCM in the most aggressive drive cycle. The portion of the US06 drive cycle shown contains two of the highest power spikes of the cycle, which is consistent with the two highest die temperatures experienced in the cycle. All cases show a reduction in the maximum temperature experienced, but only the erythritol-copper composite was able to keep the peak temperature near 150 °C with ten die. Indium also performed well, but its higher transition temperature and lower enthalpy of melting were a disadvantage. Pure erythritol and erythritol–nickel had the highest enthalpy of melting, but the performance of both PCMs was hindered by their poor thermal conductivity. In all cases, the ΔT experienced in the package was also reduced, with the results varying as expected with the PCMs' FOM.

While the best results were shown with the erythritol-copper composite, the addition of PCM to the single-sided package improved its thermal performance in all cases. The single-sided package with no PCM required 24 SiC die to keep a maximum temperature of 150 °C during the drive cycle, which was assumed to be the maximum allowable junction temperature in this study (with the exception of the use of indium). With the addition of pure erythritol to the package, the maximum temperature was reduced to 147.9 °C, but 24 die were still required to achieve this temperature (Table 2). Peak temperatures could be reduced to 142 °C with 24 die and the erythritol–nickel composite. The temperature could also be kept below the target temperature while reducing the number of die to 22, and peak temperatures were comparable to the package with no PCM with 20 die. To utilize the thermal storage potential of indium, the maximum allowable junction temperature was assumed to be 175 °C due to the higher melting point of indium. The package required 18 die to keep the temperature below that point, while the addition of indium reduced to necessary number of die to 12.

In simulations of a dual-sided package model with 24 die, the addition of PCM was less effective at reducing peak temperatures and can increase the maximum temperatures experienced in the package in many configurations. For example, Fig. 9 shows the temperatures experienced in a dual-sided package with 24 die and erythritol-copper composite in different configurations during the portion of the US06 drive cycle with the highest average power (20 kW). The package temperatures never reach the transition temperature of the PCM, and as a result, the thermal storage potential of the PCM is not utilized. The addition of PCM to the periphery of the package (top right) has little to no effect on package thermal performance. Adding PCM into the emitter/collector (bottom left) provided additional thermal resistance to the respective package layer, limiting heat spreading and increasing the maximum temperature in the package by over 3 °C. Incorporating erythritol into the DBC (bottom right) showed a slight decrease in the maximum die temperature. This suggests that placing PCM directly in the thermal path, but far enough away from the die to allow for heat spreading is the most suitable placement. These results also suggest that care must be taken when adding PCM to a dual-sided package to ensure that the transition temperature is reached; otherwise, the thermal storage potential is not utilized, and the lower thermal conductivity can negatively impact the packages' thermal management properties.

Due to the advantage of dual-sided cooling, the dual-sided package without PCM was able to maintain a peak junction temperature of 150 °C during the drive cycle with only ten SiC die. PCM was incorporated into different layers of the dual-sided package models to test the effectiveness of the PCM in improving the packages' thermal management performance. The maximum temperature reached during the cycle occurs at 575 s. The addition of the composite PCM to the periphery of the package reduced the maximum temperature from 149.9 to 145.1 °C (Fig. 10). While successful, the indirect placement of the PCM in relation to the thermal path allowed less than 10% of the PCM to melt throughout the cycle. The composite was the most successful when placed directly in the thermal path. When placed in substrate layers of the package, either the emitter and collector or the top layer of DBC, the peak temperature was reduced to below 145 °C. PCM placed closest to the die, in the emitter and collector, reached nearly 70% melting and reduced the peak temperature to 144 °C. The peak temperature was further reduced to 143.1 °C with placement in the top layers of the DBC. While only 35% of the PCM melted in this location, the placement allowed for more heat spreading and less thermal resistance in the substrate layers closest to the die.

Other materials modeled showed different results according to where they were placed in the package. Figure 10 also shows the temperatures experienced by the die in a dual-sided PE package with erythritol placed in the same configurations. The addition of the lower-k erythritol to the periphery of the package reduced the maximum temperature at 575 s from 149.9 to 149.3 °C, but less than 25% of the PCM melted during the cycle due to the indirect placement relative to the thermal path. Placing erythritol directly in the thermal path had mixed results. The lower-k erythritol showed the ability to disrupt the thermal path when placed in layers closest to the SiC die, resulting in an increase in maximum temperature to 153.5 °C. The PCM melted completely during the cycle, but the lower-k of erythritol increased thermal resistance of the substrate layer. Placement in the DBC allowed for more heat spreading closer to the die and a reduction of peak temperature to 146.4 °C though only 25% of the PCM transitioned during the cycle. Again, care must be taken when incorporating PCM into the dual-sided package so as not to negatively impact its thermal performance.

While all PCMs chosen for this study showed the ability to reduce temperatures in the packages modeled, the erythritol-copper composite showed the best results and was used in further drive cycle simulations. The US06 is an aggressive drive cycle and was chosen to evaluate PCM performance under extreme conditions, with speeds reaching over 80 mph and rapid decelerations, creating transient power spikes of over 80 kW. Figure 11 shows the temperatures experienced in the single-sided package during the portion of US06 drive cycle with the greatest power spike (80.1 kW) and the highest sustained average power (20 kW). The top figure shows the package with 24 die and no PCM. The most significant temperature increase can be seen between 565 and 575 s, where the junction temperature jumps from 96 °C to 150 °C and creates a temperature difference between package layers of over 20 °C. These large temperature variations in the package create thermomechanical stress in substrate layers that can reduce both performance and reliability throughout its life. To mitigate these temperature fluctuations, an addition of 2.5 cm of erythritol-copper composite PCM was added to the single-sided package. Figure 11 (middle) shows that the maximum junction temperature is reduced to below 125 °C, and temperature variation throughout the package is significantly reduced. The PCM is effective at reducing both the transient temperature spikes as well as the temperature variation in the package, therefore likely reducing the thermomechanical stress in the package. In this case, the PCM temperature rarely goes above the melting temperature and acts mostly as a thermal mass, with less than 2% of the PCM undergoes phase change throughout the drive cycle. Though it does not impede the thermal pathway, the latent heat storage potential of the PCM is not being thoroughly utilized in this case.

To increase PCM utilization, the number of die was reduced to increase the amount of heat dissipated. The bottom of Fig. 11 shows the temperatures experienced in a single-sided package with ten die and the addition of 2.5 cm of erythritol-copper composite PCM. The maximum junction temperature of the die reaches 150 °C, but the number of die necessary to achieve this temperature was reduced by over 50%. For reference, the same package without PCM reached a peak junction temperature of 228 °C, with temperature fluctuations approaching 130 °C during the cycle. The latent heat storage is being fully utilized in this case as 100% of PCM melts earlier in the cycle. The transition back from liquid to solid can be seen near 500, 535, 545, and 565 s. The reduction of temperature variation in the package during these times is shown due to the temperature release during this transition. This reduction in temperature variation throughout substrate layers may increase the package lifespan due to the likely reduction of thermomechanical stress in the package.

In addition to the single-sided package, the impact of erythritol-copper composite was determined using the best performing configuration of a dual-sided package: in the DBC. Figure 12 shows the temperatures experienced in the dual-sided package with and without PCM during the same portion of US06 drive cycle. The top figure shows a package with ten die and no PCM. The most significant temperature increase can be seen between 565 and 575 s, where the junction temperature jumps from 98 °C to 150 °C and creates a temperature difference between package layers of over 25 °C. The bottom figure shows the same package with erythritol-copper placed in the DBC. The addition of the PCM is effective as increasing package thermal management performance, reducing the peak temperature by 6 °C. While PCM is effective at reducing the transient temperature spikes during the aggressive drive cycle, there is little effect on the temperature variation throughout the package due to its limited time at transition temperature, the small volume of PCM used, and its confinement to a single substrate layer.

The EPA Urban Dynamometer Driving Schedule is a less aggressive drive cycle and was used to simulate PCM performance during the stop and go conditions of city driving. Figure 13 shows the temperatures experienced in the single-sided package during the portion of the drive cycle with the highest average power (10 kW). Figure 13 (top) shows the package with 24 die and no PCM. The maximum temperature experienced by the SiC die is approximately 122 °C at 190 s. The largest temperature increase can be seen between 190 and 200 s, where the junction temperature increases by 20 °C and the temperature variation in the package increases to from 2 °C to 12 °C. Incorporation of a PCM mitigates these challenges. The middle figure shows the temperatures experienced in a single-sided package with 24 die and the addition of 2.5 cm of erythritol-copper composite PCM. The maximum junction temperature was reduced to approximately 110 °C, and temperature variations experienced in the package were reduced by 50% relative to the baseline case without PCM. The PCM is effective at reducing both the transient temperature spikes as well as the temperature variation in the package, therefore likely reducing the thermomechanical stress in the package. In this case, the PCM temperature never goes above the melting temperature and acts solely as a thermal mass. Again, it does not impede the thermal pathway but the latent heat storage potential of the PCM is not being utilized in this case.

To increase the amount of melting, a single-sided package with ten die and the addition of 2.5 cm of erythritol-copper composite PCM was simulated (Fig. 13, bottom). In this case, the maximum junction temperature of the die is increased to 127 °C, but the number of die necessary to achieve this temperature was reduced by over 50%. For comparison, the same package without PCM reached a peak junction temperature of 160 °C, with temperature fluctuations of 65 °C during the cycle. Due to the lower power levels and corresponding lower temperature in this drive cycle, the latent heat storage potential is only partially utilized as only 25% of PCM melts during the cycle. Under less extreme conditions, the PCM is still effective at smoothing the transient temperatures by also acting as a thermal mass. The addition of PCM allows for both a reduction of the cost of the package, as well as possible increase in the package lifespan due to the reduction of thermomechanical stress in the package.

Figure 14 shows the temperatures experienced in the dual-sided package with and without PCM during the same portion of urban drive cycle. While the PCM is also effective at reducing the transient temperature spikes during this less aggressive drive cycle, there is again little effect on the temperature variation throughout the package due to the addition of a lower-k material into the thermal path. For example, without PCM, the maximum temperature experienced by the SiC die is 122 °C at 190 s. The largest temperature increase can be seen between 190 and 200 s, where the junction temperature jumps by 17 °C and the temperature variation in the package increases to 10 °C. In contrast, Fig. 14 (bottom) shows the same package with erythritol-copper placed in the DBC. The addition of the PCM is effective at increasing the packages' thermal management performance, reducing the peak temperature by 3 °C. Unlike the single-sided package, there is little effect on the temperature variation throughout the package in this cycle. While the placement of the lower-k material does not impede the thermal path, the PCMs' distance from the die does not allow it to reach transition temperature due to the lower power levels and corresponding lower temperatures in this drive cycle.

To better understand the impact of the PCM over the entirety of the drive cycles, histograms were created to compare the SiCs' overall time at temperature in the package configurations of interest. Histograms of the SiC time at temperature highlight the composite PCMs' ability to reduce the temperature variability experienced by the die during the two drive cycles. Figure 15(a) shows that the single-sided package with 24 die and no PCM spends 90% of the time during the drive cycle between 95 and 145 °C, with peaks up to 150 °C. The same package with the addition of PCM spends 91% of the same drive cycle between 95 and 125 °C, and 75% between 105 and 115 °C, with junction temperatures never rising above 125 °C. Keeping the PCM and reducing the number of die to ten still keep the junction temperature within a 30 °C window for 91% of the drive cycle, but shifts this window to 115–145 °C, with a few peaks up to 150 °C. One of the most common causes of failure in SiC devices is the repeated temperature fluctuation leading to temperature-induced degradation [24]. These results suggest that PCM addition to single-sided PE packages may increase the overall durability as well as allow for a reduction in the number of die necessary to control peak junction temperature.

As shown in the Impact of Phase Change Material Selection and Placement section, dual-sided cooling improves the performance by reducing the thermal resistance from the junction to the cooling fluid. Improved performance allows the dual-sided package to spend the majority of the aggressive US06 drive cycle below the transition temperature of erythritol-copper, 117.7 °C (Figure 15(b)). This limited time above transition temperature, along with PCM placement constraints of the dual-sided package, reduces the PCMs' effectiveness at reducing temperature variations between package layers and fluctuations in junction temperature. However, PCM is still effective at reducing the maximum junction temperature during the US06 drive cycle. Figure 15(b) shows overall time at temperature of ten SiC die in a dual-sided package without PCM and with erythritol-copper in the DBC. The dual-sided package without PCM spends 98% of time during the US06 drive cycle between 95 and 155 °C. The dual-sided package with the addition of PCM spends 98% of time during the same cycle between 95 and 145 °C. Some SiC devices have been found to exhibit unstable behavior above 150 °C [25–27]. Incorporating PCM into a dual-sided package may provide a buffer to aid in the reduction of peak junction temperature and improve the packages' overall thermal performance.

A histogram of the SiC time at temperature during the urban drive cycle is shown in Fig. 16. Figure 16(a) shows that the single-sided package with 24 die and no PCM spends 96% of the time during the less aggressive drive cycle between 95 and 125 °C, with peaks up to 125 °C. The same package with the addition of PCM spends 93% of the same drive cycle between 95 and 115 °C, and 75% between 95 and 105 °C, with junction temperatures never rising above 115 °C. Keeping the PCM and reducing the number of die to ten keep the junction temperature within 30 °C for 90% of the drive cycle, keeping the main temperature window from 95 to 125 °C, similar to the package with 24 die and no PCM with the exception of a few transient spikes over 125 °C. Again, the addition of PCM created a more even junction temperature distribution over the course of the drive cycle, reducing the transient spikes that can contribute to temperature-induced degradation of the device.

Figure 16(b) shows overall time at temperature of ten SiC die in a dual-sided package without PCM and with erythritol-copper in the DBC. Improved performance allows the die in the dual-sided package to spend the majority of the urban drive cycle below the transition temperature of erythritol-copper, 117.7 °C. The PCM's distance from the die due to packaging constraints does not allow it to reach transition temperature, reducing the PCMs' effectiveness at reducing temperature variations between package layers and fluctuations in junction temperature. However, PCM is again effective at reducing the maximum junction temperature during the urban drive cycle, reducing the amount of time the die spends above 115 °C by 41%.

As shown above, using the same number of SiC die in a single-sided package and adding PCM may reduce temperature fluctuations throughout the package during operation, potentially extending its operational life through the reduction of thermal fatigue. The addition of PCM could also be used to reduce the number of die in the package. Considering only raw materials, the SiC die are the most expensive portion of the package, and their reduction would serve to reduce the total material cost (Table 3) [28–30]. Due to the rapid transition from silicon-based power devices to SiC, both the cost and supply of SiC devices are extremely volatile, and demand is growing faster than supply [31].

Incorporating PCM into PE packaging may help mitigate these challenges. Table 4 was created to compare thermal performance, estimated material cost, and size of the packages modeled, using data from the US06 simulations, package geometry, material properties, and material costs from Table 3. The addition of PCM to a single-sided package with 24 die reduced the maximum junction temperature by 26 °C, while adding less than 20% to the volume and less than $1 to material costs. The addition of PCM into a single-sided package alternatively allowed for the reduction of die from 24 to 10, lowered the material cost of the package from $1368 to $570, reducing the package volume by almost 60%, and only slightly increasing the maximum junction temperature. All prices assumed the maximum cost for erythritol at $42 per kilogram and an average cost of $57 per SiC die. While the addition of PCM to the single-sided package offered significant improvements in the packages' overall thermal management performance, incorporating PCM into a dual-sided package showed mixed results. Adding PCM into a dual-sided package with 24 die had negative effects on package thermal performance, due to the low temperature experienced in the package and the addition of a lower-k material into the thermal path. When the number of die was reduced to ten, a dual-sided package had similar thermal performance when compared to a single-sided package with PCM. Incorporating PCM into a dual-sided package with ten die reduced the peak junction temperature during the drive cycle but was less effective at reducing temperature variation in package layers due to placement constraints and lower overall temperatures. The material cost of the dual-sided package is also comparable to the single-sided with the same number of die due to the small size of the packages and the fact that the SiC devices are the cost driving factor with respect to materials.

The dual-sided package may be superior in terms of thermal performance, but it has yet to be universally adopted due to a lack of understanding of its thermomechanical lifetime and the high cost of manufacturing [32,33]. Incorporating PCM into a single-sided package may be a viable alternative to improving PE reliability and thermal performance without incurring the high cost of manufacturing dual-sided packages. To better compare the performance of these two packaging approaches, Fig. 17 shows the temperature profile of a single-sided package with PCM (top) and a dual-sided package without PCM (bottom), both with ten die during the same portion of the US06 drive cycle. The junction temperature profile peaks are similar but appear more level in the single-sided package, especially between 500 and 560 s, suggesting that the PCM is effective at smoothing the transient junction temperature. The latent heat storage of the PCM also smooths the low-temperature valleys as shown at 490–505 s and 560–570 s, suggesting an overall reduction in temperature variation throughout the cycle and decreased temperature variation in the layers of the package. These reductions in the temperature fluctuation could create more temperature consistency between package layers and improve both the reliability and durability of the device.

The effectiveness of PCM in improving a PE packages' thermal performance was evaluated. The addition of PCM to a single-sided package was shown to reduce the peak junction temperature experienced by the SiC die, as well as reduce the overall temperature fluctuations throughout the package during both the US06 and urban drive cycles. The addition of PCM to a single-sided package with 24 die reduced the maximum junction temperature by 26 °C, adding less than 20% to the package volume. The addition of PCM into a single-sided package alternatively allowed for the reduction in the number of die necessary to maintain a peak junction temperature at approximately 150 °C from 24 to 10. This reduction is the number of SiC die resulted in a 58% reduction in the material cost of the package and a similar reduction in volume. A dual-sided package without PCM was also able to maintain a peak temperature below 150 °C, but experienced greater temperature fluctuations in the package throughout both cycles when compared to the single-sided package with PCM. The addition of PCM into the dual-sided package served to suppress the peak junction temperature by 6 °C was not as successful in reducing the fluctuations when compared to the single-sided package. While the latent heat storage of the PCM successfully absorbs heat in the package, the placement constraints of the dual-sided package, along with lower overall temperatures in the cycle, reduced the PCMs' effectiveness.

The authors would like to thank Dr. Mike Fish at the U.S. Army Research Lab in Adelphi for answering questions about the functionality of parapower.

• U.S. Army Adelphi Laboratory Center (ARL) (Contract No. W911NF1920252; Funder ID: 10.13039/100006754).

a =

acceleration (m s⁻²)

A =

area (m²)

c_D =

coefficient of drag resistance

c_R =

coefficient of rolling resistance

D_h =

hydraulic diameter (m)

f =

friction factor

F =

force (N)

FOM =

figure of merit (kJ m⁻⁴ s K)

g =

gravity (m s⁻²)

h =

heat transfer coefficient (W m⁻² K⁻¹)

H_f =

latent heat of fusion (kJ kg⁻¹)

k_l =

liquid thermal conductivity (W m⁻¹ K⁻¹)

m =

mass (kg)

Nu =

Nusselt number

P =

power (W)

Pr =

Prandtl number

Re =

Reynolds number

T_m =

melt temperature (°C)

u =

flow speed (m s⁻¹)

U =

overall heat transfer coefficient

V =

velocity (m s⁻¹)

Greek Symbols

η =

efficiency

μ =

dynamic viscosity (kg m⁻¹ s⁻¹)

ρ =

density (kg m⁻³)

Subscripts

b =

fin prime surface

o =

overall

t =

total fin surface