Numerical modeling and experimental validation of a phase change material-based compact cascade cooling system for enhanced thermal management

Applied Thermal Engineering 164 (2020) 114470

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Numerical modeling and experimental validation of a phase change material-based compact cascade cooling system for enhanced thermal management ⁎

Su-Ho Kima,b, Chang Sung Heub, Dong Rip Kimb, , Seok-Won Kangc,

T

⁎

a

Korea Railroad Research Institute, 176 Cheoldo bangmulgwan-ro, Uiwang, Gyeonggi-do 16105, Republic of Korea School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea c Department of Automotive Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea b

H I GH L IG H T S

multi-stage PCM structure facilitates cooling via hierarchical heat exchange. • The peak temperature was decreased because of the larger heat capacity and energy circulation. • The cooling performance was observed in continuous heating–cooling cycles. • Improved PCM nanocomposite can reduce the heat accumulation due to successive thermal loads. • The • The cascade structure allows instantaneous heat absorption of short-term energy output spikes.

A R T I C LE I N FO

A B S T R A C T

Keywords: Cascade cooling Heat transfer Heat sink PCM (Phase Change Material) Thermocouples

The thermal performance of phase change material (PCM)-based compact cascade cooling systems with an integrated heat sink was experimentally evaluated using heat-transfer measurements under constant heat flux. Numerical calculations were also performed to investigate the fundamental mechanism of the cascade cooling approach using multiple PCMs (i.e., paraffin wax) with different melting points. This structure facilitated cooling via hierarchical heat exchange without additional energy consumption. The experimental results of the cascade cooling system demonstrated that the peak temperature within a fin decreased from 123.4 to 107.2 °C in one heat-supply cycle owing to the latent heat adsorption during a phase change in the PCMs. Particularly, the cascade cooling system reduced the peak temperature by approximately 13.1% compared with natural convection in air. In addition, the time taken to reach the maximum allowed temperature from the peak temperature was decreased by 45.0% because of the larger heat capacity and cascading heat exchange of PCMs. This implies that the lifetime of a system can be increased and failure can be prevented. Improved thermal performance was demonstrated after repetitive heating–cooling cycles. Furthermore, it was numerically demonstrated that a PCM nanocomposite can reduce the heat accumulation because of the low thermal conductivities of PCMs.

1. Introduction Highly integrated, high performance electronic devices demanding more energy must be stable to ensure uniform operating temperature in the system. Devices such as MOSFETs and IGBTs dissipate more heat than conventional devices, and the system can fail if they are not cooled properly. In the case of semiconductors, when the temperature exceeds 85 °C, thermal fatigue rapidly increases, and the life expectancy of devices is remarkably reduced [1,2]. When the operating temperature of devices exceeds their maximum allowed temperature, the ⁎

environmental conditions should be controlled quickly to lower the peak temperature to prevent system failure. Various cooling strategies (such as liquid, air, or phase change cooling) can be used to prevent system failure caused by excessive thermal loads. The type of cooling fluid (e.g., air, water, or oil) used for each method is determined by the degree of thermal load [3]. However, they require additional equipment (e.g., a fan or pump) to remove the heat and consume additional energy to circulate fluids. In addition, these additional devices make it difficult to optimize the limited space utilization. Therefore, a new cooling approach must be developed for enhanced cooling efficiency by

Corresponding authors. E-mail addresses: [email protected] (D.R. Kim), [email protected] (S.-W. Kang).

https://doi.org/10.1016/j.applthermaleng.2019.114470 Received 20 February 2019; Received in revised form 26 September 2019; Accepted 29 September 2019 Available online 30 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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ω ∇ ∙

Nomenclature Symbols g k keff kl ks t → v F H K P S T Tl Ts U α γ μ ρ τ

gravitational acceleration (m/s2) thermal conductivity (W/(m·K)) effective thermal conductivity of liquid-solid mixed-phase PCM (W/(m·K)) thermal conductivity of liquid phase PCM (W/(m·K)) thermal conductivity of solid phase PCM (W/(m·K)) time (s) 3D velocity field (m/s) external body forces (N) enthalpy (J/kg) thermal conductivity of PCM (W/(m·K)) static pressure (N/m2) volumetric heat source term (W) temperature (K) liquidus temperature of PCM (K) solidus temperature of PCM (K) velocity (m/s) thermal diffusivity (m2/s) PCM volume fraction dynamic viscosity (Pa·s) density (kg/m3) stress tensor (N/m2)

measurement uncertainty spatial gradient (vector) operator vector dot product

Abbreviations DAQ HS P P1-1 P1-2 P1-3 P1-4 P2 PCM S1 S2 S3 TIM

data acquisition heat source phase change material (paraffin) temperature sensing point at the lower position of PCMl temperature sensing point at the middle position of PCMl temperature sensing point at the upper position of PCMl temperature sensing point at the interface of PCMu temperature sensing point at the middle position of PCMu phase change material temperature sensing point at the lower position of the fin temperature sensing point at the middle position of the fin temperature sensing point at the upper position of the fin thermal interface material

Subscripts l m s u

lower multi-stage single upper

vehicles. Here, we propose a PCM-based cascade system for effective cooling performance in a more compact manner. First, a comparative study between a single PCM and multi-stage PCMs was experimentally and numerically performed to confirm the thermal energy circulation between PCMs with different melting points. Paraffin waxes were selected as the PCMs used in this study, because they are chemically stable and have tunable temperature ranges for the phase change by changing the carbon content. Second, a parametric study on the use of a multi-stage configuration and the system performance under successive heating/ cooling cycles was conducted. Finally, the effect of a PCM nanocomposite (e.g., a mixture of paraffin wax and carbon nanotubes) on the thermal conductivity and heat transfer inside the heat sink was numerically analyzed to increase the applicability of our PCM-based cascade cooling systems.

reducing energy consumption and space optimization, through removal of the auxiliary devices. Recently, investigations of the cooling approach using phase change materials have been conducted to overcome the limit of the cooling system based on the circulation of the cooling media [4–7]. In particular, because a large amount of thermal energy is released into the air during the charge/discharge processes of an electric vehicle, a cooling system using a PCM was proposed to reduce the maximum thermal load and prevent a local temperature increase in the battery pack [8–13]. There was also a case study of a PCM-based cooling system for thermally stable operation in the transient state of the electric motor. A PCM with high thermal storability was used to maintain a low operating temperature in a harsh environment, such as in an environment where heat accumulates in an engine room due to insufficient outside air circulation [14–17]. Small electronic devices require higher cooling performance than large devices, and a hot spot due to excessive local heat can occasionally cause a critical problem during normal operation. Several researchers have explored the application of PCMs to enhance thermal performance by means of latent heat adsorption by the PCM [18–23]. In particular, the PCM was used to increase the thermal stability of high-power semiconductor devices [24]. These examples illustrate the possibility that a PCM can be used to enhance the thermal performance of electronic devices and replace existing passive cooling methods. In addition, other investigations [25–30] on the combination between passive cooling devices and PCMs show that the PCM can be used to optimize the cooling performance by integrating the PCM system with a heat sink. Recently, various studies to improve the thermal properties of PCMs have been conducted by means of synthesis with nano-materials [31–33]. In previous investigations, the multi-stage design was proposed to increase the heat capacity for thermal energy storage. The different PCMs connected in series were installed along the flow path of the heat transfer fluid, and the optimization of their configuration design was the main goal of these studies [34–37]. However, compact multi-stage PCM cooling systems without physical circulation of cooling media such as air or water among the PCMs need to be developed for wide applications, such as power electronics or electric motors in electric

2. PCM-based cascade cooling system The combination of a heat sink and PCMs facilitates cooling, as a large amount of latent heat is adsorbed by the PCMs during a phase change near their melting points. Fig. 1(a) shows the fundamental mechanism of heat removal in a PCM-based cascade cooling system. When the electric/electronic devices are subjected to thermal loads during their operation, the PCM in direct contact with a fin array (i.e., PCMl, where subscript l indicates lower) starts adsorbing heat from the heat source. Once the temperature of PCMl increases up to its melting point, the phase of the PCMl changes from solid to liquid by absorption of latent heat. In general, the fin array can be efficiently cooled by the PCMs rather than an air in the absence of forced convection, because the heat capacity of PCMs is larger than the value in air (e.g., paraffin: 2.9 kJ/(kg·K) [38]; air: 1.0 kJ/(kg·K)), in addition to the absorption of latent heat during the phase change. To continuously remove heat, after PCMl is completely changed to a liquid, thermal energy in the heated PCMl should be transferred elsewhere. In the case of a single layer system shown in Fig. 1(b), the heat adsorbed by the PCMl is released into the atmosphere. However, a multi-stage structure consisting of multiple PCMs with different melting points facilitates transport of 2

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melting point of PCMu is lower than the value of PCMl. Thus, this approach can promote the release of thermal energy away from a device without the circulation of cooling media. In contrast, the existing active cooling systems require physical circulation of a refrigerant. Thus, the energy consumed during system operation can be reduced considerably, and efficiency in design optimization can be improved. 3. Numerical modeling 3.1. Numerical method A numerical investigation was performed to verify and understand the fundamental heat transport mechanism in a PCM-based cascade cooling system. In particular, a thermal energy transport phenomenon based on convective and conductive heat transfer was analyzed by comparing single and multi-stage PCMs. In the numerical analysis, the heat flux value supplied by a heat source was calculated by assuming the efficiency of a cartridge heater was 0.9 [39]. The convective heat transfer coefficient in air at an outer surface of the heat sink was set to 5.0 W/m2·K, which is the smallest value of generally given heat transfer coefficients in natural convection (i.e., 5.0–50.0 W/m2·K) to exclude the effects of external airflow [40]. This is because it was assumed that heat loss can be minimized by installing the system in a polycarbonate environmental chamber. The size of the chamber was determined by calculation of the thermal boundary layer thickness of natural convection in air over heated-fin surface. The software Fluent v14.0 was used for this numerical study [41], and the user-defined function (UDF) code was utilized to model the temperature dependent thermo-physical properties of the simulated (e.g., aluminum and copper). All of the approximately 5.6 million grids were used in the 3D numerical model corresponding to the experimental configuration, and 13 grid lines were applied for the thin-finned region, as shown in Fig. 2(a). The temperature difference depending on the grid size exhibited a small change (less than 2.7 °C). The initial conditions were 25.0 °C for temperature and 1 atm for pressure. In addition, the boundary condition for the outer surface of the heatsinks, except for contact with PCMs, was defined as the natural convective heat transfer in air. For PCMs, the solidification and melting model was used to define the phase change process, and the heat transfer process including the liquid phase was

Fig. 1. Schematic illustration of a PCM-based cascade cooling system: schematic illustration of thermal energy transport (a) between multi-stage PCMs and (b) through single-stage PCM.

thermal energy from PCMl to the next-stage PCM (i.e., PCMu, where subscript u indicates upper). Because the total amount of heat absorbed by multiple PCMs is absolutely larger than that from a single PCM, the temperature rise in PCMl is attenuated and its maximum temperature is sustained at a lower level than the single layer system. Accordingly, PCM-based cooling systems (e.g., single or multi-stage types) provide immediate heat transport in the form of short-term spikes, which results in better cooling performance than natural convection in air. Furthermore, the cascade structure comprising PCMs with different melting points was dedicated to energy circulation due to a complementary relationship between the PCMs. In particular, the use of a fin array between the heat source and PCMl and a reverse fin array made of copper between PCMl and PCMu facilitates more efficient heat transport inside the heat sink, as shown in Fig. 1(a). The phase change of PCMu inhibits the temperature rise induced by heat transport from PCMl through the reverse fin array because the

Fig. 2. (a) Numerical modeling of the heatsinks for PCMs-based cooling system and (b) electrical circuit modeling for calculation of thermal contact resistance. 3

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modeled based on assumptions for incompressible and laminar flows. The numerical analysis was performed with a transient state simulation technique and 60 s time steps. The time step and number of grids were defined based on a grid dependency test and parametric analysis. The second-order upwind scheme was used for solving the energy and momentum equations, and the least-squares cell-based and PRESTO interpolation methods were selected for gradients and face pressure calculations. Convergence criteria of 10−3 and 10−6 were defined for the continuity/momentum and energy equations, respectively. The fundamental governing equations such as the continuity, momentum, and energy equations [41] for the numerical investigation for this study are as follows:

→ ∂ρ + ∇ ·(ρU ) = 0 ∂t

(1)

→→ → ∂ → → + ∇ ·→ (ρU ) + ∇ ·(ρU U ) = −∇ ·P + ρg τ +F ∂t

(2)

→ ∂ (ρH ) + ∇ ·(ρU H ) = ∇ ·(K ∇T ) + S ∂t

(3)

4. Experimental details 4.1. Experimental setup Fig. 3(a) shows the experimental apparatus used to demonstrate enhanced cooling performance provided by the PCM-based cascade cooling system, and to validate the numerical simulation results. The size of the entire experimental setup was approximately 215.0 × 150.0 × 189.9 mm3 (L × H × D). This apparatus was placed in an environmental chamber made from polycarbonate (10-mm thickness) for thermal insulation. In addition, to minimize heat loss due to thermal resistance resulting from an air gap between two different metal blocks and heat flow in the direction opposite the heat sinks, thermal grease (YG6111, YearMoly) with a thermal conductivity of 0.84 W/(m·K) was applied to all mechanical components; it was finally placed on the ceramic fiber (1100Felt, KCC) with thermal conductivity of 0.049 W/m-K. A rod-type cartridge heater with an electrical resistance of 34.0 Ω was used as the heat source, and 146.0 W of electrical power was applied with a power supply (EX300-8, ODA Technologies). As shown in Fig. 3(a) and (b), four thermocouples (type T) were installed along the longitudinal direction of the fin array for measuring temperature changes resulting from conductive heat transport through metals. Similarly, five thermocouples (type T) were placed in parallel with four thermocouples to monitor temperature variations resulting from convective heat transfer between PCMs and the fin array, as well as conductive heat transport in the reverse fin array, which was designed to promote heat circulation between PCMs. Temperature values at different positions within the fins and PCMs were measured with a DAQ system (cDAQ-9174, National Instruments) in real time. The experimental results were later compared with numerical simulation results obtained from the same position and under the same operating conditions. Fig. 3(c) shows the experimental apparatus covered with a visible window and filled with two PCMs with different melting points (summarized in Table 1). This apparatus is placed inside the transparent thermal insulation chamber made from 10 mm polycarbonate sheets.

In general, it has been known that the thermal contact resistance (TCR) between metals and PCMs has a small effect on the thermal performance of PCM-based heatsinks [42]. Thus, it was assumed that TCR between the metals (i.e., fins) and PCMs was not significant in this study, compared with the value between the metal blocks. Accordingly, the TCR at the interface between mechanically bonded metals (i.e., aluminum) of the heatsinks was only considered to enhance the accuracy of the numerical model. In this study, the effect of TCR can be correspondingly achieved by considering an equivalent air gap thickness. Fig. 2(b) shows a schematic concept for determination of the air gap thickness based on the electrical analogy of heat conduction between metals. Eqs. (4) and (5), used here to calculate the air gap thickness, are derived from heat transfer resistance modeling [43].

Q=

ΔT T1 − T2 T − T2 = = 3 R R1 + Rgap + R2 R3

(4)

R=

Δx A×k

(5)

4.2. Experimental procedure To evaluate the effect of multi-stage PCMs on heat transport and temperature reduction quantitatively, the cooling performance (e ) and efficiency (ε ) were defined in Eqs. (8) and (9). The cooling efficiency is the ratio of the maximum temperature reduction by convective heat transport and phase change in the PCMs to the maximum temperature reduction due to convective heat transport in air. The cooling performance refers to the difference in the time required for the peak temperature to change to the target temperature (i.e., allowed maximum temperature of, e.g., 85.0 °C) for natural convection in air and convective heat transfer with phase changes in the PCMs. For both single and multi-stages PCMs, the temperature data used to analyze e and ε were obtained from the thermocouples located at the position closest to

3.2. Thermo-physical properties In this study, we utilized C20–C33 and paraffin C16–C28 (Daejung chemicals and metals co.) as PCMl and PCMu, respectively. The thermophysical properties of PCMl [38] and PCMu [44] are summarized in Table 1. Temperature dependent density, thermal conductivity, and viscosity were used in the numerical model. The thermal conductivity of PCMs was determined depending on the phase of materials (i.e., liquid or solid phases), and the effective thermal conductivity in the transient state of the solid-liquid mixture was calculated using the mixture rule:

α=

T − Tsolidus Tliquidus − Tsolidus

kb = αksolid + (1 − α ) kliquid

Table 1 Thermo-physical properties of PCMs used in this study.

(6) (7)

Table 2 lists the thermo-physical properties of metals used to model cascade cooling heat sinks, such as aluminum [45] (e.g., heating block integrated with a cartridge heater and a fin array in contact with the 1st stage PCM) and copper [45] (reverse fin array connected with the 2nd stage PCM). Heat transport mainly occurred via conduction and convection in metals and PCMs, respectively. The temperature dependent thermo-physical properties listed in Table 2 were also used for metals to improve the accuracy and reliability of the simulation results.

PCMl

PCMu

Density (kg/m3)

800 0.001(T − 319.15) + 1

750 0.001(T − 319.15) + 1

Specific Heat (J/(kg·K)) Conductivity (W/(m·K))

2890 0.21 if T < Ts 0.12 if T > Tl

2890 0.21 if T < Ts 0.12 if T > Tl

Viscosity (Ns/m2) Latent Heat (J/kg) Solidifying Temperature (K) Melting Temperature (K)

4

(

0.001 exp −4.25 +

1, 700 T

)

(

0.001 exp −4.25 +

173,400 326.15

173,400 319.15

330.15

321.15

1, 700 T

)

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Table 2 Thermo-physical properties of metals used in this study. Al 3

Table 3 Measurement uncertainties in the experimental parameters. Cu

Parameters

Accuracy and Uncertainty

Temperatures of T-type thermocouples Thermal conductivity of TIM Electrical power of cartridge heater Temperatures monitored by DAQ

± 0.15 °C ± 0.2% ± 2% ± 0.02 °C

Density (kg/m )

(a − b (T − Tm)) × 103

(a − b (T − Tm)) × 103

Specific Heat (J/(kg·K))

4.94 + (2.96 × 10−3) T 211 2.378

5.41 + (1.4 × 10−3) T 330 8.033

3.111 × 10−4 933.5

7.953 × 10−4 1356

Conductivity (W/(m·K)) a b

Tm (K)

interface material (TIM) has uncertainties of ± 0.02% and ± 0.2%, respectively. the heat source (i.e., HS in Fig. 3b).

tpcm ⎞ e = ⎛1 − × 100 tair ⎠ ⎝ ⎜

(8)

5.1. Experimental validation

Tpcm ⎞

ε = ⎛1 − × 100 Tair ⎠ ⎝ ⎜

5. Results and discussion

⎟

⎟

The appropriateness of the numerical models was validated against the experimental temperature values at specific positions without PCMs (i.e., HS, S1, S2, and S3) and the heating time (i.e., 8 h). The steady and transient state simulation results and temperature values measured at each position are shown in Fig. 4. The convective heat transfer coefficient depends on the surface temperature values or geometrical characteristics. However, because the convective heat transfer coefficient in the numerical model was assumed to be constant (i.e., 5.0 W/(m2·K)), the calculated temperature differences were compared with the experimental measurements. In addition, the calculated air gap thickness

(9)

4.3. Measurement uncertainty The measurement uncertainties of each parameter are summarized in Table 3. The temperature measurement uncertainties for the T-type thermocouples and the data acquisition system are ± 0.15 °C and ± 0.02 °C, respectively. In addition, the electrical power supplied by the rod-type cartridge heater and the thermal conductivity of the thermal

Fig. 3. Experimental setup: (a) schematic illustration, (b) installed positions of thermocouples (T-type), and (c) experimental apparatus. 5

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bottom of the fin in the case of multi-stage PCMs, compared with the natural convection in air. The fin array attached to the heat sink and the reverse fin for heat conduction from PCMl to PCMu were designed to promote heat transfer by their increased surface area and by compensating for the low thermal conductivity of PCMs. It is crucial to balance the large heat capacity of PCMs and the high thermal conductivity of the metal fin array for optimized cooling performance, which depends on the absolute magnitude of thermal loads and their operational characteristics. Fig. 6 shows the numerical temperature variations as a function of time for single PCM and multi-stage PCMs during one heating and cooling cycle. Unlike the case of a single PCM, both the maximum temperature and the time required to reach the maximum value decreased in the multi-stage PCMs, which resulted from the larger heat capacity provided by the hierarchical use of PCMs with different melting points, as well as enhanced heat transfer promoted by using the reverse fin between the PCMs, as shown in Fig. 1(b). Fig. 7 shows a comparison of the cooling performance obtained from the all the cooling strategies considered in this study, including natural convection, single PCM, and multi-stage PCMs. During a constant heat flux of 146.0 W for 2 h, the peak temperature observed at the fin for natural convection and multi-stage PCMs was approximately 123.4 and 107.2 °C, respectively. Accordingly, it was concluded that the cooling performance and efficiency calculated from the results shown in Fig. 7(a) improved by approximately 45.0% and 13.1%, respectively. One would commonly expect that the larger heat capacity of the PCM compared to air prevents a temperature increase. Fig. 7(b) shows the experimental temperature variations as a function of time at different measurement points for the case of multi-stage PCMs. In particular, it

Fig. 4. Comparison of numerical and experimental temperature data at each position of the T-type thermocouples: (a) steady-state and (b) transient conditions.

for thermal contact resistance between the heat source and fins was approximately 90.6 μm, using Eqs. (4) and (5). In particular, the temperature gradient between S1 and S2 is more negative in the experiments, which results from the different convective heat transfer coefficients depending at different locations, as well as the thermal contact resistance between blocks comprising the heat sink. Nevertheless, when a constant heat flux of 146.0 W is supplied by the cartridge heater for 2 h, the differences were 13.6 °C on average, and the numerical simulation results reflected the experimental temperature variations. Thus, one can conclude that the differences were considered to have no significant influence. After validation against the numerical model, numerical investigations into the enhanced thermal performance with the use of PCMs were performed for single PCM and multi-stage PCM systems. From the results, the enhanced cooling performance and efficiency provided by a single PCM was found to be 18.5% and 9.0% for constant heat flux of 146.0 W compared to natural convection in air, respectively. In addition, more enhanced performance and efficiency (i.e., 30.8% and 15.6%) were observed from the multi-stage PCMs results due to the larger heat capacity and cascading heat exchange. 5.2. Comparative studies of single and multi-stage PCM Fig. 5(a) and (b) present the temperature distribution observed by the infrared camera (Ti40, Fluke) in the experiment under the multistage PCM configuration, which was obtained in the measurement without a polycarbonate chamber for thermal insulation. It was observed that the temperature decreased by approximately 9.0 °C at the

Fig. 5. Captured images of temperature distribution observed by an infrared camera: (a) natural convection in air and (b) multi-stage PCMs. 6

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Fig. 6. Comparison of temperatures used to compare the cooling performance of (a) a single PCM and (b) multi-stage PCMs.

was demonstrated that the temperature increase over time was temporarily suspended due to absorption of latent heat during the phase change from solid to liquid at each melting point in the two PCMs. For example, the temperature increase at the sensing points of P1-1, P1-2 and P1-3 was suspended during approximately 80 and 115 min for single PCM and multi-stage PCMs systems, respectively. Fig. 7(c) shows the comparison of the phase changing time between single PCM and multistage PCM configurations. The longer phase changing time of 16 min on average was observed in the multi-stage PCM case due to the additional thermal energy absorption by PCMu. Thus, it was confirmed that the temperature increase was delayed, and the peak temperature was attenuated compared to natural convective heat transport in air. In addition, the temperatures of the sensors near the heat source (i.e., P1-1) were initially higher than the temperatures of the sensors at the upper position (i.e., P1-3). However, this trend is reversed after a phase change occurs in PCMl due to thermal energy absorption during the phase change and conductive heat transfer from the fin array. Because thermal energy is supplied more rapidly from the fin array than via convective heat transfer in the liquid PCM, conductive heat transfer from the fin is a greater determinant of temperature increase. In addition, movement of the liquid and solid PCM mixture was not observed in this experiment, which is attributed to the fact that conductive heat transfer was dominated over the convective heat transfer. The position of sensors P1-4 were near PCMu, and the temperatures of sensors P1-4 were lower than the other sensors installed inside PCMl. Because the melting point of the PCMu is lower than that of PCMl, thus that the phase of PCMu can change before

Fig. 7. Temperature variations used to analyze the cooling performance, cooling efficiency, and comparison of phase changing time between the single PCM and the multi-stage PCMs: (a) comparison of experimental measurements and numerical predictions during one heating–cooling cycle, (b) comparison of temperatures at different positions with multi-stage PCMs obtained from experimental results, and (c) phase changing time at different positions obtained from numerical results.

the phase of PCMu changes, PCMl can adsorb heat near P1-4 at that time. The heat supply stopped after 2 h and the experimental apparatus was allowed to cool. It was then observed that the temperature decrease in both a single PCM and the multi-stage PCMs were slower than in the case of natural convection in air. Although the peak temperatures in the 7

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Fig. 8 shows the cooling performance during two successive heating and cooling cycles for multi-stage PCM cascade system. It was experimentally observed that heat was accumulated in both cases when using the PCM, but the cooling performance provided by the PCM was still superior to natural convection in air. From the experimental measurements, the peak temperatures with natural convection and the multistage PCMs were 137.4 and 129.4 °C, respectively, which occurred after 2 h of heating by a cartridge heater in the second cycle. During the two successive heating and cooling cycles, the peak temperature differences reduced slightly from 16.3 to 8.0 °C, and the time differences required to recover to the target operating temperature (i.e., 85.0 °C) also decreased from 27 to 13 min. We found that the degraded cooling performance and efficiency resulted from heat accumulation due to the low thermal conductivity of the PCMs. Fig. 9 shows the temperature variations of all cases in this study during continuous heating with constant flux, which was intended to explore the heat transfer characteristics in harsh thermal environments. During the early stages of heat supply up to 2 h, the rate of temperature increase become slow in the case of the multi-stage PCMs due to adsorption of latent heat by the PCMs. However, the peak temperatures in the case of natural convection in air were lower than the multi-stage PCMs for approximately 4 h after heating. This is because hot PCMs tend to retain heat due to their very low thermal conductivity (i.e., 0.21 W/(m·K)). One solution to overcome heat retention due to the low thermal conductivity is to use a composite formed with high thermal conductivity materials. However, ensuring homogeneity of thermal properties and reliability for longterm use is an additional research topic. Therefore, an additional numerical study was performed by fabricating a composite from the PCM (i.e., paraffin) and a nanomaterial (i.e., PCNT: Carbon nanotube grafted with a polyalcohol), and the thermal conductivity of PCNT/paraffin was approximately 0.79 W/(m·K) [46]. Fig. 10 shows calculated temperature variations under continuous heat flux. The peak temperature in the case of PCNT/paraffin composite was remarkably reduced to 169.8 °C, compared to the case of natural convection in air (e.g., 180.0 °C), and the use of a PCM alone (e.g., 175.5 °C). Calculation of the ratio of temperature reduction by PCNT/paraffin (i.e., 10.2 °C) represents a 55.9% enhancement in thermal performance over multistage PCMs (i.e., 4.5 °C), which indicates the enhanced technological feasibility of the PCM-based cascade cooling strategy proposed in this study.

Fig. 8. Temperature values obtained from experimental measurements and numerical analysis at two repetitive heating and cooling cycles for different cooling approaches.

Fig. 9. Temperature values of experimental measurements and numerical analysis under continuous heat flux for different cooling approaches.

6. Summary and conclusion The thermal performance of a PCM-based cascade cooling system was numerically and experimentally evaluated based on heat transfer analysis under a constant heat flux. In particular, the numerical model was validated against experimental measurements using a heat sink integrated with cascade cooling materials. In one heating and cooling cycle, it was observed that the peak temperature in a single PCM with a fin decreased from 123.4 to 107.2 °C compared to natural convection in air, which resulted from latent heat adsorption during the phase change of the PCM. The multi-stage PCM shows more uniform and rapid heat transfer characteristics due to hierarchical heat circulation between the cascaded PCMs with different melting points. The cooling efficiency and performance was enhanced by 13.1% and 45.0%, respectively. In addition, a reduced enhancement was observed in PCMs with low thermal conductivity during successive heating–cooling cycles. However, it was numerically demonstrated that this can be overcome by composite synthesis of PCMs with high thermal conductivity nanomaterials such as CNTs. The PCM-based cascade cooling technology facilitates cooling through heat circulation without the additional energy required to circulate cooling fluids. Thus, this approach presents the possibility of designing space-optimized heatsinks. On the other hand, further investigations are required to simultaneously consider optimization in terms of space and weight. Ultimately, it is expected that this approach will enable instantaneous heat absorption of short-

Fig. 10. Comparison of temperature variations between bare paraffin and paraffin/CNT composite under continuous heat flux.

case of a single PCM and multi-stage PCMs was lower than one in the case of natural convection in air, the temperature profiles crossed each other, as shown in Fig. 7(a). One can conclude that this phenomenon resulted from the thermal energy released during solidification of the PCM. This will be not a factor to directly cause any malfunction or operation failure because the temperatures are definitely lower than the critical value, i.e., above the maximum temperatures. 8

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S.-H. Kim, et al.

term energy output spikes from heated devices, as well as enhanced cooling efficiency and performance via energy cascading between multi-stage PCMs.

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Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgment This Research was supported by grant (17RTRP-C137546-01) from Railroad Technology Research Program (RTRP) funded by Ministry of Land, Infrastructure and Transport of Korean government. This work was also supported by the 2018 Yeungnam University Research Grant. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114470. References [1] A. Vass-Varnai, Find IGBT degradation through power cycling, EDN NETWORK, 2015. [2] L. Lu, X. Han, J. Li, J. Hua, M. Ouyang, A review on the key issues for lithium-ion batterty management in electric vehicles, J. Power Sources 226 (2013) 272–288. [3] A.W. Scott, Cooling of Electronice Equipment, John Wiley & sons, Inc, 1974. [4] K. Du, J. Calautit, Z. Wang, Y. Wu, H. Liu, A review of the applications of phase change materials in cooling, heating and power generation in different temperature ranges, Appl. Energy 220 (2018) 242–273. [5] J. Jaguemont, N. Omar, P.V. Bossche, J. Mierlo, Phase-change materials (PCM) for automotive applications: a review, Appl. Therm. Eng. 132 (2018) 308–320. [6] S. Bista, S.E. Hosseini, E. Owens, G. Phillips, Performance improvement and energy consumpstion reduction in refrigeration systems using phase change material (PCM), Appl. Therm. Eng. 142 (2018) 723–735. [7] Z. Ling, Z. Zhang, G. Shi, X. Fang, L. Wang, X. Gao, Y. Fang, T. Xu, S. Wang, X. Liu, Review on thermal management systems using phase change materials for electronic components, Li-ion batteries and photovolatic modules, Renew. Sustain. Energy Rev. 31 (2014) 427–438. [8] Y. Azizi, S.M. Sadrameli, Thermal management of a LiFePO4 battery pack at high temperature environment using a composite of phase change materials and aluminum wire mesh plates, Energy Convers. Manage. 128 (2016) 294–302. [9] W.Q. Li, Z.G. Qu, Y.L. He, Y.B. Tao, Experimental study of a passive thermal management system for high-powered lithum ion batteries using porus metal foam saturated with phase change materials, J. Power Sources 255 (2014) 9–15. [10] M. Alipanah, X. Li, Numrical studies of lithium-ion battery thermal management systems using phase change materials and metal foams, Int. J. Heat Mass Transf. 102 (2016) 1159–1168. [11] R. Sabbah, R. Kizilel, J.R. Selman, S. Al-Hallaj, Active (air-cooled) vs. passive (phase change material) thermal management of high power lithium-ion pack: limitation of temerature rise and uniformity of temperature distribution, J. Power Sources 182 (2008) 630–638. [12] N. Javani, I. Dincer, G.F. Naterer, G.L. Rohrauer, Modeling of passive thermal management for electric vehicle battery packs with PCM between cells, Appl. Therm. Eng. 73 (2014) 307–316. [13] S. Shi, Y. Xie, M. Li, Y. Yuan, J. Yu, H. Wu, B. Liu, N. Liu, Non-steady experimental investigation on an intergated thermal management system for power battery with phase change materials, Energy Convers. Manage. 138 (2017) 84–96. [14] J. Bellettre, V. Sartre, F. Biais, A. Lallemand, Transient state study of electric motor heating and phase change solid-liquid cooling, Appl. Therm. Eng. 17 (1997) 17–31. [15] L.L. Vasiliev, V.S. Burak, A.G. Kulakov, D.A. Mishkins, P.V. Bohan, Latent heat storage modules for preheating internal combustion engines: application to a bus petrol engine, Appl. Therm. Eng. 20 (2000) 913–923. [16] A.L. Cottrill, G. Zhang, A.T. Liu, A. Bakytbekov, K.S. Silmore, V.B. Koman, A. Shamim, M.S. Strano, Persistent energy harvesting in the harsh desert environment using a thermal resonance device: Design, testing, and analysis, Appl. Energy 235 (2019) 1514–1523. [17] B. Shang, Y. Ma, R. Hu, C. Yuan, J. Hu, X. Luo, Passive thermal management system for downhole electronics in harsh thermal environments, Appl. Therm. Eng. 118 (2017) 593–599.

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