Composite phase change materials consisting of a high-latent-heat phase change material (PCM) embedded in a high-thermal-conductivity matrix are desirable for thermally buffering pulsed heat loads via rapid absorption and release of thermal energy at a constant temperature. This paper reports a composite PCM thermal buffer consisting of a Field's metal PCM having high volumetric latent heat (315 MJ/m3) embedded in a copper (Cu) matrix having high intrinsic thermal conductivity [384 W/(m·K)]. We demonstrate thermal buffer samples fabricated with Cu volume fractions from 0.05 to 0.2 and sample thicknesses ranging between 1 mm and 4 mm. Experiments coupled with finite element method simulations were used to determine the figures of merit (FOMs), cooling capacity ηeff, energy density Eeff, effective thermal conductivity keff, and the buffering time constant τ. The cooling capacity was measured to be as high as ηeff = 72 ± 4 kJ/(m2·K1/2·s1/2) for the 1.45 mm thick thermal buffer sample having a Cu volume fraction of 0.13, significantly higher than theoretical values for aluminum–paraffin composites [45 kJ/(m2·K1/2·s1/2)] or pure paraffin wax [8 kJ/(m2·K1/2·s1/2)]. Our work develops design guidelines for high-FOM thermal buffer devices for pulsed heat load thermal management.
The widespread use of active electronic devices and pulsed power applications has created the need for passive thermal management that can handle transient operation while maintaining mass and volume constraints.1–5 Thermal management solutions are typically sized based on peak power loads, which leads to bulky heat transfer equipment, resulting in low gravimetric and volumetric power densities.5,6 Instead, a thermal buffer analogous to a thermal accumulator offers passive thermal management capable of absorbing and conducting heat when devices generate peak heat loads. During transient peak power dissipation, the buffer can absorb the heat, conducting it to a smaller thermal dissipation system at a slower rate when peak conditions are not present. The cooling capacity of the thermal buffer is characterized by the geometric average of the energy density (the latent and sensible heat) and the power density (the effective thermal conductivity), by analogy with the thermal effusivity.7 High cooling capacity thermal buffers can respond to heat spikes quickly and absorb a large amount of heat in a short time, which can protect devices from exceeding allowable temperatures, reduce temperature oscillations, and prolong device lifetimes.3,8
Phase change materials (PCMs) present a unique opportunity to develop high cooling capacity thermal buffers by absorbing or releasing latent heat during phase change. Unfortunately, most common PCMs have a relatively low intrinsic thermal conductivity k compared with that of metals, for example paraffin waxes [≈0.2 W/(m·K)], salt hydrates [≈0.6 W/(m·K)], or metal alloys [≈20 W/(m·K)], which limits the PCM thermal buffer power density and cooling capacity.7,9,10 The cooling capacity can be increased by creating a composite material consisting of a high thermal conductivity matrix, which contains a PCM. Past approaches have attempted to disperse nanoparticles or porous conductors having high thermal conductivity directly into PCMs, or develop heat sinks by surrounding fins with PCM or filling PCM between the gaps of fins.2,4,7,11–16 Although enhancing the effective thermal conductivity via the addition of a high thermal conductivity matrix improves buffer power density, it comes at a cost of energy density due to the trade-off with PCM volume fraction. The trade-off between power and energy density has motivated researchers to seek improved PCM/conductor hybrid structures.2,7,11,17,18 Similarly, there is a need for advances in modeling and design methods that enhance understanding and development of thermal buffers. The majority of past work relies on design rules derived from the one-dimensional Neumann–Stephan problem; however, there is a need for analysis that accounts for thermal contact resistance, heterogeneous heat transfer pathways, and complicated geometries or boundary conditions. Furthermore, designers of thermal management solutions desire reduced order models and figures of merit such as cooling capacity and time constant.
This paper reports a composite PCM thermal buffer consisting of Field's metal (32.5% Bi, 51% In, 16.5% Sn) infused in a porous copper (Cu) foam matrix. We focused on Field's metal PCM due to its relatively high intrinsic thermal conductivity [≈19 W/(m·K)].19 Two types of copper foams with average pore diameters of 300 μm and 500 μm were selected due to their scalable manufacturing in addition to high interconnectivity and effective thermal transport capacity. We analyzed six samples for which the independent parameters were thickness (1 mm–4 mm) and Cu volume fraction (0.05–0.2), allowing us to investigate the roles of thermal conduction, energy storage, and interfacial thermal resistance. To understand our experimental results, we use finite element method (FEM) simulations to validate the measurements and resolve the underlying physical phenomena.
Figure 1 shows the concept of the composite PCM thermal buffer. The transient heat flux q″IN generated from the heat source [heating block, Fig. 1(a)] is partially stored by the thermal buffer and partially conducted to the heat sink [q″OUT, cooling block, Fig. 1(a)]. Heat loss due to natural convection and thermal radiation is negligible compared to the 1D conduction in the solid, and the Biot number is ∼0.001 across the width of the conductor. To investigate the thermal buffer response to a transient heat load, we implemented a 1D transient heat transfer model using FEM (see supplementary material, Sec. I). A pulsed heat flux of 15 W/cm2 was applied to the initially isothermal assembly through the heating block top boundary, with the cooling block bottom boundary maintained at 58 °C. Figure 1(b) shows predicted temperature distributions at different times. The PCM melting front (melting point of 60 °C) propagates from the hot interface (top Cu-PCM) to the cold interface (bottom Cu-PCM). The thermal buffer stores thermal energy at the rate of q″STORED = q″IN - q″OUT as shown in Fig. 1(c). In the phase change region (1.6 s < t < 17.1 s), the high energy storage rate q″STORED results in a stabilized output heat flux q″OUT as well as a slow temperature increase, compared to regions without phase change. During the initial stage of PCM melting (t < 5 s), the energy storage rate increases rapidly with the input heat flux q″IN due to the large latent heat. However, the energy storage rate drops slowly after t = 5 s due to decreasing power density from the increasing thermal resistance between the hot interface and the melting front which moves toward the cold interface. When the PCM is completely melted at t = 17.1 s, the energy storage rate reduces to a low level due to the small sensible heat capacity [300 J/(kg·K)] compared with the latent heat (34 213 J/kg). The output heat flux q″OUT increases moderately during PCM phase change and increases sharply after phase change is complete. The energy absorption and storage during phase change indicate that the composite PCM thermal buffer is capable of absorbing a large amount of thermal energy from the pulsed heat load with a limited temperature rise.
Figure 2 shows the composite PCM thermal buffer fabrication process and characterization setup. Field's metal (Roto144F, RotoMetals) was infused into the porous Cu foam [Fig. 2(a) left, CU-M-01-FM, American Elements] in a tube furnace (TF55035COMA-1, Thermo Scientific), forming the composite PCM [Fig. 2(a) right]. Use of a tube furnace flowing H2/Ar forming gas was necessary to reduce the Field's metal and the Cu foam, enabling effective wetting of the PCM in the porous network (see supplementary material, Sec. II). To ensure complete fill of the Cu foam with the Field's metal, the infused Cu foam was cut in multiple locations and inspected to confirm that no voids were present, due to the high wettability20 of reduced Cu foam with extremely wetting reduced Field's metal. To fabricate thermal buffer samples having different thicknesses, two or three Cu samples were stacked together and infused with Field's metal to form a solid interface. Figure 2(b) shows the experimental setup used for thermal measurements. The thermal buffer sample was placed between the heating block and the cooling block with extra Field's metal as the thermal interface material. Two cartridge heaters (CSH-101100/120V, OMEGA) connected to a power supply (N5752A, Keysight) generated pulsed heat loads to the heating block. A water coolant was circulated through the cooling block at a flow rate of 3.8 LPM and Reynolds number ReD ≈ 12 700, which resulted in a convective heat transfer coefficient of h ≈ 3500 W/(m2·K). The heating and cooling blocks were made of Cu and painted black to ensure a high spectrally averaged emissivity (≈ 0.94) for infrared (IR) thermal measurements (A655sc, FLIR). Three thermistors (LSMC700A010KD002, Selco Products) with an accuracy of ± 0.1 °C were inserted into each Cu block to measure temperatures T1 through T6. Temperature measurements were recorded using FLIR software for thermal videos and a data acquisition system for thermistor temperatures at a sample rate of 1 Hz.
Figure 3 shows exemplary IR thermal measurement results of a 40 mm x 40 mm × 1.45 mm sample with a Cu volume fraction of 0.13. Four thermal images were magnified in Fig. 3(a) to show the temperature distributions at t = 0 s, 60 s, 120 s, and 180 s. The heating process began at t = 0 s when a transient high power of 186 W was supplied instead of the background steady-state power of 112 W. The thermal buffer completed phase change from solid to liquid before t = 180 s. The z-axis temperature profile in Fig. 3(b) of each image was evaluated by averaging temperatures across the width of the sample. The temperature distributions in the heating and cooling Cu blocks indicated the transient input and output heat transfer rates and were approximately linear due to the high intrinsic thermal diffusivity of Cu (α = 111 mm2/s). However, the temperature profiles near the PCM-Cu interfaces were distorted due to the interfaces between the thermal buffer and the heating and cooling Cu blocks. The temperature profiles measured from both thermistors and IR images were analyzed to characterize the heat transfer rates.
Figure 4 shows the thermal performance of the buffer sample as a function of time during successive heating and cooling cycles. Figure 4(a) shows heat transfer rates into the thermal buffer QIN, out from the thermal buffer QOUT, and supplied power QSUPPLY as a function of time. Figure 4(b) shows the transient temperature THOT at the hot interface between the thermal buffer and the heating block and the transient temperature TCOLD at the cold interface between the thermal buffer and the cooling block. Heat transfer rates QIN and QOUT as well as interface temperatures THOT and TCOLD were calculated from thermistor temperature measurements by solving Fourier's law (see supplementary material, Sec. III). During heating, the thermal buffer initiated phase change when THOT exceeded the melting point TMELT (≈60 °C) and ended phase change when TCOLD > TMELT. During cooling, the thermal buffer initiated phase change when TCOLD < TMELT and ended phase change when THOT < TMELT. The gray shaded bands in Fig. 4 represent the operating regions where phase change occurred. The high energy storage rate during phase change is shown via the difference between QIN and QOUT in the phase change region when compared to the no phase change region in Fig. 4(a). Using conservation of energy, we calculated the sensible and latent energy storage components, and obtained figures of merit (FOMs) for the varying composite PCM thermal buffer designs. At steady state, with no heat absorption or release by the thermal buffer, the heat transfer rates QIN and QOUT were nearly equal and slightly lower than the supplied power QSUPPLY due to the heat loss to the ambient. We calculated the effective thermal conductivity from an energy balance on the observed heat transfer rates, and used FEM models to further explore the phase change heat transfer and determine FOMs (see supplementary material, Sec. IV).
Table I shows the FOMs and thermophysical properties obtained from experimental results and FEM simulations for all six samples. The effective cooling capacity, which represents heat absorption and conduction capability of the thermal buffer, was evaluated by:7,18
where Eeff is the effective thermal buffer energy density calculated as Eeff = HV,eff + CV,eff · ΔTMELT. HV,eff is the effective latent heat, and CV,eff is the effective volumetric sensible heat capacity, which represents the energy storage ability of the thermal buffer. The term ΔTMELT is the difference between the PCM melting temperature and the ambient temperature (ΔTMELT = Tm - Tambient). The effective thermal conductivity was calculated by considering measured temperatures at steady state during no phase change:
|Sample .||Cu volume faction, ϕCu .||Sample thickness, d (mm) .||Method .||ηeff [kJ/(m2·K1/2·s1/2)] .||Eeff [MJ/m3] .||keff a [W/(m·K)] .||τ (s) .||CV,eff [MJ/(m3·K)] .||HV,eff (MJ/m3) .|
|Sample .||Cu volume faction, ϕCu .||Sample thickness, d (mm) .||Method .||ηeff [kJ/(m2·K1/2·s1/2)] .||Eeff [MJ/m3] .||keff a [W/(m·K)] .||τ (s) .||CV,eff [MJ/(m3·K)] .||HV,eff (MJ/m3) .|
keff was obtained experimentally and includes the interface contact thermal resistance on both sides of the sample.
To characterize the effective operation time associated with the thermal buffer, we define a time constant τ as the period when the temperature difference THOT – TCOLD across the buffer changes 95% of the total variance during cooling or heating. Buffer properties Eeff, CV,eff, and HV,eff were evaluated using QIN and QOUT and T1 through T6 by applying energy conservation within the buffer (see supplementary material, Sec. V).
The thermal buffers have cooling capacity ηeff as high as 72 kJ/(m2·K1/2·s1/2) (Table I), significantly better than 45 kJ/(m2·K1/2·s1/2) for aluminum-paraffin or 8 kJ/(m2·K1/2·s1/2) for pure paraffin wax buffers.7,10 The six samples show comparable ηeff despite the variation in the Cu volume fraction and thickness, due to the trade-off between Eeff and keff. The effective energy density was as high as Eeff = 398 MJ/m3, of which 185–319 MJ/m3 was latent and 1.9–4.8 MJ/(m3·K) was sensible. Thermal buffers with a lower Cu volume fraction at 0.06 (A1, A2, and A3) had higher Eeff due to the larger amount of PCM contributing a larger latent heat. The sensible heat accounts for less than 20% of Eeff for ΔTMELT = 35 °C. The effective thermal conductivity of our thermal buffer was measured to be keff = 9.5–14.1 W/(m·K), and was affected by thermal contact resistance at interfaces as well as the volume fraction of the high thermal conductivity Cu. All samples have thermal contact resistance at the top and bottom surface, and some samples have additional internal thermal resistances at the interfaces between adjacent Cu sections. The thermal contact resistance is in the range 33 (mm2·K)/W to 74 (mm2·K)/W and explored in supplementary material, Secs. VI and VII. The time constant τ is in the range of 124 s–359 s and depends on thermal buffer thickness. The thermal time constant of thermal buffers is significantly larger than that of a single PCM-filled pore (∼0.1 s). Thicker samples have larger time constants due to larger amounts of PCM. Thicker samples also had lower thermal conductance than thin samples, which reduced their ability to absorb power spikes, thus presenting a trade-off between the time constant and the maximum power. The experimental FOMs differed less than 10% from the FEM simulations (Table I). Error analysis appears in supplementary material, Sec. VII.
We analyzed the theoretical thermal conductivity and tradeoffs between the high thermal conductivity of the Cu matrix and the latent heat of the Field's metal by solving the Neumann-Stephan problem with St < 0.5 and expressing ηeff as a function of ϕCu by the geometric average of keff and Eeff [Eq. (1)]. The effective thermal conductivity of the composite PCM was calculated using the differential effective-medium (DEM) approximation,21 assuming that the Cu matrix remains connected homogeneously and neglecting thermal contact resistance. The effective energy density Eeff was calculated using the weighted linear combination of the thermal properties.7 The maximum theoretical cooling capacity is 223 kJ/(m2·K1/2·s1/2), about 5X higher than the theoretical value for an Al-wax hybrid heat sink10 at 45 kJ/(m2·K1/2·s1/2) and 28X higher than paraffin wax7 at 8 kJ/(m2·K1/2·s1/2). The maximum cooling capacity corresponds to Cu volume fraction of 0.83, effective thermal conductivity of 297 W/(m·K), and energy density 167 MJ/m3 (see supplementary material, Sec. VIII).
Future research on thermal buffers may consider improvements as follows. The thermal contact resistance should be reduced if possible, to achieve good contact between the buffer and adjacent structures.22 Improved thermal buffers may have anisotropic properties, perhaps by leveraging recent advances in Cu nanowires.23 To enable the integration of thermal buffers with devices such as power electronics, FEM simulations are required to predict buffer performance as a function of pulsed power rates and duty cycles. Finally, the buffer samples demonstrated here are homogeneous; however, spatially varying volume fractions of PCM and the metal matrix could enable new performance characteristics.24
In summary, we demonstrated a composite PCM thermal buffer utilizing a low-melting-point Field's metal PCM infused into a Cu metal foam. Experiments and simulations explored heat transfer for varying thermal buffer thicknesses and Cu volume fractions. We found good agreement between measured and modeled heat transfer performance. The thermal buffers exhibited high cooling capacities up to 72 kJ/(m2·K1/2·s1/2) and thermal time constants as high as 359 s. Our buffers provide a passive thermal management solution for devices generating pulsed heat loads by reducing the need for dynamic control and size of the thermal dissipation system.
See the supplementary material for device fabrication, thermal characterization, modeling, FOMs calculation, and error analysis.
This work was supported by the National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal systems (POETS) with cooperative Agreement No. EEC-1449548. N.M. gratefully acknowledges funding support from the International Institute for Carbon-Neutral Energy Research, Kyushu University (No. WPI-I2CNER).