A conceptual design of a thermal switch capacitor in a magnetocaloric device: experimental characterization of properties and simulations of operating characteristics

The quest for better performance from magnetocaloric devices has led to the development of thermal control devices, such as thermal switches, thermal diodes, and thermal capacitors. These devices are capable of controlling the intensity and direction of the heat flowing between the magnetocaloric material and the heat source or heat sink, and therefore have the potential to simultaneously improve the power density and energy efficiency of magnetocaloric systems. We have developed a new type of thermal control device, i.e., a silicon mechanical thermal switch capacitor ( TSC). In this paper we first review recently developed thermal switches based on micro-electromechanical systems and present the operation and structure of our new TSC. Then, the results of the parametric experimental study on the thermal contact resistance, as one of the most important parameters affecting the thermal performance of the device, are presented. These experimental data were later used in a numerical model for a magnetocaloric device with a thermal switch-capacitor. The results of the study show that for a single embodiment, a maximum cooling power density of 970 W m−2 (510 W kgmcm −1) could be achieved for a zero-temperature span and an operating frequency of 5 Hz. However, a larger temperature span could be achieved by cascading multiple magnetocaloric elements with TSCs. We have shown that the compact TSC can be used in caloric devices, even with small temperature variations, and can be used in a variety of practical applications requiring thermal regulation.


B
Magnetic field (T)

Introduction
The efficient and controlled thermal management of a system is crucial for high energy efficiency, optimized performance, high reliability and safety. It is becoming evident that conventional thermal management methods, such as macroscale heat exchangers, thermal resistors (i.e., conventional thermal insulation), and capacitors (conventional thermal storage), cannot meet the requirements for thermal control in advanced, especially small-scale systems, with higher power densities or potentially fluctuating hot and cold spots. To overcome these limitations, new thermal control devices such as thermal switches, diodes, and capacitors have emerged. Thermal control devices enable the non-linear, switchable, and active control of heat, in a similar way to their electrical counterparts manage electrical current. These thermal control devices can be applied in small-scale systems from below 1 µm to the larger-scale systems below 100 mm. In the last two decades, intensive studies have been conducted on different types of macroscopic, mechanical and MEMS thermal switches [1][2][3][4], which also includes their integration in caloric (ferroic) technologies [5]. By focusing on the last 5 years, and considering (micro)mechanical thermal switches and their applications in cooling, heating or thermal energy harvesting using ferroic materials, the majority of research activities were performed in the field of electrocalorics [6][7][8][9][10][11][12][13][14][15][16][17][18][19] or pyroelectrics [20][21][22][23][24]. A much smaller number of publications can be found for the domains of magnetocalorics [17,[25][26][27] and pyromagnetics (thermomagnetics) [28][29][30][31][32][33][34] or elastocalorics [35][36][37]. A common feature of all these studies is a large difference between the results of pure numerical work (usually leading to superior performances from the devices) compared to real experiments. One of the important reasons for this is the missing information on realistic properties related to TCRs, the thermal mass of particular parts, different heat losses/gains, including the disregarded heat generation, which can affect the performance of a device. For this reason, we placed special emphasis in our study on the experimental determination of thermal properties and TCRs and used these data in a numerical simulation. The performance of the micro-electromechanical TSC was numerically evaluated in a magnetocaloric device, but this solution can also be applied in other caloric technologies or applications with cyclic temperature changes. High-quality integration of the mechanical thermal control devices in different applications requires a good knowledge of the interfaces to solve the problems, or tune the properties of TCRs.
Efficient and rapid dissipation of heat from localized hotspots to the surroundings is a critical aspect of thermal management in various applications. This is especially important for electronic components, as some studies show that their performance decreases significantly with increasing operating temperature [38][39][40]. When heat is dissipated by conduction between contacting elements, TCR is the most critical part limiting heat transfer between surfaces and is generally considered as the less-known feature of the system. The actual contact area between contacting surfaces is much smaller than the nominal contact area because surfaces are never perfectly flat or smooth [41,42]. Consequently, some heat is conducted through the surface-asperity micro-contacts, but a much smaller fraction is transferred through the air-filled micro-gaps [43]. Since the thermal conductivity of air is rather low (0.026 Wm −1 K −1 at 300 K), various methods have been used to enhance the effective thermal conductivity and thus increase the heat flux across the contact surface. The two most common methods to increase the actual contact area of solid-solid interfaces without using thermal interface materials to fill uneven surfaces, are reducing the roughness and increasing the contact pressure [42,44,45], which we also studied.
The main objective of our work was twofold. First, we have experimentally evaluated the thermal properties and TCR between gadolinium/SU-8, gadolinium/Kapton, silicon/SU-8, and silicon/Kapton at various temperatures and contact pressures. These materials are integral components of a TSC device. Second, the numerical simulations were performed to evaluated the realistic performance of a magnetocaloric device with a TSC, using the experimentally determined thermal properties and TCRs. Gadolinium was chosen as the MCM because it is one of the most representative examples. The other materials we studied, silicon (Si), SU-8, and Kapton, are widely used in the semiconductor industry, robotics, and smart electronic devices, where effective thermal management is a major challenge due to high power density, miniaturization, safety, and performance degradation caused by inefficient heat dissipation [46]. Therefore, this manuscript provides new insights for a broader audience, including those outside the field of caloric cooling and heat pumps. We further report on the results of an investigation into TCRs under different contact pressures, from 1 kPa to 200 kPa, and at different temperatures: −40 • C, −10 • C, 20 • C, 50 • C, 80 • C.

Thermal switch capacitor
A conceptual design of the TSC assembly presented here is illustrated in figure 1. The system includes two silicon TSCs, namely TSC 1 and TSC 2, which are a combination of a thermal switch and a thermal capacitor in one element and are used for heat transfer in a device with hot/cold spots. TSC 1 moves between the heat source and the hot/cold spot (upper part of the device) and TSC 2 moves between the hot/cold element and the heat sink (lower part of the device). In this study, the MCM represents the hot/cold spot, but it can be any element or device with fluctuating temperature. Ideally, the thermal resistance is zero when the TSC is activated, and conversely, the thermal resistance is infinite when the switch is deactivated. When TSC 1 is activated, it transfers heat between the heat source and the cold spot. At the same time, TSC 2 is deactivated to minimize the heat flow between the cold spot and the heat sink. The analogous (reverse) operation is also taking place when TSC 2 is activated and TSC 1 is deactivated. TSC 2 then transfers heat from the element that is now the hot spot to the heat sink. The described concept proposes to actuate the TSC motion electrostatically because this type of actuation has a short switching time (∼ms) [14,47], low power consumption [48,49], and most importantly, the contact pressures in the range of ∼kPa can be achieved [16,49]. The upper and lower part of the device consists of the same elements, namely: a TSC made of electrically conductive material, which serves simultaneously as an electrode and heat transporter, heat exchanger and hot/cold spot. The additional electrodes needed for electrostatic actuation are made of highly conductive material such as graphite, which is sprayed onto the heat exchanger and the hot/cold spot. The spray-coated electrodes are covered with a dielectric layer to prevent short circuits. The TCR between the dielectric layer and the spray-coated electrode with a thickness of only few nanometers was not considered in this study. If the hot/cold spot is made of electrically conductive material, as in the case of the MCM, it can serve as the electrode for electrostatic actuation, and no additional spray-coated electrodes are required. To establish the activated state, the voltage is alternately applied between the TSC and MCM and between the TSC and the electrode at HEX on the same side (upper or lower side). The switching of the electric field between the two pairs of electrodes creates an attractive electrostatic force that causes the free-standing electrode, in our case the TSC, to move. The deactivated state is achieved when a constant voltage is applied to the TSC and the electrode on the HEX side and no movement occurs. The position of the TSC changes depending on applied electric field and is independent of gravity. A thin spacer made of a low-thermal conductivity material separates the heat reservoirs and the hot/cold spot (the dark green element in figure 1). Most thermal switches in caloric technologies that use electrostatic forces for actuation are attached to the spacers on both sides [14,16,17,49,50]. This establishes the thermal connection between the heat sink and the heat source, which increases the heat losses. In order to increase the thermal performance and avoid additional heat losses due to conduction, the studied TSC is free-standing and not attached to spacers. Silicon was chosen as the heat sink/source material because it has an extremely smooth contact surface that would help reduce TCR in future experimental proofs of concept. The contact pressure between the TSC and the active electrodes is calculated as follows: where ε r is the vacuum permittivity, ε DL is the dielectric constant of dielectric layer, U is the voltage and L DL is the thickness of the dielectric layer. Two different materials were considered for the dielectric layer: Kapton and SU-8 (ε DL, Kapton = 3.5, ε DL, SU8 = 3). Preliminary experimental results showed that a voltage in the range 600-900 V is required to actuate a 200 µm-thick Si plate, but the values of the electric current are much lower (∼mA). Furthermore, it has been experimentally proven that up to 84% of the input electric energy can be recovered for a similar design [14]. In our case the contact pressure is about 28 kPa for Kapton and about 24 kPa for SU-8 as a dielectric layer with a thickness of 25 µm. The switching ratio r is a figure of merit for the TSC and represents the ratio between the highest achievable thermal resistance (the activated or 'on' state) R on , and the smallest achievable thermal resistance (the deactivated or 'off ' state) R off . This value can be calculated using the following formula:

A conceptual design of a thermal switch capacitor in a magnetocaloric device
The single-stage concept with the TSC is proposed to be located within the air gap between the two windings in a magnetocaloric device, as schematically shown in figure 2(A). Our concept design involves using a static electro-permanent magnet, for which it has been experimentally proven that frequencies up to 50 Hz can be achieved [51]. The working principle includes four main steps as shown in figure 2(C  [26]. Achieving high operating frequencies in caloric devices requires TCDs with fast switching and response times. Therefore, TCDs must have switching times that enable quick transitions between activated and deactivated states while maintaining a time response of approximately milliseconds.  [26]. Adapted with permission from [26]. CC BY-NC-ND 4.0 .

Thermal diffusivity
The thermal diffusivity of the samples was measured using the laser-flash-analysis (LFA) method (LFA 467 Hyper Flash, NETZSCH, Germany) in the temperature range from −40 • C to −80 • C with an accuracy of ±3%. To determine the thermal conductivity of the samples using this data, the specific heat and density of the materials must be a priori known. The relationship between the given variables can be expressed as (equation (3)): where α is the thermal diffusivity (m 2 s −1 ), ρ is the mass density (kg m −3 ) and c p is the specific heat at constant pressure (J kgK −1 ). For convenience, the density was treated as a constant in this study. The thermal diffusivity α can be obtained using Parker's equation [52], which describes the analytical relationship between the sample's surface temperature on the laser-source side and the time needed for the surface temperature to reach half of the maximum temperature rise t 0.5 : where L (m) represents the thickness of the sample. It is approximated that heat conduction is one dimensional and that no heat losses to the ambient occur. Due to the significantly shorter duration of the laser pulse compared to the characteristic time t 0.5 , the energy absorption process in the material is considered instantaneous. A detailed explanation of the calculation procedure is given in Stephen and Turriff [53] and Parker et al [52]. For further information on sample preparation and experimental determination of thermal diffusivity and specific heat (see supplementary materials S1).

Materials
In order to experimentally investigate the TCRs between the components of the TSC structure, we must first determine the thermal diffusivity and specific heat of each layer. We investigated two different types of materials: • Conductive layer: gadolinium, silicon (high thermal conductivity materials) • Dielectric layer: SU-8, Kapton (low thermal conductivity materials) Gadolinium (Gd) with a high purity was used as an MCM. The silicon samples were prepared from a two-sides polished wafer (100 orientation) with a total thickness variation <5 µm (MicroChemicals, Germany). Commercially available Kapton polyimide film with a silicone adhesive was manufactured by FabConstruct (Germany). For some tests the adhesive was removed using isopropanol in an ultrasonic bath. The SU-8 photoresist was produced by Gersteltec (Switzerland) and was later spin coated to reach the desired thickness, as described in supplementary materials S2. All the samples were cleaned in acetone before the measurements. Supplementary table 1 summarizes the physical properties of the samples. Three different tests were performed for each type of material. In the first case, the thermal diffusivity of a single-layer sample (figure 3(A)) was measured using LFA. In the second case, two single-layer samples of the same size (configurations: Gadolinium/SU-8, Gadolinium/Kapton, Silicon/SU-8, Silicon/Kapton) were placed in direct contact ( figure 3(B)), and the thermal diffusivity of two-layer samples was measured and later the TCR was determined using these values. In this case, a contact pressure of 1-200 kPa was applied to the sample by precisely tightening the fixing nut with a torque wrench (see supplementary materials S4). In the third case, no pressure was applied, and the conductive layer and the dielectric layer were bonded together either by spin coating or adhesive forces, and again the thermal diffusivity of the two-layer sample was measured ( figure 3(C)).
For a determination of the thermal diffusivity of the single-layer samples the transparent model applied in the Netzsch Proteus analysis software was used. This model uses a modification of equation (4) developed by Mehling et al [54], which also considers radiative heat transfer between the front and back surfaces of the sample, as well as the heat losses not considered in equation (4). This model is particularly suitable for optically thin samples and for materials with opaque edges, such as the SU-8 and Kapton samples in our case. In order to be able to compare the results under the same conditions, the same model was used for all samples.

Thermal contact resistance
In a two-layered system, the total thermal resistance is a combination of the thermal resistances of the individual layers and the TCR in between the layers. The thermal resistance network model of a two-layered sample is schematically presented in figure 4. The previously determined thermal diffusivities of the individual layers were used as input parameters, as well as the specific heat, density and the sample's geometry. The total thermal resistance R tot of the two-layered configuration can be determined as follows: where R cl and R dl are the thermal resistances of the conductive and dielectric layer and R c is the TCR between the conductive and dielectric layer. L cl is the thickness of the conductive layer, and L dl is the thickness of the dielectric layer. The TCR can be directly calculated from equation (6), knowing the thickness and material properties of each layer:

Experimental analysis
The study focused on an analysis of the TCR in the temperature range from −40 • C to 80 • C, with a temperature step of 30 K. To evaluate the TSC in the magnetocaloric device, the study examined the TCR between the heat exchanger and the dielectric layer Rc hex-di , between the MCM and the dielectric layer Rc mcm-di , and between the TSC and the dielectric layer Rc tsc-di . The described TCRs in the TSC configuration are shown in figure 1. Two different dielectric materials were investigated, i.e., Kapton and SU-8, to find out which material has the better thermal performance and the lower TCR values, and is therefore more suitable for the thermal management applications. For Rc hex-di and Rc mcm-di , the dielectric layer was deposited on the substrate either with spin coating (SU-8) or bonded to the substrate with adhesive (Kapton). For Rc tsc-di , the direct contact between the moving TSC and the dielectric layer was investigated at different contact pressures. In general, the TCR values are higher for the two-layer samples with Gd (supplementary figure S1(A)) than for the two-layer configurations where one of the materials in the pair is Si (supplementary figure S1 (B)). This is due to the fact that the real contact area is smaller for the gadolinium sample with a relatively rough surface than for a finely polished silicon wafer. Therefore, the use of Si is a better alternative for applications where heat conduction by direct contact is used. Additional information on the experimental determination of the TCR at different contact pressures is given in supplementary materials S5.

Numerical simulations
The one-dimensional transient numerical model used for the TSC evaluation in the magnetocaloric device is described in detail in Petelin et al [26]. The heat-transfer equation, combined with the magnetocaloric effect, was numerically solved using the finite element method. The selected thermodynamic cycle of magnetic refrigeration was the Brayton cycle without regeneration. The magnetocaloric effect was applied to each node of the MCM as the adiabatic temperature change with the adequate and simultaneous specific heat change (see supplementary materials S6). The magnetocaloric properties of Gd were taken from [55], which uses mean field theory to determine entropy values as a function of temperature and internal magnetic field. The maximum adiabatic temperature change achieved for gadolinium (Gd) after magnetization (B on = 1 T) is 3.97 K at 292 K and 3.98 K at 295.9 K after demagnetization (B off = 0 T). A magnetization and demagnetization time of 5 ms was used in the simulations. This value was experimentally demonstrated by Tomc et al [51] in the development of a static and hybrid electro-permanent magnet. The numerical model is not limited to Gd as a MCM, but can be used for any MCM if the entropy values and thermal properties are known. In this study, a 250 µm thick Gd was used in all simulations. It is important to note that TCR is one of the parameters that affect thermal performance. The choice of the MCM considering its maximum adiabatic temperature change, density and specific heat as well as its thickness are also important parameters. We discussed the latter in our earlier study [26], which we encourage the reader to read for further insights.
To simulate realistic operating conditions, the numerical model includes experimentally determined thermal properties (see supplementary materials S7) and experimentally determined TCRs between the elements (table 1). The thermal properties for the temperatures between the measurement points were determined as the average of the neighboring measurement points. The geometrical properties and operating conditions are summarized in table 2. Due to electrostatic actuation, Joule heating was included in the numerical model as generated heat in the active electrodes and calculated as follows: where I is the electric current and R is the electrical resistance. The graphite-sprayed electrode on the heat sink and heat source was not included in the numerical simulations due to its high thermal conductivity and negligible thickness of only a few nanometers, resulting in an insignificant contribution to the device performance. Instead, the heat generated by the Joule effect in the electrodes was considered as the heat generated at the heat sink/source and the MCM. Heat losses due to heat conduction through low thermal conductivity spacers at the edges of the device are also considered negligible. The device temperature span and cooling power density are the two most important parameters for evaluating a magnetocaloric cooling device. Generally, the maximum temperature span between heat sink and heat source is obtained when the cooling-power density is zero (no-load condition) and conversely, the maximum cooling-power density is achieved when the temperature span between heat sink and heat source is zero. The thermal performance of the magnetocaloric device with the TSC was analyzed in terms of cooling-power density for operating frequencies in the range 1-15 Hz. To simulate different cooling-power densities, the constant heat flux was defined as a boundary condition on the heat source side. The convection boundary condition on the heat sink side was defined by the ambient temperature and the convective heat-transfer coefficient. In order to focus on the thermal performance of the TSC, a high value of convective heat-transfer coefficient (h ∞ = 10 000 W m −2 K −1 ) was chosen to obtain a nearly constant temperature on the heat sink side. Such high values of the convective heat-transfer coefficient h ∞ can be obtained with an microchannel liquid cooling [56,57] or a heat-pipe system [58]. Figure 6 shows that the temperature span decreases linearly with increasing cooling-power density from 1 W m −2 to 1000 W m −2 . Although electrostatic actuation of the device can operate at higher frequencies, the maximum cooling performance of the single-stage cooling device was achieved at a frequency of 5 Hz. At higher operating frequencies the time for the heat transfer in steps 2 and 4 (figure 2(C)) is insufficient and the thermal performance of the device decreases. The maximum cooling-power density obtained for a single-stage unit with Kapton was 970 W m −2 at a zero-temperature span. This value corresponds to a specific cooling powerq c of 510 W kg mcm −1 for 250 µm-thick Gd. When the cooling power density is further increased, the heat source temperature rises above the ambient temperature (295 K) because the device is no longer able to dissipate all the heat from the heat sink. As a result, the heat source heats up, negating the cooling performance. The device with SU-8 achieves a lower maximum power density due to the higher TCR and lower thermal conductivity values. In this case, the maximum cooling-power density was 772 W m −2 (405 W kg mcm −1 ) at an operating frequency of 5 Hz and a zero-temperature span, as shown in figure 6(B). However, the temperature span between the heat sink and the heat source is higher at lower cooling-power densities (q c < 150 W m −2 ) for devices with SU-8 as the dielectric layer. This is due to the lower thermal mass (ρc p ) of the SU-8 layer, by almost 42%, compared to Kapton. These results suggest that the cooling performance can be improved by using a dielectric layer with low thermal mass and high thermal conductivity. Another straightforward approach to reduce the thermal resistance and increase the temperature span would be to minimize the thickness of the dielectric layer.
The effectiveness of the TSC embodiment is evaluated from the switching ratio r. The switching ratio was determined for isofield cooling r cooling (figure 2(C), steps 2a and 2b) and isofield heating r heating (figure 2(C), steps 4a and 4b). The two switching ratios differ due to the different boundary conditions on the sink and heat source sides. During the isofield heating process, heat is transferred from the MCM to the heat sink and the convection (h ∞ = 10 000 W m −2 K −1 ) was assumed as the boundary condition on the heat sink side. During the isofield cooling process, heat is transferred from the heat source to the MCM and adiabatic wall on the heat source side was used as the boundary condition. The maximum switching ratio for the device with SU-8 is r = 4.51 (cooling isofield process) and r = 4.21 (heating isofield process) at an operating frequency of 3 Hz, as shown in figure 7(A). When the frequency exceeds 3 Hz, the switching ratios and temperature span begin to decrease, indicating that the elements in contact do not reach thermal equilibrium and that heat-transfer time is too short. Similar observations can be made for the device with Kapton, where these values are lower than the device with SU-8 due to the smaller temperature span between the heat sink and the heat source, as shown in figure 7(B). In order to achieve a larger switching ratio, adopting a TSC with a larger thermal mass or increasing the air gap would be a practical solution. However, in both cases a larger electrical field would be needed to actuate the TSC. Figure 8 shows the maximum cooling power and temperature span as a function of operating frequency for magnetocaloric devices described in the literature. The numerically determined value of the maximum cooling power in our case is lower than the best values reported in the literature for gadolinium-based devices. However, the temperature span of the device can be increased if the device contains more cascade layers with different MCMs based on their Curie temperature and by using materials with more pronounced magnetocaloric effect [59,60]. When cascading multiple MCMs with different Curie temperatures, the maximum operating frequency at which the maximum cooling power is observed should be similar to a single-stage device if the TSCs have the same performance, and all magnetocaloric elements have similar magnetocaloric effect, thermal mass, and thermal conductivity as in this study. Increasing the electrostatic force is another way to improve the cooling performance. By simply tuning the magnitude of the voltage, the contact pressure and thus the TCR between the TSC and the active electrode can be easily modulated. A lower TCR and the use of a dielectric layer with a lower thermal mass and a higher thermal conductivity would increase the operating frequency at which the maximum cooling power is achieved, further improving the thermal performance of the device.

Conclusions
This study numerically evaluates the performance of a mechanical TSC with a temperature-changing element, a heat sink, and a heat source, using MCM as the element that changes temperature with time. An accurate determination of the contact resistance between the elements is crucial for a numerical evaluation of the device, as this information is often missing in the literature. To address this, we experimentally measured the thermal properties and contact resistances between the different elements in contact and used this data in a numerical model. We evaluated two different dielectric layers, Kapton and SU-8, for an electrostatically actuated TSC and found that two-layer samples with Kapton had lower thermal resistance values than samples where one of the materials in contact was SU-8. At the same contact pressure, the use of smooth surfaces, such as silicon, is a better alternative than rough surfaces for applications where thermal conduction occurs by direct contact. Increasing the contact pressure from 1 kPa to 200 kPa improved the TCR by 74.7%, 77.1%, 62.4%, and 72.3% for Gd/SU-8, Gd/Kapton, Si/SU-8, and Si/Kapton, respectively. This contact pressure can be achieved by increasing the electrostatic field between the active electrodes. Therefore, simply tuning the operating voltage between the active electrodes can improve or even tune the thermal performance of the device as the contact pressure influences the TCR.
We used a transient numerical 1D model to evaluate the magnetocaloric device with integrated thermal switched capacitor. The numerical results show that the maximum cooling power density of the magnetocaloric device with embodied TSC is 970 W m −2 (510 W kg mcm −1 ) at a zero-temperature span. By cascading multiple magnetocaloric elements with different Curie temperatures and employing thermal regeneration, we can achieve a larger temperature span. To increase the temperature span and cooling-power density of a single unit device, we can improve the TCR, either by selecting smoother materials or by increasing the electrostatic force. Employing a dielectric layer with a lower thermal mass and a higher thermal conductivity, adopting a TSC with a higher thermal mass, or selecting MC materials with a more pronounced magnetocaloric effect should also help to improve the thermal performance of the device. These findings can be extended to other caloric domains, such as electrocalorics or other applications with a temperature-fluctuating element.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

Data and code access statements
• All data reported in this article will be shared by the lead contact upon request.
• The code with instructions reported in this article will be shared by the lead contact upon request.
• Any additional information required to analyse the data reported in this study is available from the lead contact upon request.