# Natural rubber based elastocaloric solid-state refrigeration device: design and performances of a single stage system

Marianne Sion, Jacques Jay, Gildas Coativy, Atsuki Komiya, Gaël Sebald

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Marianne Sion, Jacques Jay, Gildas Coativy, Atsuki Komiya, Gaël Sebald. Natural rubber based elastocaloric solid-state refrigeration device: design and performances of a single stage system. Journal of physics, 2024, 6 (2), pp.025003. 10.1088/2515-7655/ad20f4. hal-04567628

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Natural rubber based elastocaloric solid-state
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To cite this article: Marianne Sion et al 2024 *J. Phys. Energy* **6** 025003

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# Natural rubber based elastocaloric solid-state refrigeration device: design and performances of a single stage system

Marianne Sion¹,²,³,* Ⓓ ID, Jacques Jay², Gildas Coativy⁴ ID, Atsuki Komiya¹,³ ID and Gaël Sebald¹,∗ ID

¹ ELyTMaX IRL 3757, CNRS, University Lyon, INSA Lyon, Centrale Lyon, Université Claude Bernard Lyon 1, Tohoku University, Sendai, Japan

² Université de Lyon, CNRS, INSA-Lyon, CETHIL UMR 5008, Villeurbanne F-69621, France

³ Institute of Fluid Science, Tohoku University, Sendai, Japan

⁴ Université Lyon, INSA-Lyon, LGEF EA682, Villeurbanne F-69621, France

* Authors to whom any correspondence should be addressed.

E-mail: marianne.sion@insa-lyon.fr and gael.sebald@insa-lyon.fr

Keywords: elastocaloric, solid-state refrigeration device, single stage, natural rubber

## Abstract

The elastocaloric effect denotes the ability of a material to release or absorb heat when the material is stretched and released respectively. This effect may be used to design an alternative cooling device. This work focuses on the development of a cooling device using natural rubber (NR) as the elastocaloric material. It consists of a solid-solid heat exchange between a cyclically stretched elastocaloric material and two exchangers, respectively put in contact with the elastocaloric material when it is stretched or released. An experimental device was designed and tested in order to assess the temperature span and cooling power (PC) achievable by NR based single stage device. The effect of the thickness of the NR is also discussed. It is shown that it was possible to transfer nearly 60% of the heat absorption potential of the NR from the cold heat exchanger. From the measurements, the highest PC was found to be 390 mW (430 W kg⁻¹) for a 600 µm thick sample, and 305 mW (540 W kg⁻¹) for a 400 µm thick sample. The temperature span was found to be similar for both materials, ranging 1.5 °C–1.9 °C.

## 1. Introduction

Nowadays, vapor compression is the most commonly used technology for refrigeration systems. However, this raises questions about the toxicity of the refrigerant gas, their efficiency and potential environmental impact. Alternative refrigeration principles need to be explored, for more environmentally friendly refrigeration. For small cooling power (PC), Peltier effect [1] or Stirling cycles [2] may be used although the efficiency is questioned. In recent years several proofs of concept were proposed using so-called caloric materials [3–5]. Caloric materials constitute a category of materials whose entropy may be driven by an electromagnetic field, electric field, pressure or a uniaxial stress, called respectively magnetocaloric materials [6, 7], electrocaloric [8, 9] and mechanocaloric materials, comprising barocaloric [10] or elastocaloric materials [11–13]. Despite highly promising performances in terms of PC, the question of the efficiency, temperature, cost, abundance and environmental impact may be raised. In this context, polymers deserve attention thanks to their potential low CO₂ footprint and availability. Especially, natural rubber (NR) may be biosourced in addition to the previous advantages, and caught attention because of its high elastocaloric effect. The elastocaloric effect occurs when the elastocaloric material is submitted to a cycle of mechanical loading and unloading. When the material is loaded by applying a mechanical force, its temperature increases (in adiabatic condition) or the entropy decreases (in isothermal condition). When the force is released, opposite variations occurs. From the state-of-the-art, two type of systems using elastocaloric materials for refrigeration were proposed: the regenerative systems with solid-solid heat exchangers [14–16] and single stage systems with solid-liquid heat exchangers [17–19]. The majority of the literature work focused on shape memory alloys, like NiTi alloys, showing very high specific and absolute PC ranging the Watt to the hundreds of Watt range, although requiring high driving forces. Conversely, it is expected that using NR may require
much smaller force. However, the very low thermal conductivity of polymers may constraint significantly the geometry of the devices, by challenging the effectiveness of the heat transfer between the elastocaloric material and heat exchangers. The goal of this work is to assess the possibility of ensuring a proper utilization of the potential heat release and absorption of NR in an experimental proof of concept of device.

This work focused on the development of a single stage 4-step cooling device. The performances of this device (temperature span, *PC*, coefficient of performance (COP)) for two thicknesses of NR films were tested. Section 2 presents the experimental methods, followed by the results in section 3 and a discussion in section 4.

## 2. Experimental methods

### 2.1. 4-step refrigeration cycles

The experimental setup worked on a 4-step basis shown on figure 1. During the first step, the NR was stretched to an elongation ($\lambda$) of 600% ($\lambda$ = 6) of its original length, thus producing an increase of its temperature in adiabatic regime (during stretching time). In the second step, the hot heat exchanger (HHEX) was put in contact with the NR film, causing a heat transfer from the NR to the HHEX. After an adjustable contact time (1 s to 7 s in these experiments), the HHEX was moved back to its original position. The third step consisted in releasing the rubber until it reached to an elongation of 400% ($\lambda$ = 4), resulting in a temperature decrease. Finally, the fourth step was to put the cold heat exchanger (CHEX) in contact to the NR film to transfer the heat from the CHEX to the NR, removing the CHEX exchanger after the same contact time as HHEX. Then the 4-steps cycles are repeated, inducing an increase of the temperature difference between both exchangers, noted as temperature span ($\Delta T_{span}$). The temperature span between the CHEX and HHEX increased until it reaches a plateau after typically 500 s to 1000 s.

In order to maintain the same condition of heat transfer between the NR and both exchangers, a stabilization of the temperature of both exchangers near ambient temperature has been proposed. After the stabilization of the temperature span, heat was gradually injected in the CHEX in order to reduce the temperature span of the cooling device. When the CHEX temperature reaches the ambient temperature, the heat injected was a mean to measure the maximum cooling power ($PC_{max}$) of the device. For maintaining the HHEX temperature near to the ambient, forced air convection is used.

### 2.2. Description of the refrigeration proof of concept

A single stage experimental setup has been developed (figure 2). The setup consisted of two actuators, which were placed perpendicularly to each other. One of the actuators was stretching and releasing the NR film, which was fixed on one side on a fixed jaw and on the other side to the motor. The second actuator was moving two heat exchangers to put them alternatively in contact with the NR film. The HHEX was put in contact to the NR when stretched, in order to collect the produced heat. When the rubber was released, the CHEX was put in contact with the rubber film in order to absorb heat from CHEX and decrease its temperature further. The HHEX was made of a metal block equipped with cooling fans in order to stabilize it at ambient temperature. The CHEX was made of a thin stainless-steel plate representing the cold zone. It was thermally insulated on one side by a polystyrene block. Electrical flat resistors were added between the polystyrene block and metal plate, to be able to determine the *PC* as described above. The whole system has been put in an insulating box in order to stabilize the ambient temperature.

Different sensors were implemented to measure the force, displacement, heat flux and various temperatures. The force was measured by a load cell (RS PRO 50 kg compression & tension load cell) (response time ~5 ms) placed between the fixing jaw of the NR and the base structure. A position laser sensor (SICK sensor intelligence) (response time ~5–10 ms) measured the main actuator displacement, with a measurement range of 0 mm to 300 mm. Four type K thermocouples (response time ~100 ms) were installed: one thermocouple in the HHEX, in contact with the metal block, the second one in the CHEX in between the polystyrene block and the thin metal plate, the third thermocouple in the insulating box for ambient temperature measurement, and the fourth thermocouple outside the box. A data acquisition system (Krypton, Dewesoft, Slovenia) was used to measure sensors and temperature signals, with a sampling rate of 20 kHz for sensors signals and 100 Hz for thermocouples.

### 2.3. NR characterization

NR samples were purchased to Xinyinte Rubber Products Co., Ltd, China, in two different thicknesses (400 µm and 600 µm). It has been cut into dog-bone shape films to ensure a proper grip by the fixing jaws and a homogeneous stress.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** 4-steps cycle of the experimental setup for cooler proof of concept: (1) no contact and NR stretched to 600%; (2) HHEX contact leading to a heat transfer from NR to HHEX; (3) no contact and NR released to 400%; (4) CHEX contact leading to a heat absorption from NR to CHEX.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Picture of the 4-step experimental setup. (a) Complete experimental setup; (b) close up of the HHEX and the NR film; (c) close up of the exchangers and the sensors of the setup.</figcaption></figure>

Prior to the refrigeration device testing, the same experimental setup has been used to determine the adiabatic temperature change ($\Delta T_{adiab}$) of the NR when stretched between an elongation of 4–6. In this characterization both exchangers were removed.

For polymers, successive cycles may lead to an initial remnant deformation and a degradation of the elastocaloric activity [20, 21]. Therefore, for the characterization of the elastocaloric rubber, a training was performed before the adiabatic temperature measurements. Once the sample was setup, it was elongated several times from an elongation ($\lambda$) of $\lambda = 1$ to $\lambda = 5$. Then it was released to $\lambda = 1$ and several cycles were performed from $\lambda = 1$ to $\lambda = 6.3$. Once all the cycles were performed, the sample is released back to $\lambda = 1$. After a waiting time of 2 min, the sample retracted back almost to its original shape showing however a small remnant deformation. The sample was then mounted again to get rid of the residual deformation and the new length of the sample is considered as the initial length of sample. The successive characterization cycles did not reveal particular fatigue or evolution from one cycle to another.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Temperature (°C) measurement using IR image of the 400 µm thickness NR film at elongation 4 (top) and elongation 6 (bottom) for the Δ*T*<sub>adiab</sub> measurements.</figcaption></figure>

Therefore, for the experiments of the cooler proof of concept, no training cycles were performed beforehand. The sample was first setup in the experimental device and then stretched several times from $\lambda = 4$ to $\lambda = 6$, in order to prepare the system for the experiments. The samples were submitted to a high number of cycles (for example for 0.3 s of stretching time and 1 s of contact time cycle, the sample had been submitted to around 1100 cycles or 1350 cycles, depending on the sample tested). After all experiments were conducted, the NR 400 (400 µm NR thickness) was subjected to 6500 cycles for 16 experimental conditions (4 stretching times and 4 contact times) and the NR 600 (600 µm NR thickness) to 2800 cycles (1 stretching time and 4 contact times).

The adiabatic temperature span was measured by an infrared camera during cyclic stretching cycles between elongations from 4 to 6, in order to determine the adiabatic temperature variation ($\Delta T_{adiab}$) of the NR. The $\Delta T_{adiab}$ is determined using the IR pictures (figure 3). The initial active area of the samples, considered as that between the jaws in unstretched condition, was of size 40\*40 mm. The sample mass was 0.56 g for the 400 µm rubber film and 0.9 g for 600 µm one. Rectangular waveform of elongation was applied to the samples. The maximum average temperature over the measuring area was obtained from the picture at elongation 6 and the minimum average temperature was obtained from the elongation of 4. The difference of these two values is the $\Delta T_{adiab}$. It was determined, for the different elongation duration plateau of 1 s, 3 s, 5 s, 7 s, to be respectively 4.7 °C, 4.9 °C, 5.1 °C, 5 °C for the 400 µm and 4.6 °C, 4.7 °C, 4.8 °C, 4.9 °C for 600 µm respectively. This increase of $\Delta T_{adiab}$ might be associated with the crystallization kinetics [22, 23]. It might also be associated with the small difference in stress for the two different samples, as shown in figure 4, the stress for the NR 600 film is slightly higher (10% higher) than the NR 400 film for a given elongation, which may have an impact on the $\Delta T_{adiab}$. The figure 4 shows the stress-elongation curves of two NR film samples, the NR 400 and NR 600. Both samples were stretched from the elongation $\lambda = 4$ to $\lambda = 6$. The force and position were measured to obtain the engineering stress and elongation. Both stress-elongation curves have the same hysteresis shape, however the maximum stress is around 3.5 MPa for NR 400 and 3.9 MPa for NR 600.

Figure 5 shows the adiabatic variation of temperature of the sample NR 400. First, it shows a variation of around 4.6 °C. The $\Delta T_{adiab}$ for heating (loading) and cooling (unloading) of the material is remarkably symmetric as shown in figure 5(b). An indirect evidence is also the absence of temperature base line drift, showing the extremely low mechanical losses of the sample, and therefore the identical $\Delta T_{adiab}$ for loading and unloading steps.

For the adiabatic temperature measurements, the stretching time was 0.14 s (strain rate of 14 s⁻¹). It was a higher strain rate than the cooling experiment, as slower motions were needed in order not to have collisions between the moving parts of the setup. A higher strain rate for the characterization was preferred in order to minimize the thermal losses by convection and determine the elastocaloric properties more precisely. During cooling experiments, with a lower strain rate, the $\Delta T_{adiab}$ was monitored using the infrared camera and showed however similar results as the $\Delta T_{adiab}$ characterization measurements.

## 2.4. Experimental test campaign

The two different thicknesses (400 µm and 600 µm) of NR were tested in the cooling proof of concept. In the following the NR samples will be named NR 400 for the 400 µm thickness and NR 600 for the 600 µm thickness. Two parameters have been tested to evaluate their influence. First, the stretching time was tested for four different values (0.3 s, 0.5 s, 1 s, 2 s) for the NR 400. This parameter was tested to determine the
<figure><img src="image_7.png" /><figcaption>Figure 4. Engineering stress-elongation hysteresis of two samples of natural rubber films NR 400 (left) and NR 600 (right).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 5. (a) Adiabatic temperature measurement for NR 400 sample; (b) zoom on a few periods of the adiabatic temperature as a function of time.</figcaption></figure>

influence of the stretching time on the refrigeration device performances. Then for both samples, the contact time between the heat exchanger and the NR has been tested for four contact times (1 s, 3 s, 5 s, 7 s) in order to investigate the impact of the contact time of the effectiveness of the heat transfer between NR and the heat exchangers. Figure 6 gives the rectangular waveform used during the experimental campaign. The sample is quickly stretched then it stays loaded while it is in contact with HHEX. Then it is unloaded and stays released for during the contact time with CHEX.

For a stretching time of 0.3 s, the minimum cycle time is 3.6 s ($f = 0.3$ Hz) and the maximum cycle time is 15.6 s ($f = 0.06$ Hz), which represented 1100 and 250 cycles respectively for the cooler temperature span and PC determination.

## 2.5. Methodology for performances calculation

The different sensors of the experimental setup allow to determine different useful parameters to have a better understanding of the performances of the system. The force and the displacement gave the instantaneous mechanical power $P_{\text{mech}}$ in the setup.
<figure><img src="image_9.png" /><figcaption>Figure 6. Waveforms of the elongation for the cooling characterization experiments, (a) 1 s of contact time; (b) 7 s of contact time.</figcaption></figure>

By using the resistors, the PC was obtained, which allowed obtaining the COP of the system knowing the mechanical work. The following formulas were used:

$$P_{\text{mech}} = f \int_{0}^{\frac{1}{f}} F \frac{\partial u}{\partial t} dt \qquad (1)$$

where F, u, and 1/f are the mechanical force of the actuator, its displacement, and the period of the cycle, respectively, with f being the frequency

$$PC = RI^2 \qquad (2)$$

where R and I are the resistance value and the applied DC current

$$COP = \frac{PC}{P_{\text{mech}} + P_{\text{actuator 2}}} \qquad (3)$$

$P_{\text{actuator 2}}$ is the average power from actuator 2 over one cycle, which is the actuator moving the exchangers. Since it is only moving the exchangers to put them in contact alternatively with the NR film, there was negligible force between the exchangers and the NR (<0.1 N). Therefore $P_{\text{actuator 2}}$ was neglected in the COP calculation.

## 3. Results

Figure 7 shows the evolution of the temperatures as a function of time for the two samples NR 400 and NR 600 under the same experimental conditions of 0.3 s of stretching time and 1 s of contact time (f = 0.3 Hz). Each plateau corresponded to a 50 mW increment of the PC leading to a PCmax of 300 mW and 350 mW respectively for the NR 400 and NR 600. The temperature of HHEX was continuously stabilized at ambient temperature using forced air convection.

Before supplying the heating resistances, the CHEX temperature decreased until the maximum temperature variation $\Delta T_{\text{span max}}$ was reached. Once its stabilized, heat was injected in the resistors gradually to decrease the $\Delta T_{\text{span}}$ until the temperature of CHEX reached or exceeded the temperature of the HHEX. The maximum PCmax of the NR film is determined by the last value of heat injected in CHEX before the temperature of the HHEX exceed ambient temperature.

For the NR 400, four different stretching times were tested. Figure 8 gives the maximum temperature span ($\Delta T_{\text{span max}}$) and the PCmax as a function of the contact time. A stretching time of 0.3 s was found to maximize both $\Delta T_{\text{span max}}$ and PCmax. Since 0.3 s of stretching time appeared to be the best stretching time in this case, the value was kept for the following tests. Higher stretching time decreased the performances of the system ($\Delta T_{\text{span}}, PC$).
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Temperature profile of the NR 400 (left) and NR 600 (right) for 0.3 s of stretching time and 1 s of contact time. The different plateaus correspond to the increase of the injected heating power (50 mW each), in order to determine the cooling power of the cooler.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 8.** Maximum temperature span ($\Delta T_{span max}$) and maximum cooling power (PC$_{max}$) as a function of contact time for 4 different stretching times for NR 400.</figcaption></figure>

The thicker rubber, the NR 600, exhibited a slightly higher $\Delta T_{span max}$ than the NR 400 for all tested contact times (figure 9). The highest $\Delta T_{span max}$ was achieved for 3 s of contact time for NR 400 and 5 s for NR 600. Similar optimum conditions can be seen for the PC. The coolers characteristics, i.e. temperature span versus PC, are displayed for both rubber thicknesses and various contact times in figure 10. The results show very similar linear decrease of the $\Delta T_{span}$ with increasing PC for the different contact time and for the two rubber thicknesses. NR 600 sample exhibited higher $\Delta T_{span}$ and higher PC than the NR 400. After 3 s of contact time, the PC tended to decrease for both samples. For higher contact time (5 s and 7 s), the PC is slightly higher for the NR 600 around 350 mW. However, the four different contact times show relatively comparable performances for both NR 400 and NR 600. The NR 600 shows slightly higher $\Delta T_{span}$ and PC for 7 s of contact time ($f = 0.06$ Hz) than the NR 400. Figure 10 also shows that after 3 s of contact time, no significant improvement in the performances of the system was found.

## 4. Discussion

The different results presented before suggested that among the experimental conditions tested, a stretching time of 0.3 s was maximizing the $\Delta T_{span}$ and PC for both samples. It also appeared that there is an optimal contact time of 3 s to 5 s, respectively $f = 0.13$ Hz and $f = 0.09$ Hz. For longer contact time of 7 s ($f = 0.06$ Hz), there is no improvement for the temperature span while the PC decreased by approximately 30% from its maximum. The PC$_{max}$ measured was almost 400 mW for a 3 s contact time which seemed to be the PC$_{max}$ that can be experimentally measured for these samples of NR.

The $\Delta T_{span}$ of the different experimental conditions appeared to be lower than the adiabatic temperature change of either material, with a maximum temperature span ($\Delta T_{span max}$) of 1.9 K compared to an adiabatic temperature change ranging between 4.7 K and 5.1 K, which is around 40% of the $\Delta T_{adiab}$ at the most. This difference between the temperature span of the system and the adiabatic temperature span was similar than for NiTi alloys from literature. In Ossmer and al [16], the temperature span of their heat pump reached about 5 K, whereas the adiabatic temperature difference achievable by the NiTi alloys was 16 K. However, in
<figure><img src="image_12.png" /><figcaption>**Figure 9.** Maximum temperature span ($\Delta T_{span max}$) as a function of contact time for a stretching of 0.3 s for both rubber samples (left), Maximum cooling power (PC$_{max}$) as a function on contact time (right).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Temperature span ($\Delta T_{span}$) as a function of cooling power (PC) for different contact times for NR 400 and NR 600. The stretching time was 0.3 s for all of the contact times: (a) 1 s of contact time (f = 0.3 Hz); (b) 3 s of contact time (f = 0.13 Hz); (c) 5 s of contact time (f = 0.09 Hz); (d) 7 s of contact time (f = 0.06 Hz).</figcaption></figure>

an ideal system without thermal losses, the $\Delta T_{span max}$ should reach the $\Delta T_{adiab}$ of the material. One explanation might be that the thermal losses of the CHEX were responsible for the reduced temperature span. A second explanation can be the presence of a gradient in the NR film, leading to a temperature on the side on contact with HHEX to be different than the temperature on the side in contact with CHEX, leading to a reduced heat transfer. In addition, when the temperature reaches the $\Delta T_{span max}$ in the absence of heating source in the CHEX, the NR still continuously extract heat from the CHEX, in order to compensate for the thermal losses. It should be noted that on the heat pump characteristics, the $\Delta T_{span}$ vs. PC showed very similar linear trends, which may be associated with the thermal losses too. The problem of the thermal losses was probably linked also to the mass ratio of the system (heat exchangers) compared to the elastocaloric material, because the material surface area is small compared to that of the various components of the system. This enhanced the passive thermal losses in the heat exchangers, which may reach that extracted by the elastocaloric material in each cycle even at reduced temperature span. The thermal losses are not yet been clearly quantified and should be further investigated in order to optimize the heat transfer and enhance the
performances of the system. The direct thermal exchanges between HHEX and CHEX (by radiation for example) had been considered negligible as both exchangers moved in a synchronized manner and were separated by the film of rubber. However, each heat exchanger is subjected to thermal losses with outer medium by conduction (fixing parts), convection and radiation, leading to a $\Delta T_{span}$ lower than $\Delta T_{adiab}$.

During the motion of the NR film, the material being in contact with the ambient air, an additional possible heat loss of heat might occur. In order to check this point—and more generally speaking to assess the heat transfer performance—it is defined in this work a coefficient of Heat Transfer effectiveness ($HT_{eff}$). It consists of the ratio between the actual PC of the system and the maximal theoretical PC. This latter theoretical PC is calculated from the isothermal entropy change of the NR film being estimated from the adiabatic temperature change,

$$Q_{ult} = \rho C_p V \Delta T_{adiab} \quad (4)$$

where $\rho$, $C_p$, $\Delta T_{adiab}$ and $V$ are the density of the NR, its heat capacity, the adiabatic temperature change, and the volume of the film in contact with the heat exchangers respectively. It corresponds to the maximum heat that the NR may extract from the CHEX at each cycle in an ideal case at no temperature span.

It is indeed assumed an ideal case where the heat transfer between the elastocaloric rubber and the heat exchanger is complete, i.e. no thermal resistance at the interface and infinite diffusivity within the rubber film. Therefore, $Q_{ult}$ is independent of the conductivity and independence of the actual time constant of the heat exchange. $Q_{ult}$ being the maximum value attainable by the heat flux in case of a perfect heat exchange, a comparison with experimental values, gives an estimate of the effectiveness of the heat transfer.

The ultimate cooling power $PC_{ult}$ was then calculated from the cycle duration $1/f$:

$$PC_{ult} = Q_{ult} / \frac{1}{f} \quad (5)$$

The heat transfer effectiveness is defined as being the ratio of the actual $PC_{max}$ and the ultimate one (case of an ideal heat exchange)

$$HT_{eff} = PC_{max} / PC_{ult} \quad (6)$$

where $PC_{max}$ is the maximum value of the PC

Figure 11 shows that the NR 400 exhibited a similar $HT_{eff}$ than the NR 600. Indeed, the NR 400 and NR 600 could reach almost to 60% for 7 s of contact ($f = 0.06$ Hz). The sample size use for the calculation was 40*40 mm. The $HT_{eff}$ did not reach 100% for the longest contact time. This might be due to the fact that not all the sample was in contact with the CHEX. For all the tested contact time values, the NR 400 presented is slightly higher $HT_{eff}$. This can be explained by the thickness of the rubber, a thinner sample facilitates the heat transfer to the exchangers. However, for the NR 600, the rubber being thicker, a higher temperature gradient may be generated within the rubber film, leading to a less effective heat transfer to the heat exchanger. It seems that for a long contact time, a limit of $HT_{eff}$ is reached, that might be due to the thermal heat losses during the heat transfer.

In the case of NiTi alloys in similar single state device, considering the data from Ossmer et al [15, 16], it can be inferred similarly from their work an ultimate cooling power around 56 mW for an actual cooling power measured on the device of 45 mW, showing also a heat transfer effectiveness that may be nearly 80%.

On the contrary, regenerative systems usually present a gain in temperature span that could reach several times the adiabatic temperature change (called regeneration factor), at the price of a degraded heat transfer effectiveness. For example, in Sebald et al [24], a maximum experimental PC of around 1.5 W was found, for a total mass of rubber of 10.6 g and 0.1 Hz working frequency, thus 142 W kg⁻¹, leading to an ultimate cooling power of around 6.8 W calculated with equation (5) (heat transfer effectiveness of around 22%). In Ahčin et al [25], a maximum specific PC as high as 3700 W kg⁻¹ was experimentally obtained, whereas the ultimate cooling power is about 9600 W kg⁻¹ (frequency of 2 Hz, specific heat of 0.32 J (g K)⁻¹ adiabatic temperature variation of 15 K), denoting a heat transfer effectiveness of about 40%. From the results presented here, and from literature data on other single stage systems, it may be confirmed that the single stage process may lead to a higher heat transfer capability of the elastocaloric material, but limits the temperature span of the device.

During the experiment, the maximum COP (COP$_{max}$), was determined in order to assess the cooling capacity effectiveness of the device. The COP, was calculated as a ratio of the $PC_{max}$ and the average of the mechanical power ($P_{mech}$). In order to calculate $P_{mech}$, the force and position of the actuator of the NR were measured. Figure 12 shows the force and speed of the actuator as well as the resulting $P_{mech}$. It shows that $P_{mech}$ signal had a symmetric shape when stretched (positive values) and released (negative values). The two
<figure><img src="image_14.png" /><figcaption>Figure 11. Heat transfer effectiveness as a function of the contact time for NR 400 and NR 600.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 12. Experimental mechanical force, speed and mechanical power for several contact times and a stretching time of 0.3 s; for a contact time of 1 s (f = 0.3 Hz); (a) force measurement; (b) speed measurement; (c) instantaneous mechanical power; for a contact time of 3 s (f = 0.13 Hz); (d) force measurement; (e) speed measurement; (f) instantaneous mechanical power; for a contact time of 5 s (f = 0.09 Hz); (g) force measurement; (h) speed measurement; (i) instantaneous mechanical power; for a contact time of 7 s (f = 0.06 Hz); (j) force measurement; (k) speed measurement; (l) instantaneous mechanical power.</figcaption></figure>

peaks appeared to be almost of the same area, showing that the elastic energy is fully recovered when unstretching. This result is in line with other observations of the ultra low mechanical losses in elastocaloric polymers [24, 26, 27].

The released energy when unstretching being slightly smaller than the energy acquired through the stretching, the average mechanical power was found to be much lower than the peak value (around 0.02 W in the case of a contact time of 3 s). In the case of a stretching time of 0.3 s and a contact time of 3 s, the maximal PC being 0.30 W, the ratio of PC and $P_{\text{mech}}$ was found to be around 15. Of note, the determination of the average mechanical power was conducted using a conservative correction of the time delay of the sensors in order to maximize the average mechanical power and to avoid any overestimation of the COP given in table 1.
<table><caption>**Table 1.** COP<sub>max</sub> values measured for NR 400.</caption><thead><tr><th>Contact time (s)</th><th>1.00</th><th>3.00</th><th>5.00</th><th>7.00</th></tr></thead><tbody><tr><td>NR 400</td><td>9.8</td><td>15.2</td><td>13.4</td><td>12.2</td></tr></tbody></table>

The determination of the COP<sub>max</sub> (at maximal power and ΔT<sub>span</sub> = 0) remained difficult because of the very small level of mechanical losses in the NR film. P<sub>mech</sub> values (being the average power over one cycle) are very small compared to the peak power observed during the refrigeration cycle, its determination is therefore highly sensitive to the noise level. Consequently, the COP is only presented for the cases where its determination was undoubtful (table 1). For example, in Sebald et al [24], using a regenerative system based on NR film, the COP obtained is around 6, lower than the COP presented here, however the temperature span is much higher, more than 8 K, than 1.9 K found in this work, these differences in performances might be due to differences in the heat transfer strategy.

## 5. Conclusion

This work addressed the design of an elastocaloric cooling proof of concept, using solid-solid heat exchange between the elastocaloric material and the heat exchangers. The temperature span, the PC and the COP were experimentally determined for various operating conditions. Two thicknesses of rubber were investigated, the NR 400 and NR 600, respectively of 400 µm and 600 µm. The study of the most interesting stretching time has shown that 0.3 s was the best value, in the cases considered, maximizing both the temperature span and the PC. It has also been shown that the optimal contact time was 3 s for NR thicknesses of 400 µm and 600 µm. Longer contact time led to a decrease of the PC due to the increase of the cycle duration time, not compensated by a higher heat exchange with the NR. The highest PC was found to be 390 mW (430 W kg<sup>-1</sup>) for the NR 600, and 305 mW (540 W kg<sup>-1</sup>) for the NR 400, whereas the temperature highest span was 1.8 °C. The measurement of the heat transfer effectiveness—defined as the ratio of the actual heat absorbed from the CHEX to the theoretical one—increased with the contact time thanks to a better heat transfer between the rubber and the heat exchangers. For NR 400 and NR 600 nearly 60% the heat absorption of the rubber was reached for a contact time of 7 s. The COP<sub>max</sub> of the system was determined to be around 15 (3 s of contact time) for the NR 400. In conclusion, it was found that the single stage principle with solid-solid heat exchanges resulted in a higher PC and heat transfer effectiveness compared to regenerative solid-liquid heat exchange, at a price of much lower temperature span. In further work a special attention should be paid on the thermal losses quantification that reduced the temperature span of the system, as well as testing other elastocaloric polymer samples, with different chemical composition and different fabrication process, in order to find an optimal material in terms of elastocaloric activity and thermal properties.

## Data availability statement

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

## Acknowledgments

This work was performed within the framework of the International Research Network ELyT Global.

## ORCID iDs

Marianne Sion https://orcid.org/0009-0007-2536-9719

Gildas Coativy https://orcid.org/0000-0003-1390-8686

Atsuki Komiya https://orcid.org/0000-0002-1645-6040

Gaël Sebald https://orcid.org/0000-0003-4725-3489

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