General Concepts
More than 20% of overall energy usage is made up of refrigeration and air conditioning. The most popular cooling method nowadays is Vapour Compression (VC), which is not environmentally friendly due to the usage of refrigerants that contribute to the greenhouse effect and because its technological capabilities have been achieved. This explains why the scientific community is interested in creating novel, non-conventional refrigeration technologies. Among them there are solid-state refrigeration-based technologies that benefit from: (i) use of solid refrigerants with no direct greenhouse effect, since zero is their Global Warming Potential (GWP); (ii) energy performance potentially up to +50 + 60% than VC systems [
1]. The caloric effect of solid-state refrigerants manifests itself as a temperature variation of the caloric material in an adiabatic transformation changing the intensity of the applied field. In the solid-state refrigeration technologies one of the most promising is that based on elastoCaloric Effect (eCE) [
2]. Shape Memory Alloys (SMA) are used as solid refrigerants and exhibit superelasticity and the shape memory phenomenon, meaning that they may return to their original shape after being stressed or relaxed. A SMA can exist in the structural states of austenite and martensite, and the transition from one state to the other can also be obtained by the loading and the unloading process [
3].
The elastoCaloric (eC) SMAs’ above-mentioned behavior enables the design of two different thermodynamic cycles. The direct thermally driven cycle, which could be used in a heat engine, and the inverse stress-driven cycle, which could be used in a cooling or heating pump system. In many well-known thermodynamical cycles, the inverse stress-driven cycle can be used to influence how a cooling system behaves [
4]. The reverse Brayton-based AeR cycle, also known as the Active elastocaloric Regenerative refrigeration (AeR) cycle, is the most used eC refrigeration cycle. The elastocaloric SMA also serves as a means of regeneration in an AeR-based system, and a secondary fluid acts as a means of heat transfer. Regeneration allows for the recovery of heat that would otherwise be lost in a single stage cycle. As a result, the AeR cycle can ensure that the temperature spread across the regenerator is bigger than the adiabatic temperature jump (Δ
Tad), which belongs exclusively to eCE and to the material itself, it is defined as the temperature change that occurs when the elastocaloric material undergoes adiabatic deformation, i.e., deformation without heat exchange with the external environment. The maximum temperature span that can be detected in the regenerator without regeneration is capped by the Δ
Tspan.
When the elastocaloric material is loaded, its temperature rises; next, a Heat Transfer Fluid (HTF) is crossed over it to release heat; next, it is unloaded, causing its temperature to drop and finally, a cold HTF is crossed over it to absorb heat from the thermal load. The benefits of elastocaloric refrigeration include: (1) readily available and inexpensive refrigerant materials; and (2) ease of delivering a mechanical field of high intensity to the material.
State of the Art
Ten years ago, elastocaloric refrigeration came into the public eye. Since then, scientists have concentrated their efforts on developing the devices and finding new promising materials that are appropriate for cooling and heat pumping. Additionally, modeling is important because it is linked to the branch of device realization and aids in optimization.
a) Nickel Titanium is the benchmark elastocaloric substance that has been investigated and used the most. Even if it can withstand up to 9% strain, the binary alloy contacts 25.5 K and 17 K for 5% strain (loading and unloading) [
5,
6]. The binary alloy also has other benefits, such as strong shape memory qualities, widespread market availability, and a tolerable fatigue life for eC applications. The latter is essential since a material with a short fatigue life has a short service life. Hysteresis can be reduced or the fatigue life can be improved with the aid of Ni–Ti alloys made of three or four components [
7]. Chluba et al. investigated and showed in 2015 [
8] that the addition of Cu to Ni–Ti alloys can offer up to 10
7 cycles of loading and unloading before cracks emerge. Due to their cheaper prices and potential for eCE to develop under stress values lower than those for NiTi-based alloys, Cu- and Fe-based alloys were also used in eC procedures. The greatest Δ
Tad reported for the Fe-based alloys is 5 K, while the highest Δ
Tad detected in Cu-alloys is 15 K under 130 MPa of stress. Shape Memory Polymer (SMP) is a new class of elastocaloric materials that also includes natural or synthetic rubbers [
9‐
11]. The rubbers’ biggest drawback is the extreme elongation required for eCE manifestation (strain up to 600% of the unloaded length).
b) To the best of our knowledge, there have been slightly more than fifteen elastocaloric devices created in laboratories up to the year 2023 [
12]. Some of these devices experiment with the AeR cycle, while others use the solid-to-solid cycle. While some of them are rotary, some of them are forced by linear drives. Cui et al. [
13] unveiled the first eC prototype in 2012; it was a rotating device made of two rings through which NiTi wires were fastened. The maximum temperature span (Δ
Tspan) recorded was 17 K but, due to the device's design, the lifetime of the refrigerant was severely constrained by how easily cracks might form. Greco et al. and Kabirifar et al. [
12,
14] examined the eC devices developed in 2019. Interesting among them was a rotary system [
15] that uses the quaternary alloy Ni
45Ti
47.25Cu
5V
2.75 to extend the life of the materials. Other smaller size elastocaloric devices were created in addition to the previously stated devices that were focused on air conditioning or heat pumps. The bridge system created by Bruederlin et al. [
16] is noteworthy since it does not require HTF because a slice of elastocaloric material is loaded through bending while also being transported up and down. The device was subsequently upgraded [
17] by using a TiNiFe slice as the refrigerant. Through the cyclical stretching of a few Ni-Ti wires, the microscale cooler developed by Snodgrass and Erickson [
18] in 2019 demonstrated the largest temperature span (28.9 K). In parallel, Ossmer et al. [
19] demonstrated a miniature elastocaloric cooler that could produce 2.9 W g
-1 of cooling power and 3.2 of coefficient of performance (COP).
The most recent elastocaloric devices were presented in 2022 by Xi'an Jiaotong University [
20], University of Ljubljana [
21], Technical University of Denmark in collaboration with the German Fraunhofer Institute for Physical Measurement Techniques [
22], and University of Maryland [
23]. Materials from the binary NiTi alloy with a variety of compositions are employed as elastocaloric refrigerants. The greatest temperature span of the Chinese prototype [
20] is 9.2 K and it uses air as the heat transfer fluid. The other three, where water circulates as HTF, are all compression-loading based. The Slovenian device [
21] (mounting tubes of Ni
55.8Ti
44.2) reached the maximum temperature span of 31.3 K, which is the highest value ever at best we know. On the other hand, the DTU device’s [
22] peculiarity is to demonstrate a promising 1071 W kg
−1 as specific cooling power, determined by using Ni
56.25Ti
43.75 tubes in an AeR cycle. The University of Maryland’s prototype [
23] is a linear alternate mounting of a staggered Ni
50.5Ti
49.5 tube. The highest temperature range that has been observed is 16.6 K, however no information regarding cooling power or COP has yet been provided.
In 2022 the group of University of Naples Federico II introduced a hydraulic-driven rotary elastocaloric device [
24]. The elastocaloric material is shaped as 600 wires (diameter 0.5 mm and length 300 mm) arranged in the annular section between two concentric cylinders (internal radius of 120 mm, an external radius of 135 mm, and a length of 300 mm). A maximum COP of 6.22 (corresponding to a second law analysis efficiency of 60%) was evaluated under an airflow speed of 6 m s
-1 and a frequency of 0.3 Hz, corresponding to a utilization factor of 0.44. 28.5 K and 5400 W kg-1 are the reached peaks of temperature span and cooling power [
25,
26].
One can see from the state of the art that there are still many steps to be done before an elastocaloric device can be produced on a wide scale. One of the causes is the lifespan of the devices as a whole and the eC materials used. The many studied and investigated areas of application for eC technology are refrigeration and air conditioning.
The short fatigue life of the eC materials combined with the type of applied stress (to make eCE manifest in the AeR cycle) as well as the achievement of optimal operational conditions is the bottleneck of the eC technology. Modeling allows for the optimization of the device’s dimensions and operational circumstances. With the exception of the models created by Cirillo et al. [
27], where a group of wires was two-dimensionally studied, the majority of eC models established are 1D [
28].
Regarding the type of loading used, it is unavoidable that cracks may develop over time due to the mechanical solicitations the material is subjected to throughout the cycles of loading and unloading. Xu et al have deeply reviewed tension-compression pro and cons of NiTi alloys [
29] The crack growth that occurs during loading and unloading cycles is a drawback of tension. Cycles of SMA trainings before employment can improve the resistance to fatigue life of NiTi alloys [
2,
30]. Compression has the drawback of reducing the amount of available heat transfer surface [
31]. Although there have been several studies on the fatigue life of SMAs (mainly the binary NiTi alloy) under tension, there have been far fewer investigations on the same issue under compression. Studies, for instance, demonstrate that a durable operation (10
5 cycles) can be accomplished in the NiTi alloy with strains of around 2%, which translates to a comparatively tiny ΔT
ad. With the potential to attain up to 70 million loading/unloading cycles, the first investigations on NiTi cylinders and cubes under compression revealed a considerable improvement compared to tension [
32,
33]. In addition, a recent study [
34] focused on torsion as an alternative to compression and tension, showing a substantial increase in the material's lifetime even with a smaller amount of adiabatic temperature change. It appears that bending is a good solution for both the issue of cracks and acceptable temperature variations. According to Sharar et al. [
35], axisymmetric bending permits a fivefold decrease in the force needed for similar COP and temperature span, which directly translates to a decrease in the size, weight, and power input needed for eC cooling systems. These advantages of loading by bending can all be seen as a promising way to get over some of the major obstacles that elastocaloric system realization faces.
Aim of the Investigation
CHECK TEMPERATURE is the acronym of “Controlling the Heating of Electronic Circuits: a Key-approach Through Elastocaloric Materials in a Prototype Employing them as Refrigerants of an AcTive Ultrasmall Refrigerator”. In order to cool electrical circuits, the CHECK TEMPERATURE project aims to create the first elastocaloric device customized for this purpose. The plan has been to create a device based on the AeR as the thermodynamic cycle and bending as the loading/unloading mode, even if it is small-scale and unlike the ones that already exist.
The purpose of this study is to provide the findings of a numerical analysis used to build the CHECK TEMPERATURE prototype, which involved optimizing both the working environment and the geometrical configuration for the assembly of the elastocaloric material in the channel.
The following are the primary novelties in this paper:
-
The area of application. In reality, the cooling of electronic circuits is an intriguing yet unexplored area for elastocaloric refrigeration. There are several applications where a more sophisticated cooling system is necessary to prevent the devices’ working temperatures from continuously rising. The failure probability of electrical circuits increases exponentially as temperature rises. The previously reviewed elastocaloric devices don’t specifically target this field.
-
The numerical model and analysis were accurate and comprehensive throughout. The majority of elastocaloric system models that have been created and presented to the scientific community are 1D [
28] and there are not published studies that draw broad maps of elastocaloric device performances on a small scale while simultaneously optimizing the geometrical design and operational parameters.
The specifications for electronic cooling depend on the specific requirements of the application and the electronic components involved. Some of the key parameters may include determining the maximum allowable temperature for electronic components during operation and calculating the amount of heat produced by electronic components, which must be dissipated to prevent overheating. In the specific case under consideration, the cooling of a computer server has been examined, which cannot exceed a temperature of 85 °C and has a power dissipation requirement of approximately 50 W. The values of ΔT (temperature variation) and the cooling powers that the EC device should meet depend on the specific application and cooling requirements. Optimal ΔT values should be at least 10 K. A computer server typically uses a system of fans and a bulky finned structure to dissipate heat. The term 'ultrasmall' implies that the device is extremely small in size compared to those commonly used for these applications. The reduced size can be advantageous in terms of space and weight.