Luca Cirillo
| Sabrina Gargiulo | Adriana Greco | Claudia Masselli | Vincenzo Orabona | Lucrezia Verneau*
© 2025 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
As electronic devices become increasingly powerful, the demand for efficient and sustainable cooling solutions has intensified. Traditional cooling methods, such as air and liquid cooling, face limitations in energy efficiency and scalability. The CHECK TEMPERATURE project explores an innovative approach to thermal management by leveraging elastocaloric technology for electronic circuit cooling. Elastocaloric cooling is based on the stress-induced phase transformation in shape memory alloys (SMAs) enabling highly efficient employment as solid-state refrigerants. The elastocaloric technology offers high thermal performance, compact design, and environmentally friendly operation, eliminating the need for conventional fluids refrigerants based on vapor compression. To evaluate its potential, a 2D numerical model of CHECK TEMPERATURE has been developed to analyze the energy performance of the system and simulate the elastocaloric effect in electronic cooling applications. The model provides insights into heat transfer dynamics, material behavior, and overall efficiency, guiding the optimization of elastocaloric cooling architectures. The elastocaloric effect shown by the binary Ni-Ti alloys has been also modelled, investigated and integrated into the 2D numerical tool. This contribution will cover theoretical modeling, numerical analysis, and analysis of the energy performance of elastocaloric cooling for electronic circuits. The results demonstrate the potential for a promising, scalable, and sustainable cooling technology, addressing the increasing thermal management challenges of next-generation electronics.
elastocaloric cooling, electronic circuits cooling, shape memory alloys, 2D numerical model, phase transformation, sustainable cooling
This work introduces two elastocaloric cooling system configurations designed for electronic applications, namely a bending-based and a tensile-based prototype as visible in Figure 1. Both systems utilize Ni50.8Ti49.2 shape memory alloy wires as the active cooling medium and air as the Heat Transfer Fluid (HTF).
The bending-mode configuration comprises two stacked microchannels, each containing arrays of NiTi wires. The core mechanism is a central oscillating plate that cyclically deflects upward and downward, inducing mechanical bending in the wires located in either channel. The air passes through these channels in counterflow during alternating thermal phases, thereby promoting effective heat exchange. This architecture benefits from faster heat cycling due to the simultaneous operation of the upper and lower wire sets during different AeR cycle phases.
In the tensile design, the elastocaloric wires are mounted in two parallel beds and loaded axially via a piston-driven support mechanism. This setup allows for symmetric stress application and partial energy recovery, as the unloading of one bed assists the loading of the other. The air flows through each bed in a direction coordinated with the thermal phase of the wires. Although this configuration offers robust thermal gradients, it requires more complex mechanical actuation.
(a) Bending
(b) Tensile
Figure 1. Layouts of system configurations
Both prototypes incorporate a common hydraulic loop, consisting of dual fans, insulated galvanized steel ducting, and electronic control valves. Motorized dampers regulate airflow distribution, while embedded thermocouples and Resistance Temperature Detector (RTD) sensors track temperature profiles. Additional instrumentation includes anemometers and pressure sensors for fluid dynamics analysis. To simulate a realistic electronic thermal load, a resistive heating element is attached to the target cooling surface.
A two-dimensional (2D) Finite Element Method (FEM) model was implemented in COMSOL Multiphysics to simulate the thermal behavior and energetic performance of the two configurations. The model simulates a full AeR cycle: loading, heat rejection, unloading, and heat absorption.
3.1 Governing physics and boundary conditions
The model solves the coupled Navier-Stokes, energy, and phase transition equations for both air and the elastocaloric wires. Airflow is considered incompressible and adiabatic, with negligible viscous dissipation:
$\left\{\begin{array}{c}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0 \\ \frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}=-\frac{1}{\rho_{\text {air }}} \frac{\partial p}{\partial x}+v\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right) \\ \frac{\partial v}{\partial t}+u \frac{\partial v}{\partial x}+v \frac{\partial v}{\partial y}=-\frac{1}{\rho_{\text {air }}} \frac{\partial p}{\partial y}+v\left(\frac{\partial^2 v}{\partial x^2}+\frac{\partial^2 v}{\partial y^2}\right) \\ \frac{\partial T_{\text {air }}}{\partial t}+u \frac{\partial T_{\text {air }}}{\partial x}+v \frac{\partial T_{\text {air }}}{\partial y}=\frac{k_{\text {air }}}{\rho_{\text {air }} c_{\text {air}, p}}\left(\frac{\partial^2 T_{\text {air }}}{\partial x^2}+\frac{\partial^2 T_{\text {air }}}{\partial y^2}\right) \\ \rho_{\text {SMA }} c_{\text {SMA}, p} \frac{\partial T_{\text {SMA }}}{\partial t}=k_{\text {SMA }}\left(\frac{\partial^2 T_{\text {SMA }}}{\partial x^2}+\frac{\partial^2 T_{\text {SMA }}}{\partial y^2}\right)+g^{\prime \prime \prime}\end{array}\right.$ (3)
Heat generation in the SMA wires is captured through transient source terms that model latent heat effects and mechanical work input:
${g}'''=\frac{\rho cT\left( \xi \right)}{{{t}_{load}}}$ (4)
where, ΔT has been evaluated through the Lagoudas Model [12]:
$\Delta T_{a d}(\xi)=-\frac{\frac{\xi \rho b^M-\sigma H-\frac{1}{2} \Delta S M_s}{\rho \Delta s_0}\left(\alpha^A+\xi\left(\alpha^M-\alpha^A\right)\right)-\left[\frac{H s g n(\sigma)+\Delta S \sigma}{\rho \Delta s_0\left(M_s-M_f\right)}\left(-Y+\xi b^M \rho-\sigma H-\frac{1}{2} \Delta S \sigma^2+\rho \Delta S M_s\right)\right]}{\rho c-\left[\frac{\rho \Delta s_0}{\rho \Delta s_0\left(M_s-M_f\right)}\left(-Y+\xi b^M \rho-\sigma H-\frac{1}{2} \Delta s \sigma^2+\rho \Delta S M_s\right)\right]} \Delta \sigma$ (5)
The thermal hysteresis of the SMA is considered by adopting different values of latent heat for loading and unloading, as well as the work required [13]. According to Tušek et al. [14], it is possible to estimate the net-work as the area enclosed by the hysteresis cycle defined by the transformations in s-T plane as:
${{w}_{net}}={{w}_{load}}-{{w}_{unload}}$ (6)
The kinetics of the martensitic transformation are modeled using phase fraction rate equations from Qian et al. [15], incorporating transformation probabilities dependent on stress and temperature.
The martensite volume fraction ${{\dot{\xi }}_{M}}$ is evaluated through the Eq. (6):
${{\dot{\xi }}_{M}}=-{{\xi }_{M}}{{\text{ }\!\!\psi\!\!\text{ }}^{MA}}\left( {{T}_{SMA}},\sigma \right)+{{\xi }_{A}}{{\text{ }\!\!\psi\!\!\text{ }}^{AM}}\left( {{T}_{SMA}},\sigma \right)$ (7)
during the A-M and the M-A transformations:
${{\xi }_{A}}+{{\xi }_{M}}=1$ (8)
The transition probabilities ${{\psi }^{MA}}$ and ${{\psi }^{AM}}$ are calculated through the approach proposed by Qian et al. [15]:
${{\text{ }\!\!\psi\!\!\text{ }}^{AM}}\left( {{T}_{SMA}},\sigma \right)=\frac{1}{\text{ }\!\!\theta\!\!\text{ }}\frac{\text{exp}\left( -a{{\left( \frac{{{\sigma }_{AM}}\left( {{T}_{SMA}} \right)-\sigma }{{{E}_{A}}} \right)}^{2}} \right)}{\text{erf}\left( \sqrt{a}\frac{{{\sigma }_{AM}}\left( {{T}_{SMA}} \right)-\sigma }{{{E}_{A}}} \right)+\text{erf}\left( \sqrt{a}\frac{{{\sigma }_{AM}}\left( {{T}_{SMA}} \right)+\sigma }{{{E}_{A}}} \right)}$ (9)
${{\text{ }\!\!\psi\!\!\text{ }}^{MA}}\left( {{T}_{SMA}},\sigma \right)=\frac{1}{\text{ }\!\!\theta\!\!\text{ }}\frac{\text{exp}\left( -b{{\left( \frac{{{\sigma }_{MA}}\left( {{T}_{SMA}} \right)-\sigma }{{{E}_{M}}} \right)}^{2}} \right)}{\text{erfc}\left( \sqrt{b}\frac{{{\sigma }_{MA}}\left( {{T}_{SMA}} \right)-\sigma }{{{E}_{M}}} \right)}$ (10)
where:
$a=\frac{{{E}_{A}}{{V}_{SMA}}}{2B{{T}_{SMA}}}$ (11)
$b=\frac{{{E}_{M}}{{V}_{SMA}}}{2B{{T}_{SMA}}}$ (12)
Boundary conditions include a fixed air inlet temperature (293 K), controlled inlet velocities (3–11 m/s), and thermally insulated outer surfaces. The model captures heat transfer during both during mechanical actuation and airflow stages.
3.2 Material properties and kinetics
The employed SMA is Ni50.8Ti49.2 [16] subjected to treatments that ensure a longer fatigue-life. An 8% strain with a strain rate of 0.025 s-1 is considered for loading/unloading cycles. A 0.2 s time of loading/unloading is selected, so the transformation can be considered as adiabatic.
Ni50.8Ti49.2 wires are modeled with a thermal conductivity of 15 W/mK, specific heat of 550 J/kgK, and density of 6500 kg/m³. Latent heat and transformation hysteresis differ between tensile and bending configurations.
3.3 Mesh and solver configuration
Mesh independence, the solution's independence from the spatial grid was examined by conducting simulations using several grids under identical initial, boundary, and operational conditions. The evaluated grids consisted of: sparse (comprising 81,218 volumetric triangular elements), normal (containing 137,084 elements), and dense (including 384,424 volumetric elements). Regarding the temperature profiles in the last phase of the AeR cycle, we observed a strong correlation between the solutions for 137084 and 384424, with a maximum divergence in air temperatures of less than 0.03 K. Consequently, to reduce calculation time, we have opted to utilise a standard grid including 137,084 volumetric triangular pieces. Final simulations used the "normal" mesh for computational efficiency. Time integration was conducted using a BDF solver, and simulations continued until thermal cyclic steady state was achieved.
To ensure model accuracy, validation was performed using experimental data from a campaign involving trained NiTi wires subjected to rapid loading and unloading. Temperature variations were recorded using an infrared camera system, and results were compared with a simplified 1D MATLAB-based simulation. The experimental setup involved tensile loading of NiTi wires using an Instron test bench, with stress ramps up to 550 MPa at 0.2 s-1 strain rates. The temperature evolution observed during stress cycling matched the model predictions within a 1℃ deviation. This confirmed that the phase transformation kinetics and elastocaloric behavior were accurately captured. Further details are reported by Cirillo et al. [17].
Simulations were conducted for both prototypes over a range of airflow velocities and heat exchange durations. Key performance metrics include the temperature span (ΔTspan), cooling power, and COP:
$\Delta {{T}_{span}}=\left( {{T}_{env}}-\frac{1}{{{t}_{cycle}}}\mathop{\int }_{0+n~{{t}_{cycle}}}^{{{t}_{cycle}}+n~{{t}_{cycle}}}{{T}_{air,outlet}}\left( t \right)dt \right)~$ (13)
${{\dot{Q}}_{ref}}=\underset{~{{t}_{load}}+~{{t}_{fluid+}}~{{t}_{unload}}+n~{{t}_{cycle}}}{\overset{{{t}_{cycle}}+n~{{t}_{cycle}}}{\mathop \int }}\,{{\dot{m}}_{air}}{{c}_{air}}\left( {{T}_{env}}-{{T}_{air,outlet}}\left( t \right) \right)dt$ (14)
$C O P=\frac{\dot{Q_{\text {ref }}}}{\dot{W}}$ (15)
Figures 2 illustrate the temperature range over time for fluid flow, parameterised by air velocity for the two geometries: (a) tensile and (b) bending. Figure 3 illustrates the cooling power as a function of fluid blow duration, parameterised by fluid velocity for both configurations: (a) tensile and (b) bending. Figure 4 presents the COP as a function of air velocity, parameterised by blown duration for both architectures: (a) tensile and (b) bending.
Figure 2. Temperature variation over time for fluid flow parameterised by air velocity: (a) tensile load; (b) bending
Figure 3. Cooling power as a function of time for fluid flow, parameterised by air velocity: (a) tensile load; (b) bending
Figure 4. Coefficient of performance versus time for fluid flow parameterised by air velocity: (a) tensile load; (b) bending
At shorter fluid interaction times (4–6 s), both configurations yielded similar ΔTspan. However, at longer durations (up to 12 s), the tensile setup demonstrated higher ΔTspan, reaching up to 9 K compared to 7.2 K for the bending setup. This advantage arises from the larger adiabatic temperature change achievable with tensile loading. Cooling power increased with airflow velocity due to greater mass flow, peaking at 76 W for the tensile setup and 65 W for bending. However, performance declined when fluid flow time exceeded optimal durations, especially for bending due to thermal saturation. While the tensile prototype achieved higher ΔTspan, the bending configuration consistently outperformed in terms of COP, reaching a maximum of 7.7. This reflects its lower mechanical energy input requirement, enhancing system-level efficiency.
This study presents a novel elastocaloric cooling concept tailored for electronics. A comparison between tensile and bending configurations was conducted using validated FEM simulations.
The following conclusions can be drawn:
The findings affirm the viability of elastocaloric cooling in compact electronics and encourage for further development of bending-based AeR systems.
The paper is an outcome of the project CHECK TEMPERATURE that is financially supported by the 2021 internal grant reserved for Fixed-Term Research of Department of Industrial Engineering, University of Naples Federico II.
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Roman symbols |
|
|
A |
Austenite phase temperature, K |
|
AeR |
Active elastocaloric regenerator |
|
a |
Grouping factor |
|
B |
Boltzmann constant, m2·kg·s-2·K-1 |
|
b |
Grouping factor |
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c |
Specific heat capacity, J·kg−1·K−1 |
|
COP |
Coefficient of performance |
|
E |
Young modulus, MPa |
|
f |
Frequency, Hz |
|
FEM |
Finite Element Method |
|
g |
Elastocaloric term, W·m-3 |
|
GWP |
Global Warming Potential |
|
H |
Latent heat, J·g−1 |
|
HTF |
Heat Transfer Fluid |
|
k |
Thermal conductivity, W·m−1·K−1 |
|
M |
Martensite phase temperature, K |
|
$\dot{m}$ |
Flow rate, kg·s−1 |
|
n |
Number of times |
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p |
Pressure, Pa |
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$\dot{Q}$ |
Cooling power, W |
|
S |
Entropy, J·kg·K |
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SMA |
Shape Memory Alloy |
|
T |
Temperature, K |
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t |
Time, s |
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u |
x-velocity field component, m·s−1 |
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v |
y-velocity field component, m·s−1 |
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VC |
Vapor Compression |
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w |
Loading/unloading work, J·g-1 |
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x |
Longitudinal spatial coordinate, m |
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y |
Orthogonal spatial coordinate, m |
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Greek symbols |
|
|
Δ |
Finite difference |
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$\text{ }\!\!\varepsilon\!\!\text{ }$ |
Strain, N |
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θ |
Relaxation time constant for martensitic phase transformation [s] |
|
υ |
Cinematic viscosity, m2·s-1 |
|
ξ |
Phase fraction, - |
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$\dot \xi$ |
Instantaneous phase fraction, s-1 |
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ρ |
Density, kg·m−3 |
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σ |
Uniaxial stress, MPa |
|
ψ |
Probability, - |
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Subscripts |
|
|
0 |
Initial |
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1 |
Final |
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A |
Austenitic |
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AM |
Austenite-to-Martensite transformation |
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ad |
Adiabatic |
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air |
Air |
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CHANNEL |
On the single channel |
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CHECK |
On the whole device |
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cool |
Cooling |
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cycle |
Cycle |
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env |
Environment |
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f |
Finish |
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fluid |
Fluid |
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load |
Loading |
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M |
Martensitic |
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MA |
Martensite-to-Austenite transformation |
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net |
Net |
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outlet |
Outlet |
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p |
Constant pressure |
|
ref |
Refrigeration |
|
s |
Start |
|
SMA |
Shape Memory Alloy |
|
span |
Span |
|
unload |
Unloading |
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