Version of Record: https://www.sciencedirect.

com/science/article/pii/S0306261919309377
Manuscript_9e1593d44c27ee10af7e104b4ca1a673

Shape memory alloy engine for high efficiency low-temperature gradient

thermal to electrical conversion

Prashant Kumara*, Ravi Anant Kishorea,e, Deepam Mauryaa, Colin J Stewarta, Reza Mirzaeifarb,
Eckhard Quandtc, and Shashank Priyaa,d*

a Center for Energy Harvesting Materials and Systems (CEHMS), Virginia Tech, 310 Durham
Hall, Blacksburg, VA 24061, USA

b Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA

c Kiel University, Institute for Materials Science, Kaiserstr. 2, 24143 Kiel, Germany

d Materials Research Institute, Penn State, University Park, PA 16802.

e National Renewable Energy Laboratory, 15013 Denver West Pkwy, Golden, CO 80401, USA.

Abstract

More than half of the energy generated worldwide is lost as unused thermal energy because of
the lack of efficient methodology for harnessing the low-grade heat. Here we demonstrate that
shape-memory alloy can be an effective mechanism for recovering low-grade heat. Shape
memory alloys exhibit thermally induced martensite to austenite phase transformation and super-
elasticity (stress-induced martensitic transformation). Employing these two characteristics, we
demonstrate a thermal engine for harnessing waste energy through all modes of heat transfer:
convection, conduction, and radiation. In this work, we performed material and heat transfer
analysis for achieving high frequency, sustainable and efficient operation of our engine. An
optimized shape memory alloy engine generated 36 W from 1 kg or 234 kW of electricity from 1
m3 of active material. A continuous three-day operation of several SMA engines could generate
7.2 kWh of electricity when installed on a 500 m long hot pipe network. This generated power
can reduce the carbon footprint by 5.1 kg of CO2 illustrating the promise of this technology for
addressing climate change.

Keywords: Shape Memory Alloy (SMA); Martensite; Austenite; Pseudo-elasticity; Heat engine;
Energy harvesting.

*Corresponding author: pkumar14@vt.edu, sup103@psu.edu

© 2019 published by Elsevier. This manuscript is made available under the Elsevier user license
https://www.elsevier.com/open-access/userlicense/1.0/
Introduction

Among the various forms of environmental energy available around us, thermal energy is the
most abundant and ubiquitous. Thus, there have been considerable efforts made towards
developing techniques for conversion of thermal energy into electrical energy. Thermal energy is
usually classified as high-grade, medium-grade and low-grade based in its temperature [1]. As
shown in Fig.1(a), low-grade waste heat provides a huge work potential as it is abundantly
present around us. In most of the industrial processes, a large amount of waste heat is generated,
where, a major portion of this thermal energy is available in the form of low grade waste heat
[2]. Harvesting this low grade thermal energy is highly desirable for efficient industrial process
and environmental impact [3]. The thermal to electrical conversion process, however, becomes
complex with the decrease in heat source temperature. The traditional steam Rankine cycle based
power plants are currently the most effective technology to obtain work from heat. However,
these systems are bulkier and not efficient for low grade heat energy harvesting [4-6]. Other
alternatives such as Organic Rankine cycle (ORC) and Kalina cycle have been deployed for low
temperature heat applications and waste heat recovery [7, 8]. The difficulty in obtaining suitable
organic fluid for ORC [9], and proprietary nature of Kalina cycle [10] limit their practical
exploitation, especially for small-scale applications. In some of the methods, heat upgrading
techniques (heat pumps and absorption heat transformers (AHTs)) are deployed to utilize the low
grade waste heat [2, 11]. However, reliability of these technologies and their environmental
effects are some of the challenges need to be solved [12].

In recent years, significant efforts have been made to explore and develop the material based
alternative technologies for low-grade thermal energy harvesting and waste heat recovery, such
as thermoelectric [13-15], pyroelectric [16-18], thermomagnetic [19, 20], thermo-acoustics [21],
and thermo-electrochemical [22, 23]. In thermoelectric generators (TEGs), a direct thermal to
electrical energy conversion takes place due to the Seebeck effect and the performance relies on
figure of merit of the material [24]. Pyroelectric devices are used to convert the fluctuating
temperature directly into electricity using ferroelectric materials [18]. Thermomagnetic device
uses magnetic materials which undergo secondary phase change on thermal loading. This
phenomenon is used to convert thermal to mechanical to electrical energy [23, 25]. In thermo-
acoustic based device, a temperature gradient is used to produce acoustic waves by utilizing

2
thermal energy, and acoustic wave is then converted to electricity by using piezoelectric material
[21]. In another example, low temperature waste heat is directly converted into electricity
through electrochemical cycle by utilizing electrode materials with low heat and high charge
capacity. Out of all these material based choices, TEGs have dominated the scientific interest in
capturing locally available thermal energy. However, there is a significant drop in the
performance of TEGs (efficiency ~1-3%), when hot-side temperature is below 100 oC [26].
Other material based techniques mentioned above in current form provide smaller output power
density and thus remain early-stage laboratory research. In trying to address this decades old
grand challenge, we made a breakthrough in demonstration of small-scale heat engine based on
shape memory alloy (SMA). SMA based engine was designed to operate at temperatures less
than 80oC with the ambient acting as heat sink. The engine relies on two fundamental properties
of SMA: (i) super-elasticity, and (ii) thermally induced martensite to austenite phase
transformation.

There have been several attempts to develop the SMA system for converting heat energy into
output mechanical work[27-29]. Recently, Sato et al. [30] have presented the large scale working
device based on SMA that demonstrated 1.155 W output power for 40.25 cm3 of active material
volume (5 belt, weight of active material ~ 0.262 kg, device dimension: 18.50 cm x 5.50 cm x 5
cm). However, most of these previous designs have remained laboratory experiments and their
reliability and durability for a long-term domestic or commercial application remains
challenging. Especially for the devices requiring rotation, challenges arise from the fact that heat
needs to be captured from the source (hot-side temperature less than 80oC) at a very fast rate
(several hundred rotations per minute) through an extremely thin interface (SMA wire diameter
less than few hundred microns). Also, the residual heat in the wire has to be completely
discarded to the ambient at equally fast rate to achieve continuous operation. As the size of SMA
engine is reduced, the hot-side and the cold-side come closer to each other, which results in
continuous accumulation of heat after each cycle. Eventually the accumulated heat stops the
functioning of the device due to insufficient cooling. This has been the challenge towards
realizing a small scale SMA engine for the past four decades (since 1975).

Here, we provide a breakthrough in developing small scale SMA engines operating at hot-
side temperatures less than 100 °C and overcoming all of the above mentioned challenges. The

3
potential of our SMA engine can be recognized from the data presented in Fig. 1(a). This data
shows the amount of waste heat available corresponding to different thermal gradients and low
grade heat (230 °C) is the major component of total waste heat. Fig. 1(b) shows the geothermal
locations (wells and springs) [31] across the United States, which could provide the opportunity
for deployment of SMA engine arrays demonstrated in this study. Fig. 1(c) shows various
locations of hot pipes in the industrial and residential settings with low thermal gradient waste
heat.

For harvesting this abundant amount of low grade thermal energy, the SMA wire needs to
possess a low transition temperature, smaller hysteresis, low heat capacity, high thermal
conductivity, and high thermo-elastic efficiency. Therefore, extensive investigations were
conducted on phase transition behavior, thermodynamic properties, and thermal hysteresis of
SMA wires. Using the measured SMA material characteristics, we designed an engine
comprising of two pulleys with different diameters, a thin SMA belt around two pulleys, a
metallic container for fluid storage, and a small DC electric generator (Fig. S1). Fig. 1(d) shows
array of SMA engines deployed on hot pipes (Fig. 1(c)). In this scenario, the heat from hot pipe
will be conducted to fluid through metallic base of the container. The hot fluid then heats the
SMA wire above the transition temperature to run the engine. Our SMA engine was found to
generate sufficient power needed for powering water health monitoring sensors and acoustic
devices with hot-side temperature ranging between 60-80 °C. It is worthwhile to mention that the
engine design presented here can be used at much lower hot-side temperatures (10 °C above the
ambient) if the transition temperature of SMA can be reduced by modifying its composition [32].
The long–term dynamic mechanical analysis (continuous three day operation) on the SMA wire
indicated no significant change in the thermo-mechanical properties. The calculation presented in
the supplementary file, projects that our SMA engine can generate 7.2 kWh over three-day
period in an industrial setup comprising of 500 m long hot pipe (at ~80-90oC) network. This
generated power can reduce the carbon footprint by 5.1 kg of CO2.

Methods and Experiments

The experiments consisted of three main steps. In the first step, differential scanning
calorimetry (DSC) and dynamic mechanical analyzer (DMA) studies were performed on five
different SMA wires and based upon the results most optimum wire was selected. Five samples

4
of NiTi were used in as-received form for the DSC test: Wire 1 (0.25 mm, Muscle wires), Wire 2
(0.38 mm, DYNALLOY, Inc), Wire 3 (0.2 mm, Johnson Matthey), Wire 4 (0.38 mm, DYNALLOY,
Inc), and Wire 5 (0.44 mm, Sci-supply)). The SMA wires were cut into small pieces and the test
specimens were washed thoroughly with acetone to remove any surface impurities. Before
recording the final readings, each test specimens were heated and cooled multiple times in the
temperature range of -40 °C to 100 °C in a closed furnace with heating/cooling rate of 10
°C/min. Further, DMA tests were conducted on the selected SMA wire. During these
measurements, the sample was scanned from -20 °C to 100 °C at different temperature scan rates
(1 °C/min, 2 °C/min and 3 °C/min) and frequencies (0.1 Hz,1.0 Hz, and 10 Hz). In the second
step, dynamic thermal analysis was performed on the selected wire. The goal of the experiment
was to identify the temperature distribution of the moving wire during operation, right from the
point where the wire moves out of the contact with the heat source to the point where it returns
back to make contact with the heat source. This experiment is extremely important to understand
the thermal response of the SMA wire vis-à-vis thermoelastic cycle efficiency of the SMA
material when it is pre-stressed between the pulleys. The detailed schematic of the experimental
setup is shown in Fig. S2(a). Since the SMA wire was thin (~ 0.44 mm) and moving, the
experiment was very sensitive to external factors such as ambient temperature and air speed.
Therefore, the entire experimental set-up was thermally isolated during the measurements.
Infrared (IR) camera (FLIR SC6700, FLIR Systems, Inc.) was used to capture the radiation
coming from the thin moving SMA wire and the temperature gradient was evaluated
accordingly. Before running the experiments, IR camera was calibrated with a thermocouple by
matching the surface temperature of the stationary wire under ambient condition (at 22°C). In
order to mitigate the experimental error due to the reflections from the surroundings, the entire
experimental setup was painted black and covered with black fabrics. In addition, in order to
obtain the accurate and high resolution thermal data, the entire engine was divided into small
sections and the IR radiation coming from each section was captured separately. Also, a thin
graphite layer was deposited on the SMA wire in order to enhance its surface emissivity. Before
capturing any data from the IR camera, a preliminary thermal analysis (DSC) was conducted to
understand the effect of the graphite layer on SMA wire. Fig. S2(b) shows the DSC results
before and after the graphite coating indicating very minor differences. Inset shows the scanning
electron microscope (SEM) image having a graphite coating. All the thermal videos representing

5
the dynamics of wire were processed using a MATLAB code to obtain the temperature profile.
In order to minimize the inconsistency during experiments, temperature data from several videos
were averaged and a final temperature gradient was obtained along the length of the wire. In
addition, a high resolution camera was used to capture the vibration of the moving wire along
with the thermal videos. The high resolution videos were then processed using MATLAB to
obtain vibrational characteristics such as amplitude and frequency.

In the third and last step, we measured the power output of SMA engine. Fig. S3 shows the
schematic diagram of the experimental set-up used to measure the mechanical and electrical
power output. Two pulleys of different diameters (optimized diameter ratio 1:3) were fixed on
two ends of 3-D slider stand through two small ball bearings. The SMA wire was looped around
the two pulleys. The optimal distance of 16.51 cm was maintained between the two pulleys. The
shaft through the lower pulley was connected to a small permanent magnet DC generator (rated
at 6V and Model # RF-500TB). A small portion of the SMA wire maintaining contact with the
lower pulley was heated either through hot water bath or a heat gun or radiation from a hot plate.
In order to determine the mechanical power, we first decoupled the electrical generator from
SMA engine. The angular speed of pulley was then recorded from the instant rotation starts to
the time rotation reaches the steady state. Moment of inertia (I) of the pulleys was obtained using
a CAD software, SOLIDWORKS.

The generator (coupled with engine) was connected to a resistance box (RS-201, IET LABS
Inc.) whose resistance could be varied between 0 to 500 Ω to identify the optimal load. A data
acquisition system, SIGLAB-SIGDEMO was used to acquire the voltage waveform. A voltmeter
(FLUKE 179) was also connected in parallel to the external resistance to monitor the output
voltage. An optical tachometer (SHIMPO DT-209X) was used to measure the angular speed of
the rotating pulleys.

Results and discussion

In the first stage, we performed material investigations to identify the most suitable SMA
alloy composition for engine design. Focus in this stage was on understanding the fundamental
material behavior under cyclic temperature and stress variations. In the second stage, we
performed thermal transport analysis to ensure rapid heat transfer rate across the SMA wire.

6
Lastly, in the third step, we performed systematic experiments on heat engine to fully quantify
the device performance.

SMA investigations for design of heat engine

A comprehensive DSC analysis was performed on different SMA wires to understand the
thermal deformation cycle and identify the composition which has maximum thermodynamic
efficiency at low temperatures under stress free condition. Supplementary Fig. S4(a)-(e) show
the hysteresis across phase change and the transition temperature for each sample. Using this
experimental heat flow diagram, the critical temperatures − Ms (martensite start), Mf (martensite
finish), As (austenite start), and Af (austenite finish) − for forward and reverse transformation
were quantified. It can be seen from Fig. S4 that wire 5 has the lowest forward transition
temperature of 48°C, which is most suitable for our heat engine. The difference between thermal
energy going-in and coming-out of the wires was found to be very small, which should be the
case since the DSC tests were run under no stress condition (no work). Residual heat
accumulation may cause thermo-mechanical fatigue in the system. Fig. S5 (a), (b) and (c) show
detailed results on phase transition of the annealed sample. Thermal annealing results in shift of
transition temperature from 48 °C to 54 °C. SMA wire was also characterized using dynamic
mechanical analyzer (DMA) in order to determine the force dynamics and viscoelasticity
properties. Detailed comparative study of damping and storage modulus values for as-received
and annealed SMA samples are shown in Supplementary Fig. S6-8. We observed that with the
increase of frequency the damping coefficient decreases, and with the increase of temperature
scan rate the transition temperature of the wire increases.

Thermal analysis of the heat engine

The power output of an SMA engine primarily depends on the thermoelastic cycle frequency
i.e. the rate at which the phase transition occurs in forward and reverse directions. The efficiency
of SMA engine can be enhanced by avoiding excessive heating or cooling during the thermal
cycle. In order to analyze the temperature distribution along the wire under operating conditions,
thermal videos were recorded for various sections of the wire, as shown in Fig. 2(a), while
maintaining the wire speed at 0.25 m/s. The first section was considered 1 cm above the hot
pulley to avoid the transient effects of thermal zone generated from hot source which assisted in

7
measuring the correct temperature values on wire surface. Detailed experimental configuration is
described in Fig. S2.

The vibration of SMA wire plays an important role in determining the performance of heat
engine, as it enhances the convective cooling of the wire. The convective heat transfer
coefficient, ℎ, in this case, depends on the velocity of the wire in the direction of rotation as well
as vibrational speed in the normal direction. Fig. S9(a) and (b) show the vibration profile
(captured by high resolution camera) of wire in the time domain and qualitative Fast Fourier
Transformation (FFT) response. The wire is vibrating without any fixed pattern and the
frequency response splits into many major frequencies between, ~ 0 to ~15 Hz.

Fig. 2(b) compares the temperature across a selected section of wire obtained experimentally
and empirically using equation (s7) for different values of heat transfer coefficient. It can be
noted that at h=250 W/m2-K, analytical results are in close agreement with the experimental
results (maximum deviation of less than 3%). Fig. S10 shows the heat transfer analysis of
moving wire and Supplementary Table S1 lists the thermal properties. This predicted heat
transfer coefficient includes the simultaneous effect of forced convection due to linear speed
(due to the rotation of the pulley) and vibration of the wire. Validated analytical model was used
to evaluate the temperature profile of the wire for heat transfer coefficients ranging from 200-400
W/m2-K, using Supplementary Equation (s7). As cooling coefficient approaches 320 W/m2-K
(with the wire speed of 1.8 – 2 m/s), the temperature of wire reduces by 3.75 °C more (compare
to h=200 W/m2-K) in the first section of the wire. This analysis indicates the location of wire
where the reverse phase transition temperature is achieved. We use this information to optimize
the length of the wire in order to reduce the size of heat engine.

Fig. 2(c) shows the temperature profile of wire loop starting from the emerging point near the
lower pulley to the upper pulley and from the upper pulley to lower pulley. Fig. 2(d) compares
the temperature profile obtained using our empirical model (Supplementary Equation (s7)),
experimental results, and the results obtained from the model proposed by Kase et al.[33]. Our
results differ from the model prediction of Kase et al. by 6-7%, which can be correlated with the
difference in the experimental setup and vibrational dynamics of the wire that includes the wire
curvature effect. Fig. 2(d) shows the effect of curvature near the upper cold pulley on the
temperature profile of wire.

8
SMA heat engine performance

Next, we quantified the performance of the engine by cycling the heat source (water)
temperature from 55-85 °C. The martensite to austenite transition completes at 54 °C, thus, the
hot-side temperature was maintained above 55 °C. The heat sink temperature was fixed at
ambient temperature. As shown in Fig. 3(a), the angular velocity of pulley varies in proportion
with hot side temperature. It is important to note that in Fig. S11, the angular speed of pulley
does not follow the same path during the heating and cooling cycle. Another important parameter
that affects the system’s efficiency was found to be the dip angle, the angle made at the center by
portion of the lower pulley exposed to heat source. Fig. 3(b) compares the variation in angular
speed with time at three different dip angles when the heat source is fixed at 70°C. It is
interesting to note that there exists an optimal dip angle (~ 56o) for maximum angular speed. The
angular speed was found to first increase with an increase in dip angle due to the increased heat
inflow. The angular speed is maximum when the dip angle is approximately equal to contact
angle of SMA wire with the pulley. Increasing the dip angle further reduces the angular speed.
This could happen because of increase in drag forces with increase in dip angle.

An optimized SMA engine with respect to heat source temperature and dip angle was
examined under different heating modes: hot water bath, hot air, and radiative heating from a hot
plate. Fig. 3(c) and (d) show the SMA engines speed (rotation per minute) operating under
different heat sources. The temperature of hot air was maintained at 125 °C. The hot plate
temperature was fixed at 250oC and the gap distance between hot plate and wire was 1 cm. In
order to enhance the heat transfer, silver paste was applied on inside the groove of lower pulley.
It can be noted from Fig. 3(c), that the silver paste improves the angular speed of SMA engine.
The maximum angular speed of the lower pulley in the steady state was measured to be 164 rpm
and 268 rpm for hot air and hot plate, respectively. Fig. 3(d) shows the angular speed of the
upper pulley at different hot-side temperatures after the system has reached steady state. It can be
seen that the SMA engine achieves a maximum angular speed when hot-side temperature is 80
°C and the corresponding angular speed is 420 rpm. It should be noted that the speed shown on
y-axis of Fig. 3(c) is the rpm of the lower pulley; whereas, the rpm shown in Fig. 3(d) is the rpm
of the upper pulley, which is three times lower than that of the lower pulley. From these results it
can be concluded that the SMA engine performs best when the heat source is hot water. This is

9
expected as the heat transfer coefficient in case of water is much higher than that of air.
Therefore, in the remainder of this study, hot water is used as the heat source.

In rotational dynamics, mechanical power is given as the product of torque and angular
speed, and it can be expressed as [34]:

dω
Pmech = I × ×ω (1)
dt

where I is the moment of inertia of pulleys, dω/dt is angular acceleration of pulleys, and ω is
angular speed (rad/s). Next, we measured variation of angular speed as a function of time for
upper and lower pulleys, as shown in Fig. 4(a). A sixth order polynomial function was used to
obtain a functional relationship that describes the angular speed of the pulley with respect to
time. The angular acceleration of the upper and lower pulleys can be determined by taking the
time derivative of the polynomial expression. Angular acceleration multiplied with the total
moment of inertia of the rotating body provides the torque. This torque was then used to
determine the mechanical power by using equation (1).

Fig. 4(b) and (c) show the angular speed, torque, and mechanical power of the upper and
lower pulleys, respectively, at hot water temperature ( ) of 69 °C. These figures depict that the
torque is maximum when the pulley is just about to rotate (start-up torque), it decreases as the
angular speed increases, and it diminishes to zero after the steady state is achieved. The
mechanical power is zero at the beginning (since the system is at rest), it increases with the
increase in angular speed until it gains a maximum value (when the product of torque and
angular speed is highest), and then it slowly decreases. Fig 4(d) depicts the total mechanical
power of the SMA engine at = 69 °C. The maximum mechanical power can be found to be
12.5 mW. Fig. 5(a) shows the comparison of mechanical power at two different hot water
temperatures: = 69 °C and 80 °C. The maximum mechanical power obtained by the engine
is 26mW at = 80 °C, which is more than twice the mechanical power obtained at =
69 °C. The specific mechanical power, calculated by dividing the mechanical power over the
mass of the active component (SMA wire in this case), was found to be 52 W/kg at = 80 °C.

In order to quantify the electrical power output, we connected a small permanent magnet DC
motor (rated at 6 V) with the shaft of the lower pulley. Detailed experimental setup is shown in

10
Fig. S3. Fig. 5(b) shows the variation of generator’s shaft rpm and external load resistance at
different heat source temperatures (hot water). It can be seen that at a fixed load the shaft rpm
increases with increase in the hot water temperature. At a fixed temperature, the rpm first
increases with increase in the load resistance and then saturates. Fig. 5(c) shows the output DC
voltage (V) and the output current (I) obtained for different load resistances at a fixed hot water
temperature of 80°C. V-I plots at other hot water temperatures are not shown for the purpose of
graphical clarity. The voltage follows a similar trend as the rpm of the generator’s shaft, and the
maximum output voltage of 1.7 V was obtained at 80oC when the generator has virtually no load
(at 500Ω). Fig. 5(d) depicts the electrical power output as a function of external resistance at
different values of heat source temperature. It can be seen that SMA engine generates maximum
electrical power output of 18 mW across 70 Ω load resistance when hot water temperature is 80
°C. The electrical power can be scaled up by using multiple uncoupled devices connected to a
common heat source. To illustrate the scalability of our engine, we designed experiments with
three harvesting units (Fig. S12(a)) and the corresponding results are shown in Fig. S12(b). The
maximum output power can be obtained to ~24 mW at hot-side of 69oC.

Fig. 6 compares the efficiencies calculated for SMA heat engine. SMA material’s
thermodynamic efficiency is calculated to be 5.0% using Supplementary Equation (s8). The
absolute efficiency of SMA engine is 1.5%, which is 10.5% of the Carnot efficiency. It should be
noted that although output power increases with increase in hot water temperature, the efficiency
is maximum at 70 °C. This is an important observation because the forward phase transformation
occurs at 54 °C, which is effectively achieved when hot water temperature is 70 °C. Overheating
the SMA wire beyond this temperature decreases the system’s efficiency. The optimal heat
source temperature is the one where 100% forward phase transformation is completed. This is
also true for the heat sink temperature. Over-heating or under-cooling decrease the system’s
efficiency.

The effectiveness of the SMA heat engine was compared with other existing technologies
used for thermal-to-electrical energy conversion. In this domain, a thermoelectric generator
(TEG) is the most popular device. Normally, the output power and efficiency of TEGs are not
readily available for operation below 100oC. We, therefore, developed a numerical model using
ANSYS workbench v17.0 to determine these quantities and validated our calculations with the

11
experimental results reported by Hao et al. [13]. The numerical model was then used to produce
the power and efficiency data for TEG operating below 100 °C. Fig. S14 compares the numerical
results with the experimental results, which were found to be in close agreement. The numerical
model was then modified to account for ambient as the heat sink. From this analysis, at a
temperature above 70 °C, SMA engine is competitive (Fig. 7(a)) with TEG. Fig. 7(b) compares
different power indices in terms of active material power density and active material specific
power for TEG and SMA engine. The SMA engine can be seen to be competitive with TEG in
all the attributes. Further, we compared the cost of our engine with one of the commercially
available TEG and found that SMA engine is a much cheaper solution (supplementary, section
S10). Recently, thermal energy harvesting using tensile muscles has been reported [35], which
were shown to exhibit 7.2 W/kg at temperature difference of 70 oC. Comparatively, SMA engine
provides the specific power of 36 W/kg at lower temperature difference of 58 °C. In another
recent study, a small scale thermo-magnetic harvester has been realized for harvesting thermal
gradient by using phase transformations in gadolinium [19]. On the basis of information
available, we evaluated the specific realized power as ~0.6 W/kg for the temperature gradient
(ΔT) of 80 °C. This implies that the SMA engine presented in this study exhibits improved
performance compared to all current thermal energy harvesting technologies.

Demonstrations of SMA heat engine and future impact

We successfully demonstrated several practical applications which could be powered by

SMA heat engine. In the first demonstration, we continuously operated a sound projector in both
air and water medium (supplementary movie). Fig. 7(c) shows the sound generation in water
medium. The sound pressure is recorded by hydrophone (Brüel & Kjær type-8103). Fig. 7(d)
shows the waveform for generated acoustic pressure. This demonstration paves the pathway for
self-sustained air/under-water acoustic communication. We also demonstrate the real-time water-
health monitoring using the SMA heat engine (Fig. S15). This application provides direction for
the development of self-sustained health monitoring devices that can be deployed in residential
buildings and in natural environments such as hot springs.

Next, we evaluated the impact of our heat engine at large scale for a long duration of time.
Detailed calculations are shown in supplementary (section S13). Through DMA experiments
(Fig. S16), we show that the SMA can undergo thermal cycling for three days without any

12
degradation. On the basis of these outcomes, we predict that if our heat engine is operated for 1-3
days it can generate 2.4-7.2 kWh of energy (equivalent to 1.7 – 5.1 kg of CO2). To further
strengthen our arguments for long term operation, we operated heat engine for continuous 10
hours at 65oC in laboratory environment (Fig. S17), and did not observe any change in the
performance.

The durability of our system is related to the fact that phase transformation happens
instantaneously at each point of the material which experiences the required temperature
changes. However, in a bulk material, the temperature will not rise and drop uniformly over the
whole volume (i.e. the cross-section of wire). If the temperature changes are concentrated at the
surface of the wire, the whole material would not be contributing to the phase transformation,
and thereby, reduce efficiency. Also, a non-uniform distribution of phase transformation triggers
the fatigue failure. The observed efficiency and the fatigue resistance of the system further attest
the robustness of our engine. The selection of smaller radius wire and enhanced heating time,
ensured a uniform phase transformation (forward and reverse) in the wire (see supplementary,
section S14, for more discussion).

Conclusion

In summary, we demonstrate the operation of a low grade shape memory alloy heat engine
that operates below 80oC using ambient as the heat sink. Among the different heat sources
examined, the SMA engine performed best with the hot water as the heat source. The maximum
mechanical power of the shape memory alloy heat engine was found to be 12.5 mW at 69 °C and
26 mW at 80 °C. The mechanical power density of the engine was calculated to be 52 W/kg of
the active mass (shape memory alloy wire). The maximum electrical power of the SMA heat
engine was found to be 8.8 mW at 70 °C and 18 mW at 80 °C. The electrical power density of
the engine was calculated to be 36 W/kg of the active mass (shape memory alloy wire). The
shape memory alloy material’s thermodynamic efficiency was found to be 5.0%. The maximum
thermal-to-electrical conversion efficiency of the engine was 1.5%, which is 10.5% of the Carnot
efficiency. The engine was successfully demonstrated for powering acoustic projector and water
health monitoring sensors. Results show that shape memory alloy heat engines of the dimensions
shown here can reduce 1.7 kg of CO2 (carbon footprint) production per day.

Conflicts of interest

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There are no conflicts to declare.
Acknowledgements

The authors would like to thank center for energy harvesting materials and systems (CEHMS)
for providing the facilities and infrastructure. S.P. acknowledges the financial support from
DARPA MATRIX program. P.K. acknowledges the funding from Office of Naval Research
(ONR). R.K. is supported through ICTAS Doctoral Scholarship and AMRDEC SBIR program.
D.M. acknowledges the support from Office of Basic Energy Science, Department of Energy.
We thank Dr. Bruce Orler for helping us in acquiring data from DSC and DMA.

Main figures:

14
Fig. 1: Thermal energy available at various locations (industry, home, and geothermal sites) for
potential deployment of SMA based heat engine. (a) A bar chart representing the potential of
thermal energy harvesting in various categories (subdivided on the basis of temperature range)
[6]. The graph is redrawn on the basis of data given in reference 6. (b) Geothermal locations
across the United States (in temperature range of 55-100 oC) for the deployment of SMA
engine[31]. This image was created off the NREL geothermal prospector site. The underlying
data is compiled by the National Renewable Energy Laboratory for the U.S. Department of
Energy. (c) Various home and industrial hot pipe locations for effective utilization of SMA
engine. (d) An array of SMA engines deployed on pipe (along with single device) for the
prospective utilization of hot thermal zone for maximizing the power and reducing the carbon
foot print.

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Fig. 2: Dynamic thermal investigation of thin SMA wire (active material in the engine) by IR
thermography. (a) Basic design of the SMA engine. The active material is divided into many
sections for accurate thermal profiling of thin and vibrating wires. (b) Experimentally obtained
temperature profile of moving wire (in steady state) for 1st section of active material at particular
dynamic condition and its comparison with modeled temperature profile at different predicted
heat transfer coefficients (h). Temperature profile obtained at h=250 W/K-m2 is matching with
experiments. (c) Temperature profile for the all the sections where wire is cooled continuously
after emerging from hot source. Section just before hot source acts as transition zone for heating
of cooled wire. (d) Complete thermal cycle of engine from heating-cooling-heating, and
comparison of cooling profile with predicted h value and theoretical relationship developed by
S.Kase et al.[33].
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Fig. 3: Performance characterization of optimized SMA engine for energy harvesting purposes.
(a) SMA engine performance under load for increasing and decreasing the hot side temperature
continuously. This shows the increasing and decreasing trend of RPM with respect to
temperature. (b) Performance optimization of SMA engine at different dip angles (length of wire
exposed to hot bath). (c) Engine performance (in terms of lower pulley rotation) with different
forms of non-contact heat sources such as hot air and hot plates. (d) SMA engine performance
(in terms of upper pulley rotation) at different temperatures of hot bath. A significant increase
has been observed with increasing hot side temperature.

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Fig. 4: Mechanical power calculation for SMA engine. (a) Angular velocity of upper pulley
along with 6th order polynomial curve fit when hot water is maintained at 69°C. The angular
acceleration can be determined by taking the time derivative of the polynomial expression. (b)
Angular velocity, derived torque and mechanical power (considering the upper pulley) in time
domain. (c) Angular velocity, derived torque and mechanical power (considering the lower
pulley) in time domain. (d) Final evaluated mechanical power of whole SMA engine when hot
water bath is at 69°C. The maximum mechanical power is around 12.5 mW.

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Fig. 5: SMA engine performance. (a) Mechanical power for two different thermal input
conditions. Maximum mechanical power obtained is 52W/kg (26mW) for operating range
considered in this study. (b) Generator (motor operated in reverse) shaft rotation per minute
(rpm) at different load with different thermal input temperature from hot water bath. (c) Output
current and output voltage as a function of external load resistance for particular thermal input
condition. Maximum voltage obtained is ~1.7V (at 500 Ohms) for temperature considered here.
(d) Power obtained as a function of externally applied resistance at different thermal input.
Maximum electrical power obtained is 36W/kg (18mW) within the operating temperature range

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at 69% of generator efficiency. The matching external resistance for maximum power output is
70Ω.

Fig. 6: Comparison of different type of efficiencies for the SMA engine. Carnot efficiency is
calculated from heat source and sink temperatures. Absolute efficiency is system’s actual
efficiency and evaluated as electrical power output/ thermal energy input. Material
thermodynamic efficiency is deduced from the phase transition curve of SMA wire by using
fundamentals of thermodynamics. This gives the maximum material capacity for power
scavenging. Relative efficiency is defined as absolute efficiency/Carnot efficiency. SMA engine
performs maximum efficiency when hot water bath is at 70°C.

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Fig. 7: Comparison of SMA engine with existing state of the art thermal energy harvesting
technology such as TEG, and experimental setup for powering acoustic projector. (a) Simulation
results on TEG under different boundary conditions and comparison with the efficiency of basic
version of SMA engine. At temperature above 70 °C, SMA engine is competitive with TEG. (b)
Various power density indices such as power per unit volume and power per unit mass of active
materials along with efficiency are compared for TEG and SMA engine. (c) Experimental setup
for demonstration of practical thermal energy harvesting for real-time under water acoustic
measurement. (d) Time domain acoustic pressure waveform generated in water from a small
SMA engine. The pressure was recorded at 2 cm above the device by hydrophone.

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References:

[1] Kishore RA, Priya S. Low-grade waste heat recovery using the reverse magnetocaloric effect.
Sustainable Energy & Fuels. 2017;1:1899-908.
[2] Oluleye G, Jobson M, Smith R, Perry SJ. Evaluating the potential of process sites for waste
heat recovery. Applied Energy. 2016;161:627-46.
[3] Brückner S, Liu S, Miró L, Radspieler M, Cabeza LF, Lävemann E. Industrial waste heat
recovery technologies: an economic analysis of heat transformation technologies. Applied
Energy. 2015;151:157-67.
[4] Hettiarachchi HM, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an
organic Rankine cycle using low-temperature geothermal heat sources. Energy. 2007;32:1698-
706.
[5] Barbier E. Geothermal energy technology and current status: an overview. Renewable and
Sustainable Energy Reviews. 2002;6:3-65.
[6] Johnson I, Choate WT, Davidson A. Waste Heat Recovery. Technology and Opportunities in
US Industry. BCS, Inc., Laurel, MD (United States); 2008.
[7] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cycle.
Renewable and sustainable energy reviews. 2013;24:325-42.
[8] Shi L, Shu G, Tian H, Deng S. A review of modified Organic Rankine cycles (ORCs) for
internal combustion engine waste heat recovery (ICE-WHR). Renewable and Sustainable Energy
Reviews. 2018;92:95-110.
[9] Tocci L, Pal T, Pesmazoglou I, Franchetti B. Small scale organic rankine cycle (ORC): A
techno-economic review. Energies. 2017;10:413.
[10] Bombarda P, Invernizzi CM, Pietra C. Heat recovery from Diesel engines: A
thermodynamic comparison between Kalina and ORC cycles. Applied Thermal Engineering.
2010;30:212-9.
[11] Oluleye G, Smith R, Jobson M. Modelling and screening heat pump options for the
exploitation of low grade waste heat in process sites. Applied energy. 2016;169:267-86.
[12] Chua KJ, Chou SK, Yang W. Advances in heat pump systems: A review. Applied energy.
2010;87:3611-24.
[13] Hao F, Qiu P, Tang Y, Bai S, Xing T, Chu H-S, Zhang Q, Lu P, Zhang T, Ren D, Chen J.
High efficiency Bi 2 Te 3-based materials and devices for thermoelectric power generation
between 100 and 300° C. Energy & Environmental Science. 2016;9:3120-7.
[14] Zheng X, Liu C, Yan Y, Wang Q. A review of thermoelectrics research–Recent
developments and potentials for sustainable and renewable energy applications. Renewable and
Sustainable Energy Reviews. 2014;32:486-503.
[15] Elsheikh MH, Shnawah DA, Sabri MFM, Said SBM, Hassan MH, Bashir MBA, Mohamad
M. A review on thermoelectric renewable energy: Principle parameters that affect their
performance. Renewable and Sustainable Energy Reviews. 2014;30:337-55.
[16] Ravindran S, Huesgen T, Kroener M, Woias P. A self-sustaining micro thermomechanic-
pyroelectric generator. Applied Physics Letters. 2011;99:104102.

22
[17] Sebald G, Guyomar D, Agbossou A. On thermoelectric and pyroelectric energy harvesting.
Smart Materials and Structures. 2009;18:125006.
[18] Sebald G, Lefeuvre E, Guyomar D. Pyroelectric energy conversion: optimization principles.
IEEE transactions on ultrasonics, ferroelectrics, and frequency control. 2008;55.
[19] Chun J, Song H-C, Kang M-G, Kang HB, Kishore RA, Priya S. Thermo-Magneto-Electric
Generator Arrays for Active Heat Recovery System. Scientific Reports. 2017;7:41383.
[20] Elliott J. Thermomagnetic generator. Journal of Applied Physics. 1959;30:1774-7.
[21] Smoker J, Nouh M, Aldraihem O, Baz A. Energy harvesting from a standing wave
thermoacoustic-piezoelectric resonator. Journal of Applied Physics. 2012;111:104901.
[22] Abraham TJ, MacFarlane DR, Pringle JM. High Seebeck coefficient redox ionic liquid
electrolytes for thermal energy harvesting. Energy & Environmental Science. 2013;6:2639-45.
[23] Lee SW, Yang Y, Lee H-W, Ghasemi H, Kraemer D, Chen G, Cui Y. An electrochemical
system for efficiently harvesting low-grade heat energy. Nature communications. 2014;5:3942.
[24] Lee H, Sharp J, Stokes D, Pearson M, Priya S. Modeling and analysis of the effect of
thermal losses on thermoelectric generator performance using effective properties. Applied
Energy. 2018;211:987-96.
[25] Chun J, Kishore RA, Kumar P, Kang M-G, Kang HB, Sanghadasa M, Priya S. Self-Powered
Temperature-Mapping Sensors Based on Thermo-Magneto-Electric Generator. ACS applied
materials & interfaces. 2018;10:10796-803.
[26] Ismail BI, Ahmed WH. Thermoelectric power generation using waste-heat energy as an
alternative green technology. Recent Patents on Electrical & Electronic Engineering (Formerly
Recent Patents on Electrical Engineering). 2009;2:27-39.
[27] Wakjira JF. The VT1 shape memory alloy heat engine design: Virginia Polytechnic Institute
and State University; 2001.
[28] Schiller EH. Heat engine driven by shape memory alloys: prototyping and design: Virginia
Tech; 2002.
[29] Avirovik D, Kumar A, Bodnar RJ, Priya S. Remote light energy harvesting and actuation
using shape memory alloy—piezoelectric hybrid transducer. Smart Materials and Structures.
2013;22:052001.
[30] Sato Y, Yoshida N, Tanabe Y, Fujita H, Ooiwa N. Characteristics of a new power
generation system with application of a shape memory alloy engine. Electrical Engineering in
Japan. 2008;165:8-15.
[31] https://maps.nrel.gov/geothermal-prospector/.
[32] Villanueva A, Gupta S, Priya S. Lowering the power consumption of Ni-Ti shape memory
alloy. SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring:
International Society for Optics and Photonics; 2012. p. 83421I-I-12.
[33] Kase S, Matsuo T. Studies on melt spinning. I. Fundamental equations on the dynamics of
melt spinning. Journal of Polymer Science Part A: General Papers. 1965;3:2541-54.
[34] Kishore RA, Coudron T, Priya S. Small-scale wind energy portable turbine (SWEPT).
Journal of Wind Engineering and Industrial Aerodynamics. 2013;116:21-31.
[35] Kim SH, Lima MD, Kozlov ME, Haines CS, Spinks GM, Aziz S, Choi C, Sim HJ, Wang X,
Lu H, Qian D, Madden JDW, Baughman RH, Kim SJ. Harvesting temperature fluctuations as
electrical energy using torsional and tensile polymer muscles. Energy & Environmental Science.
2015;8:3336-44.

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