Effective Thermoelectric Power Generation in an Insulated Compartment ()
1. Introduction
Imagine two dissimilar electrical conductors or semiconductors joined in two different locations with the “hot” junction at temperature
, and the “cold” junction at
. Such device is a thermoelectric power generator (TEC-PG), and the schematic illustration of the basic unit of a TEC-PG is shown in
Figure 1(a). Solid state (above millimeter size) TEC-PGs devices used in applications consist of several of such units placed in series. The Seebeck effect (SE) in the TEC-PG is a known phenomenon in which the temperature difference
caused by heat generates a voltage difference
due to the flow of charge carriers (electrons or holes) from the “hot” junction in contact with a thermal source, to the “cold” junction, which acts as a thermal sink. In the SE, at constant temperature,
and
are causally and linearly related through the Seebeck coefficient
, such that
. Voltage production in the TEC-PG is referred to as TEC power generation
[1]
[2] . The spin SE
[3] , transverse SE
[4] , and anisotropic SE
[5] , discussed in recent literature, are examples of TEC power generation. Heat is intended as the manifestation of kinetic energy
[6] transmitted by the thermal source to the neutral particles of the alumina-ceramic plate protecting the “hot” junction of the TEC-PG. Temperature witnesses the trends of kinetic energy. Heat is transferred by convection and conduction to the “hot” junction of the TEC-PG, and contributes to the generation of the temperature difference
. The temperature difference
, in turn, generates the voltage difference
according to the SE. Given that no, or very few, charged particles are involved, radiative heat transfer is minimal in the experiments presented here. The applications of TEC power generation are numerous: thermal sensors
[2]
[7] , spacecraft heat engines and deep-space probes
[1]
[2]
[7] , laser temperature controllers
[7] , thermal cyclers for biological testing
[7] , health
[1]
[2] and vehicle climate controls
[1]
[2]
[7]
[8] , coolers
[7] , and cooling of electronic enclosures
[1]
[2]
[7] . Although controversies arose regarding the ability of research efforts to improve the efficiency and performance of the TEC-PGs
[7]
[8] , TEC power generation is still proposed for additional and larger-scale applications which require materials with large TEC parameters, such as the figure of merit
[1]
[2]
[7] , and the Seebeck coefficient
. In the expression for
,
is the thermal conductivity and
the electrical resistivity. Under the assumption that the TEC parameters have a fixed value in a particular material and device, the design of the material and its composition are considered the most important factors in improving the performance and efficiency of the TEC-PGs
[1] -
[3]
[7] -
[9] . Recently, also band-engineering was shown to enable improvements in the TEC-PG’s performance
[4]. In the case of miniaturized (around nanometer size) TEC-PGs with thin films as active layer, the film substrate was shown to influence the Seebeck coefficient
[10] . This work focuses on the application of solid state TEC-PG devices as energy harvesting
[1]
[2]
[8]
[11] -
[13] , and waste heat recovery devices
[7]
[8]
[14]
[15] . For these applications, the effective voltage output
and the effective Seebeck coefficient
are characterized versus time in various geometrical and environmental configurations for commercial solid-state TEC-PG devices consisting of several basic units placed in series. The effective Seebeck coefficient
refers to a device, not just to a material’s performance, and relates the effective temperature difference
, measured over time between the “hot” and “cold” junctions, and the effective voltage output
, such that
. Five different geometrical and environmental configurations are considered in the presented investigation: three geometries, two different “hot” junction finishing surfaces, and two sample holder materials, one insulating and one conducting. The investigation is performed in an insulated compartment to avoid the contributions to the effective
,
, and
of random variations of laboratory temperature, humidity, and radiation. The insulated compartment promotes small fluctuations and low errors in the measurements. The details of the geometrical and environmental configurations are described in Section 2. The findings, described in Section 3, suggest that the effective
and
are bound by a causal and linear relationship. However, the effective
and the effective Seebeck coefficient
are slightly affected by the specific geometrical and environmental configuration, in particular by the materials of the sample holder. Heat transfer calculations are unable to completely explain this phenomenon. An explanation is offered by observing that the experimental set-up involving the solid state TEC-PG device can be treated as system of two capacitors in series.
2. Experimental Set-Up and Data Analysis
The heat source used is a Corning Hot Plate Scholar 170. The instrument has a temperature range of 25˚C - 300˚C, and is located in a custom-made insulated compartment constructed of 1.27 cm thick extruded acrylic sheets. The insulated compartment is purged with a flux of N
2, which is kept at a steady flow by suction. The temperature of the hot plate during the experiment is
.
The solid state TEC-PG devices used are Custom Thermoelectric Inc. model 07111-9L31-04B devices, whose TEC-PG basic unit is schematically illustrated in
Figure 1(a). Each device has a 900 mm
2 surface area. The “hot” and “cold” junctions of the solid state TEC-PG device are protected by plates of alumina-ceramic and are at effective temperatures
and
, respectively. The junctions are separated along the vertical direction by 4 mm high pillars of an nand p-doped Bi
2Te
3-based alloy in series with each other, and by copper (Cu) plates. There are 142 of such pillars in the used solid state TEC-PG devices. In all measurements, the “hot” junction of the solid state TEC-PG device is placed parallel to the surface of the hot plate, which uniformly heats the junction. Thermally insulating sample holders made of wood are used to properly position the solid state TEC-PG devices on the hot plate, as illustrated in
Figure 1(b) and
Figure 1(c). A picture of the insulated compartment is shown is
Figure 1(d). To examine the behavior of the effective
and
with time, two geometrical configurations were considered: the “away” horizontal and “toward” horizontal. In these configurations, the hot plate is in horizontal position inside the insulated compartment as in
Figure 1(d). In the “away” horizontal configuration, depicted in
Figure 1(b), the solid state TEC-PG device is suspended above the hot plate through tape connected to the thermally insulating sample holder, and is in contact with neither the sample holders nor the hot plate. In the “toward” horizontal configuration, pictured in
Figure 1(c), the solid state TEC-PG device is physically supported by the thermally insulating sample holders above the hot plate surface. An additional geometrical configuration was considered: the “toward” vertical, which is the “toward” horizontal configuration rotated by 90˚. Furthermore, two additional environmental configurations were examined: 1) the “toward” horizontal-black tape configuration, in which a layer of black electrical tape was placed in adhesion to the surface of the “hot” junction of the solid state TEC-PG device; and 2) the “toward” vertical-aluminum supports configuration, in which the thermally insulating sample holders were substituted with thermally conducting ones, made of aluminum (Al). To measure the effective temperatures
and
, OMEGA type E Ni-Cr/Cu-Ni thermocouple probes were used. The probes are sensitive to temperatures from ‒270˚C to 1000˚C. One probe was placed on the alumina-ceramic plate protecting the “hot” junction, and the other one on the plate protecting the “cold” junction. The average difference in the temperature detected by the two probes are
and
, measured on the alumina-ceramic plate on the “hot” junction in the “away” horizontal and “toward” horizontal configurations, respectively. In all configurations, it was verified that the hot plate uniformly heats the “hot” junction. The trends of
,
, and
were collected using Keithley 2000 multi-meters. Each multi-meter is sensitive to direct current voltages from 1 mV to 1 kV, and to the same temperature range as the range of sensitivity of the chosen thermocouple probes. The data were collected for 30 hours (h) at time intervals
of 300 s using Lab View 7, and a National Instruments PXI-1042q communications chassis. Before turning-on the hot plate, the solid state TEC-PG device and the thermocouple probes relaxed in the insulated compartment for 5 - 6 hours. This time range is named Region 1. In the 400 s time segment immediately following the turning-on of the hot plate, a
of 1 s was selected for the data acquisition. Afterwards, the hot plate was kept on for the remainder of the experiment. This time range is named Region 2. In all experiments, the temperature of the ambient inside the insulated compartment, and the temperature of the sample holder were
. The laboratory hosting the instrumentation was kept dark and at a constant temperature of 20˚C. The data were analyzed using Origin Pro Data Analysis and Graphing Software. The variation effective Seebeck coefficient was derived as
in the time interval in Region 2 where steady state was achieved. The fitting of the
and
curves was performed in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate. A linear fit was employed, such that
, and
, respectively. Here,
and
are the initial offsets, while
and
are the rate of increase of
and
with time, respectively. The goodness of fitting parameters
and
qualify the accuracy of the procedure.
3. Results
Figures 2(a)-(c) show the trends of
,
and
in the in the “away” horizontal configuration. The values of mean
, standard deviation
, and relative error
of
,
, and
are summarized in
Table1
Figure 2(a) and
Figure 2(b) clearly show that
and
follow the same trends in both Regions 1 and 2. The step between Regions 1 and 2 corresponds to the turning-on of the hot plate. The average value of the effective Seebeck coefficient
in the steady state portion of Region 2 is
. The negative mean value of
agrees with electrons flowing through the 142 basic TEC-PG units to explain the effective
production
[2].
Table 1 indicates that the values of
and
in Region 2 are of the same order of magnitude for
,
and
. Only the
value for
is one order of magnitude lower than that for the effective
and
. The results are reproducible, and fully testify the existence of a causal and linear relationship between
and
, in agreement with the SE, such that
.
Figures 3(a)-(c) illustrate the trends of the effective
,
and
in the “toward” horizontal configuration. The
,
, and
values are displayed in
Table1 The results are comparable to those for the “away” horizontal configuration. The average value of the effective Seebeck coefficient
in the steady state portion of Region 2 is
. The results are reproducible, and further support the result achieved for the “away” configuration that the effective
and
are bound by a causal and linear relationship, in agreement with the SE.
Figures 4(a)-(c) illustrate the trends of
,
and
in the in the “toward” vertical configuration. The
,
, and
values are reported in
Table2 The findings again support the causal and linear relationship between
and
, in agreement with the SE, as in the previously examined configurations. It is noteworthy, however, that in this case the average value of the effective Seebeck coeffiecient
in the steady state portion of Region 2 is
, a slightly larger negative value than in the previously examined configurations. The effects of the environmental configurations are described in
Figure 5 and
Figure 6 and the corresponding
,
, and
values are summarized in
Table 3 and
Table4 Causality and linearity between
and
in agreement with the SE hold in a similar manner as for the “away” and “toward” horizontal, and “toward” vertical configurations.
Figure 5 and
Table 3 report the results for the “toward” horizontal-black tape configuration. In this case, the average value of the effective Seebeck coefficient
in the steady state portion of Region 2 is
.
Figure 6 and
Table 4 report the results for the “toward” vertical-aluminum supports configuration. In this case, the average value of the effective Seebeck coeffiecient
in the steady state portion of Region 2 is
, similar to that of the “toward” vertical configuration. Thus, the data
presented so far indicate that, in various geometrical and environmental configurations, the trends of the effective
,
and
are similar. The average values of the effective Seebeck coefficient
in the steady state portion of Region 2, however, slightly depend upon the specific configuration. The vertical configurations seems to promote a lager absolute magnitude of
. Slight instabilities in the trends of
and
, observed in
Figures 3-5, might be due to instabilities in the heated N
2 gas inside the insulated compartment. It is very interesting to observe that, when the instabilities are originated in the
graphs, they are reflected in the
trends. This is another proof of the causal
and linear relationship existing between the effective and.
In Section 2, it was noticed that there are differences in the temperatures detected by the two thermocouple probes when placed contemporarily on the alumina-ceramic plate of either the “hot” or “cold” junctions of the solid state TEC-PG device. Discrepancies were found in both in the “away” and “toward” horizontal configurations. Because of these differences, a correction to the average values of the Seebeck coefficients is needed. To obtain such correction, the temperature differences
between the two thermocouple probes in the “away” horizontal and “toward” horizontal configurations were measured and reported in
Table5 Based on the
values, the corrected
s were estimated and reported as
. Finally, using the experimental average voltage difference in Region 2 (
from
Table 1), the corrected effective Seebeck coefficients in the steady state of Region 2
are reported in
Table5 The values lie between
and
in the “away” horizontal configuration, and between
and
in the “toward” horizontal configuration. In both the “away” and the “toward” horizontal configurations, the experimentally measured average effective
values of
and
, respectively, are within the
range.
Figure 7 shows the fitting of the experimental effective
and
data in the “away” and “toward” configurations observed in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate. A linear fitting with parameters
,
,
, and
, reported in
Table 6, gave the best goodness of fitting parameters
and
. The
values vary between 0.28 (“toward” horizontal) to 1.5˚C (“toward” horizontal-black tape). On the other hand, the
values vary between
(“toward” horizontal) to
(“toward” vertical-aluminum supports). However, the rates of increase of
and
,
and
respectively, are almost constant in the examined configurations. The rate of increase of the effective
,
, is on average
, while the rate of increase of the effective
,
, is on average
. Only the
value in the “toward” vertical-aluminum supports configuration is
. In this case, the
(3.75 mV) and the average
(52.0 mV) values are the largest among all the examined cases. The value of the rate of increase of
,
, which is on average
, coincides with the rate of increase of the temperature of the hot plate surface. The linearity of the relationship between
and
in the 400 s time segment in Region 2, immediately following the turning-on of the hot plate, is strongly supported by the large values of the goodness of fitting parameters
and
.
4. Discussion
The results are reproducible and fully support the causal and linear relationship between the effective
and
in agreement with the SE,
, over the examined time range and in all the considered geometrical and environmental configurations. The average values of the effective Seebeck coefficient
in the steady state of Region 2 after turningon the hot plate, however, slightly depend upon the geometrical and environmental configuration. In particular, the vertical configuration seems to promote a lager absolute magnitude. The result holds also after the correction of the effective Seebeck coefficient
values required to adjust the systematic errors occurring in the effective
measurements. Gravity should prevent the convection of hot air to reach the higher parts of the solid state TEC-PG device, but this effect seems not to play any role. The larger
values found in the examined vertical configurations are related to the relatively large average effective
values, while the av-
erage value of the effective
is
.This situation is verified also for the “toward” verticalaluminum supports configuration. Therefore, contributions to
in the vertical configuration, especially with the Al sample holder, originate from factors other than the SE. The existence of a causal and linear relationship between the effective
and
, in agreement with the SE,
, is corroborated by the rates of increase of
and
,
and
respectively, whose values are summarized in
Table6 These values are almost constant in the examined configurations:
is on average
, while
is on average
. It is noteworthy, however, that the value of
in the “toward” vertical-aluminum supports configuration is
. In this case, average effective
achieves the value of 52.0 mV, which is the maximum detected in the presented set of experiments. Evidently, the Al sample holder promote an increase in
without affecting the heat transfer across the solid state TEC-PG device: indeed the effective
is
, very close to the average of
. The lack of correlation between
and
with the Al sample holders is supported by the existence of a bump followed by a decay in the
data of the “toward” vertical-aluminum support configuration in
Figure 6(b). This feature does not exist in the
data in
Figure 6(a). This finding implies that, given the causal relationship between
and
, the anomaly is located solely in the
production. Thus, the effective Seebeck coefficient
can be modified by the geometrical and environmental configurations in which the solid state TEC-PG device is activated. Testing other settings, such as the distance of the TEC-PG from the surface of the hot plate and its inclination on it, with the aid of either insulating or conducting sample holders, could further support this conclusion. To ascertain the role of heat transfer in explaining the described phenomena, the experimental results are compared to calculations. The hypothesis is that sample holders made of materials with different
in the “toward” configuration illustrated in
Figure 1(c) produce a different rate of heat loss
. A larger heat loss rate
would determine, in a certain time interval, a smaller effective temperature difference
across the solid state TEC-PG device, and a smaller effective voltage difference
due to the SE. The calculation of the heat loss rate
across the sample holders in the “toward” configuration is carried out through resistance equations
[16
] , and assuming Al and wood as sample holder materials. The model system is illustrated in
Figure 8. If an increase in heat loss rates
through the sample holder exists and the corresponding voltage difference
decreases, then heat transfer enables the understanding of the observed phenomena. The
values achieve a steady state value in Region 2, which is larger for the Al than for the wood sample holder, as summarized in
Table 2 and
Table4
To calculate the heat loss rate through the sample holder [16] in the steady state condition in Region 2, first the total resistance of the isolated solid state TEC-PG device depicted in Figure 8 without considering the sample holders in the right corner of the figure, is calculated as follows:
(1)
In Equation (1), is the thickness of the material in the solid state TEC-PG device depicted in Figure 8, is its surface area, and its thermal conductivity. The factors 2 in the first and second term of the equation appear because there are two alumina-ceramic and two Cu plates in the solid state TEC-PG device depicted in
Figure 8. The factor in the third term of Equation (1) appears because there are 142 pillars of a Bi2Te3based alloy in the solid state TEC-PG devices used for this experiment. The values of the thermal conductivity and of the geometrical parameters are summarized in Table7 The heat transfer rate across the solid state TEC-PG device is:
, (2)
This quantity is 0.5 W, assuming a of (where K is degree Kelvin), as experimentally determined and previously discussed.
The second step is the calculation of the heat loss rate in Region 2 due to the different sample holders in the right corner of Figure 8. The sample holder’s (SH) resistance is:
(3)
where the factor is due to the parallel resistance determined by the sample holders in contact with the solid state TEC-PG device. The values of the thermal conductivity and of the geometrical parameters of the wood and Al sample holders are reported in Table7 Assuming isotropic heat diffusion, the heat loss rate across the sample holders in Figure 8 is:
, (4)
where is the temperature difference across the sample holder: 2 K across Al, and 5 K across wood. The calculated values of are reported in Table 7, and are compared with the trends of the average effective values in the steady state in Region 2. It can be seen that the decreases and the average effective values also decrease, in order, from the Al to the wood sample holders, which is contradictory according to our hypothesis. In addition, with the Al sample holder, the heat loss rate (2.5 W) is larger than the heat transfer rate across the solid state TEC-PG device (0.5 W).The lack of correlation between the heat loss rates and the effective average values, suggests that heat transfer does not completely explain the effective voltage production in the examined cases.
These findings suggest that in solid state TEC-PG devices the effective
production might be determined by factors other than heat transfer. One of these factors could be of electrical nature. Indeed,
Figure 8 suggests that in the “toward” vertical-aluminum supports case, the 142 pillars of doped Bi
2Te
3-based alloy in the solid state TEC-PG device are embedded between two capacitors in series: one is C1, with air and one of the Cu plates as electrodes, and the alumina-ceramic plate (Al
2O
3) as dielectric layer. The other capacitor is C2, with
Figure 8. Model of the solid state TEC-PG device mounted to the sample holder used in the calculations of heat transfer rates across the solid state TEC-PG device and heat loss rates through the sample holders. Aluminum and wood are considered as materials of the sample holders. The arrows indicate the direction of flow of the heat lost through the sample holders. C1 indicates the capacitor with air and a Cu plate as electrodes, and the alumina-ceramic plate (Al2O3) as dielectric layer. C2 indicates the capacitor with the other Cu plate, and the Al sample holder as electrodes, and the Al2O3 plate as dielectric layer.
the other Cu plate and the Al sample holder as electrodes, and the Al
2O
3 plate as dielectric layer. Although the Al sample holders do not completely cover the alumina ceramic plate (the Al
2O
3 layer in
Figure 8), the total effective voltage difference
produced by such a system of capacitors in series can be approximated as:
, (5)
where
is the contribution of capacitor C1 and
is the contribution of capacitor C2. The
voltage difference influences the effective voltage difference
produced by the solid state TEC-PG device. Wood is an insulator, thus not a good electrode material. Therefore no C2 capacitor can be considered with the wood sample holder. Thus in the case of the Al sample holder, the existence of the two capacitors in series could explain the average effective
value in the “toward” vertical-aluminum supports case, which is larger than the average effective
value in the “toward” vertical case with wood sample holders.
5. Summary and Significance
In a solid state thermoelectric power generator (TEC-PG) device, the effective temperature difference
between the “hot” and “cold” junctions produces an effective voltage difference
. This work focuses on the effective Seebeck coefficient
, which refers to a device, not just to a material’s performance. The results show that effective Seebeck effect
holds over a long time of activity of the solid state TEC-PG device in an insulated compartment, and over several geometrical and environmental configurations. Within the systematic errors in the temperature measurements and the possible temperature instabilities, the relationship between the effective
and
is always causal and linear. However, the effective Seebeck coefficient
can be affected by the geometrical and environmental configurations. In particular, contributions to
, related to the motion of the charge carriers in the semiconducting pillars of the TEC-PG and not due to
, are discovered. Calculations based solely on heat transfer are not sufficient to explain the observed phenomena. However, the used experimental set-up involving the solid state TEC-PG device can be viewed as a system of two capacitors in series. This view aids in the understanding of the
production of solid state TEC-PG devices. Other configurations with different distances or inclinations of the solid state TEC-PG device with respect to the heat source should be considered to support this conclusion. The available results underline that, while materials engineering efforts are necessary to improve applications exploiting the Seebeck effect, efforts are also needed to maximizing the effective performance of thermoelectric devices. To this end, in the future experiments are planned to understand the effect of the size of the heating area, and will be accompanied by finite element analysis.
Acknowledgements
This work was supported by the US Office of Naval Research (award # N000141410378), JMU 4-VA Consortium (2013), Thomas F. Jeffress and Kate Miller Jeffress Memorial Trust (grant # J-1053), JMU College of Science and Mathematics for the Summer 2014 Faculty Assistance Grant, the JMU Center for Materials Science, and the JMU Department of Physics and Astronomy. The authors thank Profs. K. Giovanetti, J. Zimmerman, S. Whisnant, D. Lawrence, K. Feitosa, and K. Fukumura (JMU) for fruitful discussions. Thanks to Dr. X. Hu, A. Fovargue, T. Benns, and J. Jarrell, for technical support and help in the construction of the insulated sample compartment.
NOTES
*Corresponding author.