ABSTRACT

The Seebeck coefficient is a temperatureand material-dependent property, which linearly and causally relates the temperature difference between the “hot” and “cold” junctions of a thermoelectric power generator (TEC-PG) to the voltage difference. This phenomenon is the Seebeck effect (SE), and can be used to convert waste heat into usable energy. This work investigates the trends of the effective voltage output and effective Seebeck coefficient versus several hours of activity of a solid state TEC-PG device. The effective Seebeck coefficient here is related to a device, not just to a material’s performance. The observations are pursued in an insulated compartment in various geometrical and environmental configurations. The results indicate that the SE does not substantially depend on the geometrical and environmental configurations. However, the effective Seebeck coefficient and the produced effective are affected by the environmental configuration, once the temperature is fixed. Heat transfer calculations do not completely explain this finding. Alternative explanations are hypothesized.

Keywords:Thermoelectric, Heat Conduction, Energy Harvesting

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 N₂, 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 mm² 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 Bi₂Te₃-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 N₂ 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 Bi₂Te₃-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 (Al₂O₃) as dielectric layer. The other capacitor is C2, with

the other Cu plate and the Al sample holder as electrodes, and the Al₂O₃ plate as dielectric layer. Although the Al sample holders do not completely cover the alumina ceramic plate (the Al₂O₃ 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.

References

NOTES

^*Corresponding author.