World Journal of Condensed Matter Physics
Vol.4 No.3(2014), Article
ID:49395,13
pages
DOI:10.4236/wjcmp.2014.43020
Effective Thermoelectric Power Generation in an Insulated Compartment
Harkirat S. Mann1, Yosyp Schwab1, Brian N. Lang1, Jarrett L. Lancaster2, Ronald J. Parise3, Giovanna Scarel1*
1Department of Physics and Astronomy, James Madison University, Harrisonburg, USA
2Department of Nano-Science at the Joint School of Nano-Science and Nano-Engineering (JSNN), University of North Carolina at Greensboro and North Carolina A&T University, Greensboro, USA
3Parise Research Technologies, Suffield, USA
Email: *scarelgx@jmu.edu
Copyright © 2014 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Received 5 May 2014; revised 11 June 2014; accepted 5 July 2014
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.Figure 1. (a) Schematic illustration of the basic unit of the TEC-PG; (b) The “away” horizontal configuration; (c) The “toward” horizontal configuration; (d) Photograph of the isolated compartment.
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.Figure 2. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “away” horizontal configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Table 1. Mean, standard deviation, and relative error of, , and in the “away” horizontal and “toward” horizontal configurations. The values displayed for the “away” horizontal configuration are evaluated in Region 2 in the 12 - 30 hour time interval, whereas those for the “toward” horizontal configuration are evaluated in Region 2 in the 10.5 - 30 hour time interval.
Figure 3. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” horizontal configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 4. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” vertical configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 5. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” horizontalblack tape configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 6. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” verticalaluminum supports configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Table 2. Mean, standard deviation, and relative error of, , and in the “toward” vertical configuration.The values are evaluated in region 2 in the 12 - 30 hour time interval.
Table 3. Mean, standard deviation, and relative error of, , and in the “toward” horizontal-black tape configuration. The values are evaluated in Region 2 in the 20 - 30 hour time interval.
Table 4. Mean, standard deviation, and relative error of, , and in the “toward” vertical-aluminum supports configuration. The values are evaluated in Region 2 in the 20 - 30 hour time interval.
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.Table 5. Temperature difference between the two thermocouple probes; corrected temperature difference in Region 2 between the “hot” and “cold” junction of the solid state TEC-PG device; experimental average effective voltage difference in Region 2, and corrected Seebeck coefficient in Region 2. The values are analyzed in the “away” and “toward” configurations, placing the thermocouple probes either on the “hot” or “cold” junctionsof the solid state TEC-PG device, and fixing, for the corrections, either the temperature of the thermocouple normally used on the “cold” or “hot” junctions of the solid state TEC-PG device. The former setting is named cold thermocouple, the latter the hot thermocouple.
Table 6. The values of initial offsets and, and of, the rate of increase of, and of, the rate of increase of. The corresponding goodness of fitting parameters and are also reported. The parameters are obtained from the linear fitting of the experimental curves, as those illustrated in Figure 7, which were obtained in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate.
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-Figure 7. Linear fittings observed in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate of the rise in (a) and (b) in the “away” horizontal configuration, and of the rise in (c) and (d) in the “toward” horizontal configuration.
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, withFigure 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.
Table 7. Thermal conductivity () and specific physical dimensions (length, width, and thickness) of the materials involved in the heat transfer rate across the solid state TEC-PG device, and heat loss rate through the sample holders. For the two different sample holder’s materials considered (Al and wood) the heat loss rate is calculated through resistance equations [16] . The temperature differences across the sample holders are:, and. The values are the average effective voltage difference in the steady state condition in region 2 for the wood and Al cases, and correspond to those in Table 2 and Table4
, (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.
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