Effective Thermoelectric Power Generation in an Insulated Compartment

The Seebeck coefficient S is a temperatureand material-dependent property, which linearly and causally relates the temperature difference T ∆ between the “hot” and “cold” junctions of a thermoelectric power generator (TEC-PG) to the voltage difference V ∆ . 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 ( ) V t ∆ and effective Seebeck coefficient ( ) S t ′ versus several hours of activity of a solid state TEC-PG device. The effective Seebeck coefficient ( ) S t ′ 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 ( ) S t ′ and the produced effective ( ) V t ∆ are affected by the environmental configuration, once the temperature is fixed. Heat transfer calculations do not completely explain this finding. Alternative explanations are hypothesized.


Introduction
Imagine two dissimilar electrical conductors or semiconductors joined in two different locations with the "hot" junction at temperature T T T + ∆ > , and the "cold" junction at T .Such device is a thermoelectric power ge- nerator (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 T ∆ caused by heat generates a voltage difference V ∆ 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, T ∆ and V ∆ are causally and linearly related through the Seebeck coefficient S , such that * V S T ∆ = − ∆ .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 T ∆ .The temperature difference T ∆ , in turn, generates the voltage difference V ∆ according to the SE.Given that no, or very few, charged par- ticles 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 2 S T ZT κρ = [1] [2] [7], and the Seebeck coefficient S .In the expression for ZT , κ is the thermal conductivity and ρ the electrical resis- tivity.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 S [10].

S t
′ 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 ( )

S t
′ 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 ( ) 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 ( ) ( ) S t ′ 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 ( ) ( ) V t ∆ are bound by a causal and linear relationship.However, the effective ( ) V t ∆ and the effective Seebeck coefficient ( )

S t
′ 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.

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 40 C ≈  .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 ( ) T t , respectively.The junctions are separated along the vertical direction by 4 mm high pillars of an n-and p-doped Bi 2 Te 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 ( ) ( ) S t ′ 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 ( ) T t , 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 4.02 C 0.30 C − ±   and 4.96 C 0.09 C − ±   , 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 ( ) V t ∆ were collected using Keithley 2000 multi-meters.Each multi-meter is sensitive to direct current voltages from 1 µV 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 t ∆ 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 t ∆ 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 ~35 C 5 C ±   .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 qualify the accuracy of the procedure.

Figures 2(a)-(c)
show the trends of ( ) ( ) S t ′ in the in the "away" horizontal configuration.
The values of mean ( ) µ , standard deviation ( ) σ , and relative error R σ µ ( )       The effects of the environmental configurations are described in Figure 5 and Figure 6 and the corresponding µ , σ , and R values are summarized in Table 3 and Table 4. Causality and linearity between ( ) ( ) V t ∆ 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 ( ) , similar to that of the "toward" vertical configuration.Thus, the data    ( ) 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 ( ) cal T ∆ between the two thermocouple probes in the "away" horizontal and "toward" horizontal configurations were measured and reported in Table 5  ( ) V t ∆ 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 0 T ∆ , 0 V ∆ , α , and β , reported in Table 6, gave the best goodness of fitting parameters 2 R α and 2 R β .The 0 T ∆ values vary between 0.28 ("toward" horizontal) to 1.5˚C ("toward" horizontal-black tape).On the other hand, the 0 V ∆ values vary between 0.62 − ("toward" horizontal) to 3.75 mV ("toward" vertical-aluminum supports).However, the rates of increase of ( ) ( ) and β respectively, are almost constant in the examined configurations.The rate of increase of the effective ( ) 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.

Discussion
The results are reproducible and fully support the causal and linear relationship between the effective ( ) , over the examined time range and in all the considered geometrical and environmental configurations.The average values of the effective Seebeck coefficient ( ) S t ′ 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 ( )

S t
′ values required to adjust the systematic errors occurring in the effective ( ) T t ∆ 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 ( )

S t
′ values found in the examined vertical configurations are related to the relatively large average effective ( ) values, while the av- ( ) erage value of the effective ( )  .This situation is verified also for the "toward" vertical- aluminum 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 ( ) ( ) , is corroborated by the rates of increase of ( ) ( )

V t ∆
, α and β respectively, whose values are summarized in Table 6.These values are almost constant in the examined configurations: α is on average C 0.02 s  , while β is on average mV 0.03 s .It is noteworthy, however, that the value of β in the "toward" vertical-aluminum supports configuration is mV 0.08 s .In this case, average effective ( ) V t ∆ 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 ( )

( )
S t ′ 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 κ in the "to- ward" configuration illustrated in Figure 1

( )
V t ∆ 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 Table 4.To calculate the heat loss rate loss Θ through the sample holder [16] in the steady state condition in Region 2, first the total resistance TEC-PG R 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: In Equation (1), t is the thickness of the material in the solid state TEC-PG device depicted in Figure 8, A is its surface area, and κ 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  7. The heat transfer rate across the solid state TEC-PG device is: This quantity is 0.5 W, assuming a T ∆ of 16.5 C 16.5 K =  (where K is degree Kelvin), as experimentally determined and previously discussed.
The second step is the calculation of the heat loss rate loss Θ in Region 2 due to the different sample holders in the right corner of Figure 8.The sample holder's (SH) resistance is: where the 1 2 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 Table 7. Assuming isotropic heat diffusion, the heat loss rate loss Θ across the sample holders in Figure 8 is:

( )
V t ∆ 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 ( ) V t ∆ 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 2 Te 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 2 O 3 ) as dielectric layer.The other capacitor is C2, with Table 7. Thermal conductivity ( κ ) and specific physical dimensions (length l , width w , and thickness t ) of the materials involved in the heat transfer rate Θ across the solid state TEC-PG device, and heat loss rate loss Θ through the sample holders.For the two different sample holder's materials considered (Al and wood) the heat loss rate loss Θ is calculated through resistance equations [16].The temperature differences across the sample holders are:

( )
V t ∆ 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 52.0 mV V ∆ = value in the "toward" vertical-aluminum supports case, which is larger than the average effective 39.1 mV V ∆ = value in the "toward" vertical case with wood sample holders.

Figure 1 .
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.

Figure 2 (a) and Figure 2
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 flowing through the 142 basic TEC-PG units to explain the effective

Figures 3 (
Figures 3(a)-(c) illustrate the trends of the effective

Figure 7
Figure7shows the fitting of the experimental effective

Figure 7 .
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 ( ) T t ∆ (a)

Figure 8 .
Figure 8.The factor 1 142 in the third term of Equation (1) appears because there are 142 pillars of a Bi 2 Te 3based 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:

Figure 8 .
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 (Al 2 O 3 ) as dielectric layer.C2 indicates the capacitor with the other Cu plate, and the Al sample holder as electrodes, and the Al 2 O 3 plate as dielectric layer.
V ∆ 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 time interval in Region 2 where steady state was achieved.The fitting of the V t ∆curves was performed in the 400 s time segment in Region 2immediately following the turning-on of the hot plate.A linear fit was employed, such that 0 V ∆ are the initial offsets, while α and β are the rate of increase of ( )

Table 1
indicates that the values of σ and R in Region 2 are of the same order of magnitude for ( )S t′ .Only the σ value for ( )S t′ is one order of magnitude lower than that for the effective ( )V t ∆.The results are reproducible, and fully testify the existence of a causal and linear relationship between ( )V t ∆, in agreement with the SE, such that

Table 1 .
Mean ( ) µ , standard deviation ( ) σ , and relative error ( ) " 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.

Table 2 .
The findings again support the causal and linear S t′ in the "toward" horizontal configuration.The µ , σ , and R values are displayed in Table1.The results are comparable to those for the "away" horizontal configuration.The average value of the effective Seebeck coefficient ( ).The results are reproducible, and further support the result achieved for the "away" configuration that the effective ( ) S t ′ in the in the "toward" vertical configuration.The µ , σ , and R values are reported in

Table 2 .
Mean ( ) 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 µ , standard deviation ( ) σ , and relative error ( ) S t ′ in the "toward" vertical configuration.The values are evaluated in region 2 in the 12 -30 hour time interval.V t ∆ , observed in Figures 3-5,

.
Based on the corr T ∆ .Finally, using the experimental average voltage difference in Region 2 ( V ∆ from Table 1), the corrected effective Seebeck coefficients in the steady state of Region 2

Table 5 .
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 2 R α and 2 R β .Temperature difference ( ) crease of the temperature of the hot plate surface.The linearity of the relationship between ( ) V ∆ , and corrected Seebeck coefficient in Region 2 ( ) corr S′ .The values are analyzed in the "away"

Table 6 .
The values of initial offsets 0T ∆ and 0 V ∆ , and of α , the rate of increase of ( ) β are also reported.The parameters are obtained from the linear fitting of the experimental curves, as those illustrated in Figure7, which were obtained in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate.
[16]produce a different rate of heat loss loss Θ .A larger heat loss rate The calculation of the heat loss rate loss Θ 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 Figure8.If an increase in heat loss rates loss Θ through the sample holder exists and the corresponding voltage difference

Table 7 ,
and are compared with the trends of the average effective

Table 2 and
Table 4. Cu plate and the Al sample holder as electrodes, and the Al 2 O 3 plate as dielectric layer.Although the Al sample holders do not completely cover the alumina ceramic plate (the Al 2 O 3 layer in Figure 8), the total effective voltage difference