Comparison with Thermoelectrics

To compare the presented energy harvesting principles with thermoelectric devices, it is not sufficient to just consider power density or efficiency figures because of the very different design. A fair comparison with thermoelectric generators (TEG) requires to take into account a similar size and similar temperature differences. Only microTEGs al-low a high density of thermocouples and therefore noteworthy voltages at miniature size. An example for commercially available microTEGs are electroplated TEGs with sizes of 4.4 x 4.4 x 0.5 mm³ from GreenTEG [104] or sputter deposited TEGs with an overall size of 3.3 x 2.43 x 1.1 mm³ from micropelt [105]. For the sake of complete-ness, also a conventional bulk material based TEG is considered.

Besides the size of the TEG itself, also the size of the heat sink has to be taken into ac-count. For a maximum efficiency and power output, the thermal resistance of the heat sink has to be matched to the thermal resistance of the TEG [48]. In order to do so, the microTEGs need heat sinks a hundred times larger than the actual TEG-area (200x to 500x) and thousand times larger than the active TEG-volume. To guarantee a fair comparison between the microTEGs and the energy harvester presented in this work, TEGs with a heat sink of a dimension of the actual TEG-size are considered.

Comparison with Thermoelectrics 8: Comparison and Discussion

Table 8.2 summarizes the data of the microTEGs and a representative bulk TEG. For evaluation of their actual power, a heat source temperature of 170 °C and an ambient temperature of 30 °C is considered, matching approximately the operational conditions of the FSMA-based energy harvesting device using a magnetic heat source. For the mi-croTEGs two cases are investigated. For operation without any specially designed heat source, a natural convection heat transfer coefficient h of 20 W·(m² K)^-1is assumed. By implementing an additional heat source of the area of the TEG, the heat transfer coeffi-cient of 80 W·(m² K)^-1 is assumed. One has to keep in mind that such a heat source would increase the volume of the microTEG-based energy harvesting system substan-tially. For the bulk TEG a standard heat sink of 25 x 25 mm²size is assumed, having a matched thermal resistance of 20 K·W^-1.

Table 8.2: Parameters of TEGs.

micropelt DPG-655 greenTEG gSKIN bulk TEG Volume 3.3 x 2.43 x 1.1 mm³ 4.4 x 4.4 x 0.5 mm³ 20 x 20 x 4 mm³ Thermal resistance )TEG 22 K·W^-1 18 K·W^-1 20 K·W^-1

Electric resistance RTEG 210 Ω 13 Ω 11 Ω

Open circuit voltage vOC 80 mV·K^-1 4.3 mV·K^-1 28.6 mV·K^-1 To evaluate the thermal resistances of the microTEG heat sinks, the area of the mi-croTEGs A and the heat transfer coefficient are used:

Θ_sink = 1

h⋅ A. (30)

Because of the difference of the thermal resistances of the microTEGs and the heat sinks, the temperature difference across the microTEGs ∆TTEGis only part of the overall temperature difference ∆T, proportional to the ratio of thermal resistances:

ΔT_TEG

ΔT = Θ_TEG

Θ_sink+Θ_TEG . (31)

For the bulk TEG, the temperature difference is exactly 0.5, as the thermal resistance of the TEG and the heat sink are matched perfectly.

In order to calculate the electrical power, it is supposed that the load resistance match-es the electric rmatch-esistance of the microTEG. The voltage output is then half of the open circuit voltage due to the linear electric behavior of TEGs. Then, the power can be cal-culated as follows:

P=(^vOC₂ ⋅ΔT_TEG)²

R_TEG . (32)

The efficiency of the microTEG system is calculated by dividing the electrical power by the heat flux through the system:

8: Comparison and Discussion Comparison with Thermoelectrics

η = P Q = P

ΔT_TEG Θ_TEG

. (33)

For the bulk TEG, the formula of the efficiency at maximum electric power is used, which can also be found in [48]:

η_mp =η_C⋅ 1

2+ _ZT⁴ −^η₄^C . (34)

For the calculation of power density, only the volume of the active TEG material is used, which has a thickness of only 40 µm in case of the microTEGs.

The results of the calculations are given in Table 8.3. It is important to note that the temperature difference achievable along the microTEGs is very small, even using a spe-cially designed heat source with a high heat transfer coefficient of 80 W·(m² K)^-1. There-fore, the resulting overall power output, power density, efficiencies of the microTEGs are small.

Table 8.3: Characterization of TEGs at an overall ∆T = 140 K, considering power, efficiency, and power density.

micropelt, hmin micropelt, hmax greenTEG, hmin greenTEG, hmax Bulk TEG )sink 6235 K·W^-1 1559 K·W^-1 2583 K·W^-1 646 K·W^-1 20 K·W^-1

∆TTEG 0.49 K 1.95 K 0.97 K 3.8 K 70 K

P 1.83 µW 29 µW 0.34 µW 5.14 µW 93.4 mW

$ 0.0082% 0.032% 0.0006% 0.0024% 2.67%

P/V 7.9 mW·cm^-3 125 mW·cm^-3 0.9 mW·cm^-3 13.3 mW·cm^-3 194 mW·cm^-3 When comparing these numbers with the results on the magnetic SMA-based energy harvesting devices investigated in this work, most of the presented demonstrators can-not compete with the microTEG results, which have been developed and optimized over a long time. However, the FSMA-based energy harvesting device using a magnet-ic heat source already shows competitive results with an average electrmagnet-ical power of 2.4 µW and a very high power density of up to 118 mW·cm^-3, being on par with the best microTEG and almost reaching the power density of conventional bulk TEGs. The lack of need for additional heat sinking is also a key for the competitiveness of magnet-ic SMA-based energy harvesting devmagnet-ices. Heat is transferred only in a discrete and re-stricted manner, ensuring a sufficient temperature difference instead of steadily flowing through the TEG.

Therefore, a continuous optimization of the design and the material of magnetic SMA-based energy harvesting devices could lead to competitive alternatives to TEGs espe-cially on miniature scale.

Comparison with Thermoelectrics 8: Comparison and Discussion

8: Comparison and Discussion Comparison with Thermoelectrics