Continuum Theory of TE Elements

Zabrocki, Knud; Goupil, Christophe; Ouerdane, Henni; Apertet, Y.; Seifert, W.; Müller, Eckhard

doi:10.1002/9783527338405.ch2

Cited by 13 publications

(19 citation statements)

References 116 publications

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“…It is based on a constant property model, which uses effective values of the temperature dependent material properties [20]. Alternatively a cumulative property model can be used to conclude on, which was proposed by Kim et al [21] and which accounts for the temperature dependency of material properties by means of a different expression for the maximum efficiency with the use of a so called engineering figure of merit.…”

Section: Module Characterization Techniquesmentioning

confidence: 99%

“…Typically the TEM current I is varied from zero up to the short circuit case. Every change of current flow alters the heat flow through the TEM due to the Peltier effect [20]. Thus, after changing I additional stabilization time is required to reach thermal equilibrium again.…”

Section: Tem Characterization Protocolmentioning

confidence: 99%

“…The corresponding standard deviation of the linear fits is almost constant (QGHP/TGuard-GHP) = 2.5% for the tested range of TGHP. Using equation (20) gives access to the effective thermal conductance XGuard-GHP between the GHP and the guard heater system ( Figure 13). The effective heat flow through the TEM QTEM corresponds to the sum of the heat flow, which is generated by the GHP QGHP, and positive or negative contributions from the guard heater system QGuard-GHP.…”

Section: Uncertainty Of the Ghp-based Absolute Heat Flow Determinationmentioning

confidence: 99%

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Heat flow measurement as a key to standardization of thermoelectric generator module metrology: A comparison of reference and absolute techniques

2021

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Traceable and standardized metrology for thermoelectric generator modules (TEM) is a mandatory element for an industrialization of thermoelectric applications. High measurement deviations >20% have been observed in inter-laboratory tests on TEM properties. Such uncertainties are too high for scientific studies and seem insufficient to validate industrial benchmarks. Particularly, works on hightemperature TEM have to be supported by appropriate characterization techniques. This shall accelerate progress towards product releases for thermoelectric energy conversion.

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Section: Module Characterization Techniquesmentioning

confidence: 99%

Section: Tem Characterization Protocolmentioning

confidence: 99%

Section: Uncertainty Of the Ghp-based Absolute Heat Flow Determinationmentioning

confidence: 99%

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Heat flow measurement as a key to standardization of thermoelectric generator module metrology: A comparison of reference and absolute techniques

2021

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“…For anisotropic S one can write jS l = j k S kl . In that case ρ , κ are symmetric tensors of second rank (3 × 3 matrices) and S in the most general case is an asymmetric matrix . Obviously a single valued TE‐figure of merit Z ( x ) = S ( x ) 2 /( ρ ( x ) κ ( x )) is no useful concept for anisotropic materials.…”

Section: Optimization Of Te‐performance In 3dmentioning

confidence: 99%

“…The original Onsager–deGroot–Callen theory also applies to 3D TE‐device structures , and has been established even for anisotropic media . Finite Element methods have been used to investigate concrete 3D structures .…”

Section: Introductionmentioning

confidence: 99%

Thermoelectric converters with optimum graded materials and current distribution in one dimension and three dimensions

Gerstenmaier

Wachutka

2017

Physica Status Solidi (b)

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The description of TE‐converter performance with inhomogeneous material distribution is based on the classical Onsager–deGroot–Callen transport theory. A variational approach for performance maximization is generalized from previous 1D heat‐ and electric current distribution to general 3D devices by use of partial differential equations. The concept of multi‐stage (cascaded) TE‐converters in 1D is generalized to arbitrarily distributed electric current sources in the 3D case by introducing an extended version of the Onsager–deGroot–Callen theory. Originally insufficient material properties together with optimized current distribution allow for maximum performance with respect to a general distribution function of the thermoelectric figure of merit Z(x, T) depending simultaneously on 3D position x and local temperature T. Thermally isolating as well as non‐isolating boundary‐conditions are treated. Investigation of hitherto unsolved problems of the 1D theory leads to a new analytical solution of maximized generated electric power for optimized grading. In previous literature analytical formulas had been established for 1D TE‐efficiencies. For the outstanding maximization problem of cooling power improved results are obtained by fast inversion of tridiagonal matrices compared to previous findings with differential equation initial value algorithms. An analytic calculation is possible by optimizing the temperature extremum location in a piecewise linear profile. By its construction a close lower bound to the exact cooling power is formed, which is possibly identical to the exact value.

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Interlaboratory Testing for High‐Temperature Power Generation Characteristics of a Ni‐Based Alloy Thermoelectric Module

et al. 2020

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Standardization of metrology for thermoelectric generator modules (TEMs) is a necessary step toward industrialization of thermoelectric applications. Unspecified uncertainty budgets of the widely used custom‐built characterization facilities seem insufficient to validate technological developments, industrial benchmarks, or allow sound conclusions in scientific studies. Particularly, works on high‐temperature TEM have to be supported by suitable characterization techniques. This shall accelerate progress toward product releases for thermoelectric energy conversion. Herein, a Ni‐based alloy TEM is reported, which is developed at the National Institute of Advanced Industrial Science and Technology (AIST) as a prospective standard reference TEM. Comparative measurements at AIST and the German Aerospace Center (DLR) demonstrate the high repeatability and precision of custom‐built TEM characterization facilities at AIST and DLR. Tests at elevated temperatures up to 773 K hot side temperature and 450 K temperature difference reveal excellent accordance of electric measurands with a standard deviation <0.3% for the open‐circuit voltage and <0.85% for electric resistance and maximum power output. Deviations of the heat flow measurement of up to 7.22% arise from individual uncertainties of the used characterization methods and point to the importance of standardization for TEM metrology.

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Continuum Theory of TE Elements

Cited by 13 publications

References 116 publications

Heat flow measurement as a key to standardization of thermoelectric generator module metrology: A comparison of reference and absolute techniques

Heat flow measurement as a key to standardization of thermoelectric generator module metrology: A comparison of reference and absolute techniques

Thermoelectric converters with optimum graded materials and current distribution in one dimension and three dimensions

Interlaboratory Testing for High‐Temperature Power Generation Characteristics of a Ni‐Based Alloy Thermoelectric Module

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