Thermodynamics of thermoelectric phenomena and applications

Entropy

Volumn 13, Issue 8, 2011, Pages 1481-1517

  Goupil, Christophe ^a   Seifert, Wolfgang ^b   Zabrocki, Knud ^c   Müller, Eckhard ^c   Snyder, G Jeffrey ^d  

^a LABORATOIRE CRISMAT   (France)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^c GERMAN AEROSPACE CENTER DLR   (Germany)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Compatibility approach; Entropy production; Optimum device design; Thermoelectric potential; Thermoelectricity

Indexed keywords

EID: 80053521031     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e13081481     Document Type: Review

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145. A more general definition of u seems possible when writing the relative current density in terms of fluctuating currents which are indeed 3D. In this context, particle and heat flow should be considered in an anisotropic medium where the material parameters are tensors, see e.g., [174].
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147. Power output is defined here according to thermodynamic rules: quantities input to the system are positive
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149. The Carnot engine exchanges energy in a reversible form, that means after an infinite time. Therefore, the Carnot engine transforms energy efficiently but with zero power.
150. Replace in [116] Equation (9), right hand side, the ± sign by a minus sign valid for both the pump up and the pump down situation
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153. Seifert, W.; Zabrocki, K.; Snyder, G.; Müller, E. The compatibility approach in the classical theory of thermoelectricity seen from the perspective of variational calculus. Phys. Stat. Sol. A 2010, 207, 760-765.
154. r are introduced for both TEG and TEC, respectively
155. Seifert,W.; Pluschke, V.; Goupil, C.; Zabrocki, K.; Müller, E.; Snyder, G. Maximum performance in self-compatible thermoelectric elements. J. Mater. Res. 2011, in press.
156. The relative current density is defined by Equation (75); the 1D variants are u(x) = -J/κT′(x) respectively u(T) = -J/κx′(T), whereby the temperature gradient decides the sign of u. Note that T(x) peaks in the interior of the TE element only far above the optimum current for maximum efficiency and maximum coefficient of performance. Then u has a pole.
157. Note that Sherman et al. used the function ε(T) instead of optimal reduced efficiency.
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