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Unified Model for Thermoelectric Generator and Peltier Cooler
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| Organization: | Martin-Luther-Universitat Halle-Wittenberg |
| Department: | Dept. of Theoretical Physics |
| Organization: | Institut für Werkstoff-Forschung |
| Department: | German Aerospace Center (DLR) Cologne |
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2006-12-11
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Graded and segmented thermoelements have been considered for long, aiming at improving the performance of thermogenerators (TEGs) which are exposed to a large temperature difference. Proof was given recently that thermoelectric material gradients exert an essential influence also on the performance of Peltier coolers [1,2].
Recent results on the continua-theoretical solution describing stacked thermoelectric pellets and their optimization of performance [1] are complemented here by an analytical approach related to the relative current density u (ratio of current density to dissipative heat flux). This concept introduced for TEGs by Snyder and Ursell [3] has opened a new understanding of temperature-based optimization of graded and segmented TE element design. They succeeded in deducing a differential equation for u(T) from the energy balance. Its solution is enabling the calculation of the reduced efficiency \eta_r(T) as a local state variable, leading finally to the description of the overall efficiency as a function of the electric current density.
For the 1D case of constant material properties (1D-CPM) an analytical solution of the transport of charge and heat through a thermoelectric element exists which allows, in conjunction with the TE compatibility function s(T) introduced by Snyder et. al., for a rational search of efficiently graded TE systems. The new compatibility concept can be used furthermore to calculate numerically the relative current density u(T) and the efficiencies \eta_r(T) and \eta for a TEG material with the Seebeck coefficient, electrical conductivity, and thermal conductivity depending on temperature.
This work shows that the approach proposed by Snyder and Ursell can be generalized and applied also to the Peltier cooler case. Limitations and peculiarities of this description will be discussed.
[1] E. Mueller, S. Walczak, W. Seifert, C. Stiewe, G. Karpinski, in: Proc. 24th Int. Conf. on Thermoelectrics (ICT 2005), Clemson, SC, USA, 2005, IEEE, Piscataway, NJ, 2006, pp. 352-357.
[2] E. Mueller, S. Walczak, W. Seifert, C. Stiewe, G. Karpinski, D. Platzek, T. E. Svechnikova, L. E. Shelimova, in: Proc. 3rd European Conf. on Thermoelectrics (ECT 2005), Nancy, FR, 2005, pp. 22-30.
[3] G. J. Snyder, T. S. Ursell, Phys. Rev. Letters 91, No. 14, 148301-1--4 (2003).
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Peltier Cooler, Thermoelectric Generator, thermoelements, thermogenerators
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| TEGandTEC.nb (25.1 KB) - Mathematica Notebook [for Mathematica 5.2] |
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