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Modeling and Optimization of Thermoelements by a Combined Analytical and Numerical Method

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Abstract

A combined analytical and numerical process has been developed to model and optimize thermoelements. In this way, the performance of commercial n- and p-type thermoelectric materials can be optimized to deliver the maximum output power and conversion efficiency. The validity of the method is demonstrated using a silicon germanium unicouple.

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Abbreviations

dx :

Infinitesimal distance in the direction of the temperature gradient (cm)

E :

Electric field (V/cm)

FOM:

Figure of merit of element

I :

Current through thermoelements (A)

J :

Current density (A/cm2)

JL :

Product of current density J and leg length L (A/cm)

L :

Length of thermoelements (cm)

MCE:

Maximum conversion efficiency

MOP:

Maximum output power

PD:

Electric power density (W/cm3)

Q :

Heat flux (W/cm2)

Q 1 :

Input heat flux (W/cm2)

Q M :

Rejected heat flux (W/cm2)

QL :

Product of input heat flux Q 1 and leg length L (W/cm)

R :

Electrical resistance of TE module (Ω)

S :

Cross-sectional area of thermoelements (cm2)

s :

Compatibility factor (1/V)

s MCE :

Compatibility factor for maximum conversion efficiency (1/V)

s MOP :

Compatibility factor for maximum output power (1/V)

T :

Absolute temperature (K)

T C :

Cold-end temperature of TE module (K)

T H :

Hot-end temperature of TE module (K)

TE:

Thermoelectric

TEG:

Thermoelectric power generation

u :

Reduced current density (1/V)

w q :

Electrical output power (W/cm2)

z :

Thermoelectric figure of merit (1/K)

zT :

Dimensionless thermoelectric figure of merit

α :

Seebeck coefficient of TE module (μV K−1)

ρ :

Electrical resistivity of thermoelement materials (Ω cm)

σ :

Electrical conductivity [1/(Ω cm)]

κ :

Thermal conductivity of thermoelement materials (mW cm−1 K−1)

η :

Conversion efficiency (%)

\( \eta_{\rm{c}} \) :

Carnot efficiency (%)

\( \eta_{\rm{r}} \) :

Reduced efficiency (%)

Φ:

Electrical potential (V)

Δ:

Variation (e.g., ΔT = T n  − T n−1)

∇:

Gradient, for one-dimensional case \( \frac{\text{d}}{\hbox{d}x} \)

1:

First temperature cell

C:

Colder side of TE element

H:

Hotter side of TE element

M :

Last temperature cell (the legs are divided into M cells)

max:

Maximum

MCE:

Maximum conversion efficiency

MOP:

Maximum output power

n :

nth temperature cell

N :

n-Type element

P :

p-Type element

References

  1. D.M. Rowe, editor, Handbook of Thermoelectrics (Boca Raton, FL: CRC Press, 1995).

    Google Scholar 

  2. D.M. Rowe, editor, Thermoelectrics Handbook Macro to Nano (Boca Raton, FL: CRC Press, 2006).

    Google Scholar 

  3. W.L. Luan and S.T. Tu, Chin. Sci. Bull. 49, 1212 (2004).

    Article  Google Scholar 

  4. G.J. Snyder and E.S. Toberer, Nat. Mater. 7, 105 (2008).

    Article  Google Scholar 

  5. B.W. Swanson, E.V. Somers, and R.R. Heikes, J. Heat Transf. 83, 77 (1961).

    Article  Google Scholar 

  6. M.S. El-Genk and H.H. Saber, Energy Convers. Manag. 44, 1069 (2003).

    Article  Google Scholar 

  7. M.S. El-Genk and H.H. Saber, STAIF-02: Proceedings of Space Technology and Applications International Forum, AIP Conference Proceedings No. 608 (New York: American Institute of Physics, 2002), pp. 980–988.

  8. H.H. Saber and M.S. El-Genk, STAIF-02: Proceedings of Space Technology and Applications International Forum AIP Conference Proceedings No. 608 (New York: American Institute of Physics, 2002), pp. 998–1006.

  9. M.S. El-Genk, H.H. Saber, and T. Caillat, Final Report Number UNM-ISNPS-1-2004, Institute for Space and Nuclear Power Studies, the University of New Mexico, 2004. (Technical Report).

  10. T.P. Hogan and S. Tom, Thermoelectrics Handbook Macro to Nano, ed. D.M. Rowe (Boca Raton, FL: CRC Press, 2006), Chap. 12.

  11. D.T. Crane, C.R. Koripella, and V. Jovovic, J. Electron. Mater. 41, 1524 (2012).

    Article  Google Scholar 

  12. B. Sherman, R.R. Heikes, and R.W. Ure, J. Appl. Phys. 31, 1 (1960).

    Article  Google Scholar 

  13. G.J. Snyder and T. Ursell, Phys. Rev. Lett. 91, 148301 (2003).

    Article  Google Scholar 

  14. G.J. Snyder, Appl. Phys. Lett. 84, 2436 (2004).

    Article  Google Scholar 

  15. W. Seifert, E. Muller, G.J. Snyder, and S. Walczak, Phys. Status Solidi (RRL) 1, 250 (2007).

    Article  Google Scholar 

  16. W. Seifert, K. Zabrocki, G.J. Snyder, and E. Müller, Phys. Status Solidi A 207, 760 (2010).

    Article  Google Scholar 

  17. W. Seifert, E. Müller, and S. Walczak, Phys. Status Solidi A 205, 2908 (2008).

    Article  Google Scholar 

  18. W. Seifert, K. Zabrocki, G.J. Snyder, and E. Müller, J. Mater. Res. 26, 1934 (2011).

    Article  Google Scholar 

  19. T.S. Ursell, and G.J. Snyder, ICT’02: 21st International Conference on Thermoelectrics (Long Beach, CA, 2002), p. 412.

  20. G.D. Mahan, J. Appl. Phys. 70, 4551 (1991).

    Article  Google Scholar 

  21. T. Caillat, J.P. Fleurial, and A. Borshchevsky, J. Phys. Chem. Solids 58, 1119 (1997).

    Article  Google Scholar 

  22. G.J. Snyder, Thermoelectrics Handbook Macro to Nano, ed. D.M. Rowe (Boca Raton, FL: CRC Press, 2006), Chap. 9.

  23. K. Matsubara, and M.A. Matsuura, Thermoelectrics Handbook Macro to Nano, ed. D.M. Rowe (Boca Raton, FL: CRC Press, 2006), Chap. 52.

  24. J.P. Dismukes, L. Ekstrom, E.F. Steigmeier, I. Kudman, and D.S. Beers, J. Appl. Phys. 10, 2899 (1964).

    Article  Google Scholar 

  25. C.B. Vining, W. Laskow, J.O. Hanson, R.R. Van der Beck, and P.D. Gorsuch, J. Appl. Phys. 69, 4333 (1991).

    Article  Google Scholar 

  26. J. Androulakis, C.H. Lin, and H.J. Kong, et al., J. Am. Chem. Soc. 129, 9780 (2007).

    Article  Google Scholar 

  27. S.K. Plachkova and I.A. Avramova, Phys. Status Solidi (a) 184, 195 (2001).

    Article  Google Scholar 

  28. J.P. Fleurial, A. Borshchevsky, and T. Caillat, Proceedings of the 15th International Conference on Thermoelectrics (New York: IEEE, 1996), p. 91.

  29. V.K. Zaitsev, M.I. Fedorov, E.A. Gurieva, I.S. Eremin, P.P. Konstantinov, AYu Samunin, and M.V. Vedernikov, Phys. Rev. B 74, 045207 (2006).

    Article  Google Scholar 

  30. C.E. Kelly, The MHW converter (RTG): Proceedings of 10th Intersociety Energy Conversion Engineering Conference. (New York: American Institute of Chemical Engineers, 1975), pp. 880–886.

  31. General Electric Company, General purpose heat source radioisotope thermoelectric generator (GPHS-RTG) final design review (Valley Forge, PA: General Electric Company, 1980).

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Authors and Affiliations

  1. Key Laboratory of Polar Materials and Devices, Ministry of Education, and Department of Electronic Engineering, East China Normal University (ECNU), Dongchuan Road 500, Shanghai, 200241, China

    Shaohui Xu, Yi** Zhu & Lianwei Wang

  2. School of Information and Communication Technology, Royal Institute of Technology (KTH), Stockholm, 16440, Sweden

    Qiang Chen & Lirong Zheng

  3. Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

    Lianwei Wang & Paul K. Chu

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  1. Shaohui Xu
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Correspondence to Shaohui Xu.

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Xu, S., Chen, Q., Zhu, Y. et al. Modeling and Optimization of Thermoelements by a Combined Analytical and Numerical Method. J. Electron. Mater. 43, 404–413 (2014). https://doi.org/10.1007/s11664-013-2860-0

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  • DOI: https://doi.org/10.1007/s11664-013-2860-0

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