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On the posedness of thermoelectrochemical coupled systems

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Abstract

We examine the complete coupled thermoelectrochemical system that describes reaction problems. The cross effects, namely the thermoelectric (Peltier-Seebeck), the thermodiffusion (Dufour-Soret), and the electrochemical diffusion, occur as reciprocal phenomena of irreversible processes. We deal with convective/radiative heat-transfer boundary conditions on a part of the boundary. The objective is their application to electrolysis, Li batteries, and fuel cells. The existence of stationary solutions for the theoretical model is found, under different smallness conditions on the data, via a fixed point argument.

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Abbreviations

c :

molar concentration (molarity) mol · m−3

c v :

specific heat capacity (at constant volume) J · K−1 · kg−1

D :

diffusion coefficient m2 · s−1

D′:

Dufour coefficient m2 · s−1 · K−1

E :

activation energy J · mol−1

e :

specific internal energy J · kg−1

F :

Faraday constant 9.6485 × 104 C · mol−1

h :

heat transfer coefficient W · m−2 · K−1

k :

thermal conductivity W · m−1 · K−1

m :

concentration (molality) mol · kg−1

q :

specific electric charge C · kg−1

R :

gas constant 8.314 J · mol−1 · K−1

S :

Soret coefficient (thermal diffusion) m2 · s−1 · K−1

s :

specific entropy J · K−1 · kg−1

u :

mobility m2 · V−1 · s−1

z :

valence (dimensionless)

α :

Seebeck coefficient V #x00B7; K−1

μ :

chemical potential J · mol−1

φ :

electric potential V = J · C−1

π :

Peltier coefficient V

ρ :

density kg · m−3

σ :

electrical conductivity S · m−1

θ :

absolute temperature K

▽:

gradient

a:

anode

c:

cathode

i:

ionic component

w:

wall

References

  1. J. McBreen, H.S. Lee, X.Q. Yang, X. Sun, J. Power Sources 89, 163 (2000).

    Article  ADS  Google Scholar 

  2. A.M. Duffin, R.J. Saykally, J. Phys. Chem. C 111, 12031 (2007).

    Article  Google Scholar 

  3. C.M. Focken, Trans. Proc. R. Soc. New Zealand 63, 285 (1934).

    Google Scholar 

  4. A.-K. Meland, S. Kjelstrup, J. Electroanal. Chem. 610, 171 (2007).

    Article  Google Scholar 

  5. R.A. Rozendal et al., Int. J. Hydrogen Energy 31, 1632 (2006).

    Article  Google Scholar 

  6. M.Z. Bazant, K. Thornton, A. Ajdari, Phys. Rev. E 70, 021506 (2004).

    Article  ADS  Google Scholar 

  7. J. Rossmeisl, Z.-W. Qu, H. Zhu, G.-J. Kroes, J.K. Nørskov, J. Electroanal. Chem. 607, 83 (2007).

    Article  Google Scholar 

  8. D. Tianping, J.W. Weidner, R.E. White, J. Power Sources 107, 24 (2002).

    Article  Google Scholar 

  9. C.-Y. Wang, Chem. Rev. 104, 4727 (2004).

    Article  Google Scholar 

  10. H. Amann, M. Renardy, Nonlinear Differ. Equ. Appl. 1, 91 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  11. Y.S. Choi, R. Lui, J. Differ. Equ. 108, 424 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. L. Consiglieri, A.R. Domingos, Int. J. Math. Math. Sci. 2011, 862813 (2011).

    Article  MathSciNet  Google Scholar 

  13. S. Luckhaus, A. Visintin, Manuscr. Math. 43, 261 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  14. W.B. Gu, C.Y. Wang, J. Electrochem. Soc. 147, 2910 (2000).

    Article  Google Scholar 

  15. K. Kumaresan, G. Sikha, R.E. White, J. Electrochem. Soc. 155, A164 (2008).

    Article  Google Scholar 

  16. A. Latz, J. Zausch, O. Iliev, Ber. Fraunhofer ITWM 190, (2010).

  17. V. Srinivasan, C.Y. Wang, J. Electrochem. Soc. 150, A98 (2003).

    Article  Google Scholar 

  18. N. Djilali, D. Lu, Int. J. Therm. Sci. 41, 29 (2002).

    Article  Google Scholar 

  19. P.J.S. Vie, S. Kjelstrup, Electrochim. Acta 49, 1069 (2004).

    Article  Google Scholar 

  20. Y.I. Burak, T.S. Nagirnyi, Int. Appl. Mech. 28, 775 (1993).

    Article  Google Scholar 

  21. D.T.J. Hurle, J.B. Mullin, E.R. Pike, J. Chem. Phys. 42, 1651 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  22. M.T. Solodyak, J. Math. Sci. 90, 2020 (1998).

    Article  Google Scholar 

  23. L. Coury, Curr. Sep. 18, 91 (1999).

    Google Scholar 

  24. L. Consiglieri, Z. Angew. Math. Mech. 89, 218 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  25. L. Consiglieri, Ann. Univ. Ferrara 57, 229 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  26. A.B.H. Susan, A. Noda, M. Watanabe, Electrochemical Aspects of Ionic Liquids, edited by H. Ohno (John Wiley & Sons, Inc., Hoboken, New Jersey, 2005) pp. 55--74.

  27. J.E. House, Principles of Chemical Kinetics, 2nd edition (Academic Press, Elsevier Inc., 2007).

  28. S.R. De Groot, P. Mazur, Nonequilibrium Thermodynamics (Interscience, New York, 1962).

  29. L. Consiglieri, Mathematical analysis of selected problems from fluid thermomechanics. The (p − q) coupled fluid-energy systems (Lambert Academic Publishing, Saarbrücken, 2011).

  30. R.G. Mortimer, H. Eyring, Proc. Natl. Acad. Sci. USA 77, 1728 (1980).

    Article  ADS  Google Scholar 

  31. J. Geng, Adv. Math. 229, 2427 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  32. J.O. Jensen, Report PSO-F&U 2006-1-6287, KI/DTU, Ris/DTU and DONG Energy 2008.

  33. N. Dunford, J.T. Schwartz, Linear operators, Part I (Interscience Publ., 1958).

  34. K. Gröger, J. Rehberg, Math. Ann. 285, 105 (1989).

    Article  MathSciNet  MATH  Google Scholar 

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  1. 1600-256, Lisbon, Portugal

    Luisa Consiglieri

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  1. Luisa Consiglieri
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Correspondence to Luisa Consiglieri.

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Consiglieri, L. On the posedness of thermoelectrochemical coupled systems. Eur. Phys. J. Plus 128, 47 (2013). https://doi.org/10.1140/epjp/i2013-13047-7

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