On the different formalisms for the transport equations of thermoelectricity: A review

Abstract

Researchers in thermoelectricity with backgrounds in non-equilibrium thermodynamics, thermoelectric engineering or condensed-matter physics tend to use di erent choices of ux densities and generalized forces. These choices are seldom justi ed from either the dissipation function or the entropy production rate. Because thermoelectric phenomena are a primary focus in several emerging elds, particularly in recent energy-oriented developments, a review of the di erent formalisms employed is judged timely. A systematic classi cation of the transport equations is presented here. The requirements on valid transport equations imposed by the invariance of the entropy production are clearly explained. The e ective Peltier and Seebeck coe cients, and the thermal conductivity, corresponding to the di erent choices of ux densities and generalized forces, are identi ed. Emphasis is made on illustrating the compatibility of apparently disparate formalisms. The advantages and drawbacks of these formalisms are discussed, especially from the point of view of the experimental determination of their thermoelectric coe cients.

Perspectives on Thermoelectric Energy Conversion in Ion-Exchange Membranes

“…This review will, however, focus on a large class of materials which may be more accessible, namely ion-exchange materials. In the last several years, the possibility of using ion-exchange membranes in renewable energy technology is in the crosshairs [ 14 , 15 , 16 , 17 , 18 , 19 ].…”

Recent trends in thermoelectrochemical cells and thermally regenerative batteries

“…A more detailed treatment which reports also on the Soret entropy and thermodiffusion phenomena can be found in [40]- [42] and it is worth to check as these can give large contribution to the temperature coefficients as found for example in [18], [43]- [46] compared against a "simple" faradaic reaction, as those collected of Bratsch [14].…”