New Method for Evaluating the Peltier Coefficient Based on Temperature Measurements in a Thermoelectric Module

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

“…The choice of the ux densities { s − R , } was not explained or justi ed by J. Garrido in [36,37], as he does not mention the dissipation function. Interestingly, in the more recent publications [38][39][40], Garrido and A. Casanovas conclude that a combination of the formalisms presented above, in particular (12) and (20), are the most useful for the observation of thermoelectric phenomena.…”

“…Remarkably, equation (18) shows that the measured electric potential di erence 2 − 1 is related to the Seebeck coe cient in the electrochemical formalism. Because voltages are measured more easily than heat generation, the Peltier coe cient is often evaluated from Thomson's relation [9,39,40], but its relative value between two conductors can be measured. The rst term in the right-hand side of (18) vanishes, regardless of the temperature distribution, if the circuit between points 1 and 2 is made of only one conductor; a statement closely related to the law of homogeneous materials [24].…”

“…The e ect is obviously independent of our choice of uxes and forces, but it can be illustrated with the greatest simplicity in terms of the ux of energy (internal plus electrostatic). The total energy ux density E is widely employed as the "thermal" ux density [2,23,30,[38][39][40]44], and (7) allows us to identify the corresponding "electrical" driving force as e = ∇(̃ / )/ . Contrarily to e in other formalisms, named after their associated electric potential, the driving force ∇(̃ / )/ cannot be interpreted as the negative gradient of an electric potential.…”

“…Recently, a new formulation of the thermoelectricity transport equations based on experimentally observable quantities has been proposed [36][37][38][39][40]. The observable electric potential when the potential di erence in (18) is measured with probes of material R is de ned as [36][37][38] …”

“…Novel recent approaches to the subject [36][37][38][39][40] are also discussed. The prevalence of the electrochemical formalism is explained.…”