Optimal performance of thermoelectric devices with small external irreversibility

TL;DR

This paper develops a simplified model for thermoelectric devices considering both internal and external irreversibilities, deriving an expression for efficiency at maximum power and comparing it with existing models.

Contribution

It introduces a symmetric and small external irreversibility approximation within the Constant Properties model, unifying internal and external irreversibilities in thermoelectric analysis.

Findings

Derived a tractable EMP expression depending on three key parameters.

Compared the model with exact and other irreversible models, showing good agreement.

Mapped thermoelectric generators to Feynman's ratchet in high-temperature regimes.

Abstract

In the thermodynamic analysis of thermoelectric devices, typical irreversibilities are for the processes of finite-rate heat transfer, heat leak and Joule heating. Approximate analyses often focus on either internal or external irreversibility, obtaining well-known expressions for the efficiency at maximum power (EMP), such as the Curzon-Ahlborn value for endoreversible model and the Schmiedl-Seifert form for exoreversible model. Within the Constant Properties model, we simultaneously incorporate internal as well as external irreversibilities. We employ the approximation of a symmetric and small external irreversibility (SEI), allowing a tractable expression for EMP that depends on three parameters i) the ratio of internal to external thermal conductance ii) the figure of merit of the thermoelectric material and iii) the ratio of hot and cold reservoir temperatures. We study limiting forms of this EMP and compare our framework with the exact model as well as with other irreversible models in finite-time thermodynamics, such as the minimally nonlinear model. In particular, we argue that the TEG in endoreversible approximation can be mapped to the mesoscopic model of Feynman's ratchet in the high temperatures regime, thus providing an alternative to the viewpoint in literature where the TEG in linear regime is mapped to an exoreversible case. Finally, extending our study to the thermoelectric refrigerator under similar assumptions as for the generator, we analyze the efficiency at the maximum cooling power.