Thermoelectric generator at optimal power with external and internal irreversibilities

TL;DR

This paper derives exact optimal power conditions for thermoelectric generators considering both internal and external irreversibilities, providing bounds on efficiency at maximum power and analyzing different regimes.

Contribution

It offers a comprehensive analysis of thermoelectric generator efficiency at maximum power with combined irreversibilities, extending previous simplified models.

Findings

Derived bounds for EMP in various irreversibility regimes

Identified step-wise changes in EMP near equilibrium

Compared EMP properties under different thermal impedance conditions

Abstract

There are few exact results on optimal power conditions for a thermoelectric generator in the presence of both external and internal irreversibilities---modelled as non-ideal thermal contacts and Joule heating, respectively. Simplified cases, where only one kind of irreversibility is assumed, yield some well-known expressions for efficiency at maximum power (EMP), such as Curzon-Ahlborn efficiency for endoreversible model. In this work, we analyze situations under the simultaneous presence of internal and external irreversibilities. To simplify, we neglect heat leaks, and each kind of irreversibility is assumed only on the side of one of the thermal contacts. We also present the symmetric case---where each kind of irreversibility contributes with equal strengths towards the side of each thermal contact. We show the bounds satisfied by EMP in each of these regimes and compare its properties for thermal impedence matching and close to equilibrium, where we find step-wise changes in EMP.