Influence of thermal environment on optimal working conditions of thermoelectric generators

TL;DR

This paper clarifies the conditions under which thermoelectric generators can maximize power or efficiency, demonstrating that simultaneous optimization is only possible under specific environmental assumptions.

Contribution

It corrects misconceptions about simultaneous power and efficiency optimization and provides a method to determine optimal design parameters based on environmental conditions.

Findings

Power and efficiency can be maximized simultaneously under constant heat flux.

Maximizing power and efficiency simultaneously is impossible under constant temperature difference.

Provides a procedure to determine optimal design parameters for thermoelectric generators.

Abstract

Optimization analyses of thermoelectric generators operation is of importance both for practical applications and theoretical considerations. Depending on the desired goal, two different strategies are possible to achieve high performance: through optimization one may seek either power output maximization or conversion efficiency maximization. Recent literature reveals the persistent flawed notion that these two optimal working conditions may be achieved simultaneously. In this article, we lift all source of confusion by correctly posing the problem and solving it. We assume and discuss two possibilities for the environment of the generator to govern its operation: constant incoming heat flux, and constant temperature difference between the heat reservoirs. We demonstrate that, while power and efficiency are maximized simultaneously if the first assumption is considered, this is not possible with the second assumption. This latter corresponds to the seminal analyses of Ioffe who put forth and stressed the importance of the thermoelectric figure of merit $ZT$. We also provide a simple procedure to determine the different optimal design parameters of a thermoelectric generator connected to heat reservoirs through thermal contacts with a finite and fixed thermal conductance.