Optimization analyses of thermoelectric generators operation is of importanceboth for practical applications and theoretical considerations. Depending onthe desired goal, two different strategies are possible to achieve highperformance: through optimization one may seek either power output maximizationor conversion efficiency maximization. Recent literature reveals the persistentflawed notion that these two optimal working conditions may be achievedsimultaneously. In this article, we lift all source of confusion by correctlyposing the problem and solving it. We assume and discuss two possibilities forthe environment of the generator to govern its operation: constant incomingheat flux, and constant temperature difference between the heat reservoirs. Wedemonstrate that, while power and efficiency are maximized simultaneously ifthe first assumption is considered, this is not possible with the secondassumption. This latter corresponds to the seminal analyses of Ioffe who putforth and stressed the importance of the thermoelectric figure of merit $ZT$.We also provide a simple procedure to determine the different optimal designparameters of a thermoelectric generator connected to heat reservoirs throughthermal contacts with a finite and fixed thermal conductance.
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