Efficiency at maximum power of thermally coupled heat engines

TL;DR

This paper investigates the efficiency at maximum power of two thermally coupled thermoelectric generators, revealing that the optimal conditions are not unique and that the efficiency varies with working conditions, challenging some classical assumptions.

Contribution

It provides a simple analytic expression for the load resistance conditions for maximum power in coupled TEGs and analyzes how EMP varies with different working conditions.

Findings

EMP can differ from Curzon-Ahlborn efficiency depending on conditions

Optimal load resistance is not unique for maximum power

EMP remains within bounds predicted by irreversible thermodynamics

Abstract

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique. We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focuse on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: the EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We finally discuss our results in light of non-ideal Carnot engine behavior.