Formula for energy conversion efficiency of thermoelectric generator taking temperature dependent thermoelectric parameters into account

Abstract

A simple formula for maximum efficiency (ηmax) of heat conversion into electricity in a thermoelectric generator is derived and discussed in terms of a practical dimensionless thermoelectric figure of merit (ZT)PR, taking temperature dependent Seebeck coefficient, resistivity, and thermal conductivity into account. Thomson heating that comes from the temperature dependent Seebeck coefficient (d|S|/dT > 0) reduces thermal conduction loss as well as Joule heating. On the other hand, Thomson cooling that occurs in the region d|S|/dT < 0 at a high-temperature side increases the thermal conduction loss. The conversion efficiency calculated from the formula is compared with simulated results for practical thermoelectric materials such as PbTe-based materials and Mg2Si, indicating a very good agreement.