General Figures of Merit ZQ for Thermoelectric Generators Under Constant Heat-In Flux Boundary.

The thermoelectric figure of merit ZT bridges the efficiency and material parameters for a thermoelectric device operating under constant temperature of the hot- and cold-source thermal boundary (Type-I TB). However, many application scenarios fall under the constant heat-in flux (q h ) and constant cold-source temperature (T c ) thermal boundary (Type-II TB), for which a figure of merit is absent for more than half a century. This study aims to fill this gap and propose a figure of merit ZQ D for the thermoelectric devices under the Type-II TB condition, defined as Z Q D = ( Z T c Z T c + 1 ) ( h κ ) ( q h T c ) $Z{Q}_{\mathrm{D}} = ( {\frac{{Z{T}_{\mathrm{c}}}}{{Z{T}_{\mathrm{c}} + 1}}} )( {\frac{h}{\kappa }} )( {\frac{{{q}_{\mathrm{h}}}}{{{T}_{\mathrm{c}}}}} )$ , where Z, h, and κ are the traditional figure of merit, leg height, and thermal conductivity, respectively. The effectiveness of ZQ D is verified through both numerical calculations and experiments, which are more accurate and practical than ZT. Furthermore, a system-level figure of merit ZQ S is suggested after considering the external thermal resistance. Finally, optimization strategies for thermoelectric systems based on ZQ S are proposed, showing a 30% enhancement in the efficiency. ZQ D and ZQ S are expected to be widely used in the thermoelectric field.