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

ABSTRACT

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 (qh ) and constant cold-source temperature (Tc ) 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 ZQD 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 ZQD is verified through both numerical calculations and experiments, which are more accurate and practical than ZT. Furthermore, a system-level figure of merit ZQS is suggested after considering the external thermal resistance. Finally, optimization strategies for thermoelectric systems based on ZQS are proposed, showing a 30% enhancement in the efficiency. ZQD and ZQS are expected to be widely used in the thermoelectric field.