Structural and geometric optimization of thermoelectric legs under steady-state and transient thermal boundary conditions

• Uncover impacts of thermal and electric contact resistances on various leg designs. • Reveal structural features improving TEG performance under steady/transient conditions. • Study temperature, electric potential, and current density distributions of each leg design. • Propose a novel hollow trapezoidal-prism TE leg design. The thermal and electrical contact resistances (TCRs/ECRs) are crucial factors in optimizing the leg structural and geometric design of thermoelectric generators (TEGs). Nevertheless, they were often overlooked in previous relevant work. This study aims to reveal the impacts of these contact resistances on TEG performance employing various TE leg designs and thermal boundary conditions, identify essential leg structural features for performance enhancement, and elucidate the underlying physical mechanisms. Specifically, twelve distinct leg designs were studied. Their output power and output power density were numerically estimated under both steady and transient thermal boundary conditions, considering with and without the distributed TCRs/ECRs. It is revealed that TCRs/ECRs significantly impact leg designs under steady-state temperature boundary conditions; ignoring them can result in inaccurate or even misleading leg-shape recommendations. However, under steady-state heat flux boundary conditions on the hot side, inclusion of these contact resistances does not alter the performance ranking of these leg designs. The results considering TCRs/ECRs also indicate that the hollow structure and particular trapezoidal leg designs (i.e., T_low and T_upp) can substantially enhance TEG performance under both steady-state and transient heat flux boundary conditions on the hot side. These enhancements arise from the dramatically increased temperature and electric potential differences across TE legs. In light of these findings, novel hollow trapezoidal prism-shaped TE legs are proposed, which improve the output power and output power density by 50.3% and 172.7%, respectively, compared with the prevailing solid cuboid-shaped TE legs at a heat flux of 1 W from the heat source. Under transient heat flux boundary conditions, its average output power and output power density improved by 61% and 193%, respectively.