Comprehensive modeling for geometric optimization of a thermoelectric generator module

Abstract

This paper develops a one-dimensional simulation model of a thermoelectric module aiming at its characteristic exploration and output performance prediction. Almost all related effects are considered including Seebeck, Peltier, Thomson effects, the spatial- and temperature-dependent thermoelectric material properties, as well as the other irreversible factors. In order to ensure its high accuracy and computational efficiency, the differential equations built for components of non-linear physical properties, and analytical equations for the others of constant properties are jointly solved by numerical methods and implemented in MATLAB integrated development environment. A small deviation of 1.44% exists between its calculated output power and that by a previously reported three-dimensional model under a specific wide load range (0–250 Ω), validating its accuracy of this model. Besides, it indicates that both the proportions of heat leakage through the occupied air zone and its maximum output power to the input total heat flow have the same order of magnitude. A rising proportion for the former has to be paid attention in case of a higher temperature difference applied. The assumption of regarding its electrical contact resistance as an identical external resistance connected with the load in series is computationally proved to generate a negligible discrepancy in terms of TEM characteristics and its output performance. Furthermore, with respect to the impacts of TEM geometry, the pre-set fixed substrate area weakens the equivalence of regarding a thermoelectric module with larger cross-section area of thermoelectric legs as multiple identical modules with smaller leg areas connected in parallel. It accounts for the better linearity of rising output power by a long leg than that by a short leg as the leg area increases. A long thermoelectric leg means an increased induced electrical potential and inner resistance as well, thus leading to a single peak of the output power as the leg length increases. Finally, a thermoelectric geometric optimization approach abased on the Hill-climbing algorithm is introduced and first applied for the maximum output. Its accuracy and efficiency are validated and analyzed detailedly by supplying different variables as initial search point. All the methods and conclusions in this paper can assist thermoelectric generators’ performance estimation and guide the geometric optimizations regarding their large-scale applications in the future.