Weighted sum optimization for combined thermoelectric geometry and electric pulse using finite elements

Abstract

Thermoelectric materials assembled in Peltier cells are an increasingly widespread option for generating electricity from residual sources and refrigeration, even at the nanoscale. These cells can cool below the nominal temperatures with an electric pulse, during short periods and for applications such as laser devices or microchips. The present article uses heuristic algorithms to improve the response of a Peltier cell by concurrently optimizing the pulse and geometry of its thermoelements. The study is based on the Finite Element method, handling full coupling and dynamics of the thermal, electric, and mechanical fields and temperature dependency of the material properties. The optimization algorithm is Simulated Annealing, capable of discarding local minima to reach robust results and permitting set limiting factors such as the maximum stress. The main novelty lies in multilayered geometries and pulse shapes that can reproduce any geometry and pulse virtually. First, a complete parametric analysis under constant pulse is presented to understand the complexities of the temperature, electric flux, and stress distributions in these layered geometries. Second, combined optimizations are discussed. The targets are overcooling temperature, time to reach it, overheating minimization, overcooling duration, and combinations. In the best cases, the first target is doubled, the second is reduced to a few milliseconds, the third is null, and the duration can be 95% of the pulse while reducing the stress up to 40%.