This paper presents a numerical study on the influence of pulsed electric signals applied to the overcooling of thermoelectric devices. To this end, an experimental setup taken from the literature and a commercial cell are simulated using a complete, specially developed research finite element code. The electro-thermal coupling is extended to include the elastic field, demonstrating that the increment of cooling can produce mechanical failure. Numerical results are developed and the variation of overcooling versus pulse gain and versus duration is validated towards a new analytical expression and the experimental data. The issue of optimal intensity at steady-state is also newly developed. Thermal and mechanical trends are presented using constant and variable (with temperature) material properties for a single thermoelement. While some of the first trends are similar to those of published works, others are different or directly new, all closer to those of the experiments. The mechanical results have not been thoroughly studied until recently. The three-dimensional finite element mesh includes non-thermoelectric materials that are fundamental for the current study. Distribution of stresses during steady and transient states are shown inside the thermoelement, for five components and for the combined Tresca stress. Concentrations at corners of the lower side appear close to the cold face. Due to these concentrations, 27-node isoparametric, quadratic brick elements are used. It is shown that the mechanical field is an important factor in the design of pulsed thermoelectrics, since for practical applications the stress levels are close or slightly above the admissible limits.

Highlights • We present a complete formulation for thermo-electro-elastoplastic behavior that is developed in a consistent manner by using conservation principles along with the definition of a free-energy potential. • FE implementation in the most general 3D framework, by using 8-node hexahedral finite element for constructing semidiscretization, along with the global phase of time discretization by the Newmark scheme. • This development provides the sound basis for practical applications, such as the pulsed Peltier Cells.

The objective of this work is to determine the optimal shape, gains and duration of an electric pulse applied to a Peltier cell, together with the length of the thermoelectric to maximize cooling while minimizing electric consumption. For this purpose, a fully coupled, multiphysics, dynamic finite-element model, which solves for the thermal, electric and mechanical fields is used. Because of the demanding computing requirements of the optimization process, a special mesh is designed and a convergence analysis is carried out before using the multiphysics model. The highly nonlinear optimization is done by simulated annealing, a heuristic algorithm in the Markov chain Monte-Carlo family. A preliminary parametric investigation is presented, analyzing the impact of some of the parameters. The results of this preliminary analysis help to understand the effect of the different shapes in the evolution of the cold face temperature. Some of these results are expected and have already been discussed elsewhere, but others can only be explained after further analysis and a full system modeling. Pulse optimization is multiobjective and multiparametric, i.e., it can consider several targets such as maximizing the cooling temperature, the cooling duration or others. The trade-offs between the different targets are studied. In all cases, stresses inside the thermoelement are examined at all points, and the pulses must meet the restriction that an equivalent stress is not above the allowable value.

In this paper we propose different multi-field variational formulations for electrostatics and magnetostatics, which can provide optimal discrete approximation of any particular vector field. The proposed formulations are constructed by appealing to mechanics point of view amenable to using general constitutive equations, which is quite different from electrostatics and magnetostatics formulations typical of physics and electrical engineering focusing on the corresponding global form suitable only for linear case. In particular, the formulations we propose can be combined with mixed discrete approximations that can ensure the continuity of tangential component of electric or magnetic field and normal component of electric displacement and magnetic flux even for low order interpolations. The choice of this kind is quite different from currently favorite choice of high order finite element interpolations used for coupling electromagnetism with mechanics. The discrete approximation is based upon Whitney's interpolations representing the vector fields in terms of corresponding differential forms, with electric and magnetic fields as one-form and electric displacement and magnetic flux as two-form. The implementation of interpolations of this kind is made for 3D tetrahedron elements with non-standard approximation parameters defined not only at vertices (for zero-form), but at edges (for one-form) and at facets (for two-form). The results of several numerical simulations are presented to illustrate the performance of different formulations proposed herein.