A new set of ANSYS coupled-field elements enables users to accurately and efficiently analyze thermoelectric devices. This paper reviews the finite element formulation, which, in addition to Joule heating, includes Seebeck, Peltier, and Thomson effects. Examples of steady-state and transient simulations of a thermoelectric generator and a single-stage Peltier cooler are presented for thermoelectric analysis verification. An analysis of a multistage thermoelectric cooler is performed to

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... te ANSYS parametric analysis capability. Introduction The finite element method (FEM) has become an essential solution technique in many areas of engineering and physics. The FEM versatility lies in its ability to model arbitrary shaped structures, work with complex materials, and apply various types of loading and boundary conditions. The method can easily be adapted to different sets of constitutive equations, which makes it particularly attractive for coupledphysics simulation. The ANSYS finite element program has a large library of elements that support structural, thermal, fluid, acoustic, and electromagnetic analyses, as well as coupled-field elements that simulate the interaction between the above fields. Examples of ANSYS coupled-physics capabilities include thermal-structural, fluid-structure, electromagnetic-thermal, thermal-electric, structural-thermal-electric, piezoelectric, piezoresistive, magneto-structural, and electrostatic-structural analyses [1]. Until recently, the ANSYS thermal-electric analysis only accounted for the Joule heat as a coupling mechanism between the thermal and electric fields. However, over the past few years, there has been an increase in the number of requests for the simulation of thermoelectric devices for applications such as electronic and optical component cooling, MEMS, thermal energy harvesting and many others, which require modeling the Seebeck and Peltier effects. While simple one-dimensional analytical models are frequently being used to predict the performance of such devices [2], the diversity and complexity of thermoelectric applications typically necessitates a full three-dimensional (3-D) numerical analysis. To answer these needs, the thermal-electric analysis has been enhanced in ANSYS 9.0 to incorporate the above effects. In the following sections, a general 3-D finite element formulation is introduced and illustrated by several numerical examples.