With developing interest in power generation applications of thermoelectrics and the growing influence of advanced materials on thermoelectric device fabrication, there is an increased demand for better understanding of module-level behavior. Likewise, novel module geometries are being explored for higher performance and require sophisticated modeling methods. In addition to new geometrical design, transport phenomena, such as Thomson heating and contact resistances, aggravate the complexity of modeling thermoelectric modules (TEMs) and thus limit design capability. Typically, these effects are either approximated (or in some cases neglected entirely) with little exploration in to the validity of the underlying assumptions associated with the approximation. As such, standard models are often predicated on assumptions that cannot be made beyond very limited operating regimes. Consequently, most TEM analysis generally utilizes simplistic methods of modeling on a module-level scale, which introduce inaccuracies that must be redressed. Particularly with larger temperature gradients, typically negligible effects could begin to impact overall system performance. Material property temperature-dependency, combined with leakage effects, leave much to be desired of the simple property-average-based models. Additionally, one-dimensional (1-D) models neglect the contribution of three-dimensional (3-D) module facets that can significantly impact TEM performance. To compound the analytical issue, complex material technologies are emerging that will require robust models for module design. With burgeoning focus in using thermoelectrics for waste heat recovery in automobiles, industrial processes and power plants, new application and commercial development of high temperature TEMs is imminent. However, modeling design and optimization of TEMs has been piecemeal at best. Hence, it is imperative that a comprehensive model be developed for TEMs that addresses some of the analytical problems stemming from over-simplification. The primary intention of this work is to develop and validate a comprehensive model that can be used as a TEM design tool and to quantify the error in the simple 1-D analytical models. The scope of this work is multifaceted. First, several models are developed, implemented and compared to each other as design tools that are useful for determining material performance and also for optimizing TEM performance. An improved 1-D analytical model, a unique asymptotic model and a comprehensive 3-D finite element (FE) model are created and established. These models are compared to each other for both validation and for quantification of error in the analytical models. Secondly, the quantification of error in 1-D analytical models based on module parameters, called error mapping, can be used as a design tool in and of itself to either identify regimes where a 1-D model is inaccurate (and thus establish when 3-D FE modeling is required), or as a corrective factor to a 1-D model. Thirdly, an experimental test stand is developed for device characterization, to be used either for system-level integration or for future model validation. Finally, the Thomson effect is analytically explored and detailed, and its contribution to the overall performance of a TEM is quantified. The role of the Thomson effect in previous analyitical models is nebulous, but has been elucidated in this thesis both with derivation and the development of the asymptotic model, which is the first analytical solution to the non-linear thermoelectric governing equations. Ultimately, this thesis defines the advantages and limitations of current TEM models, quantifies their error and provides several new design tools that can be used for material selection, module optimization and system-level design. These new design tools will provide new leverage to advance thermoelectrics as a robust power generation technology at a time when such capability is critical.

Library of Congress Subject Headings

Thermoelectric generators--Mathematical models

Publication Date


Document Type


Department, Program, or Center

Mechanical Engineering (KGCOE)


Stevens, Robert


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