SEL has been involved in a range of thermoelectric modeling approaches which will be helpful to engineering both advanced thermoelectric modules and next generation of applications.
Module Characterization and Basic Modeling
SEL has developed a test apparatus to characterize current and future modules under a wide range of temperature and loading conditions. In addition to temperatures and electrical performance metrics, heat rates and mechanical loading conditions can be monitored. The developed technique extracts module parameters, which can be used for system-level design, measure performance of advanced thermoelectrics, and validate theoretical models for module design optimization. SEL continues to improve upon basic thermoelectric models by accounting for thermal losses and heat leakage.
Accounting for the Thomson Effect
Most thermoelectric device modeling to date uses a “standard model” that neglects the non-linear bulk Thomson effect in order to develop a closed-form solution to the governing heat equation. This model utilizes an averaged Seebeck coefficient as a method of accounting for the neglected term. While the standard model can be appropriate for materials that do not have a significant temperature-dependency of the Seebeck coefficient, there has been no assessment of this simplified modeling approach. SEL has rigorously demonstrated the accuracy and limitations of the simplified modeling approach through analytical derivation and comparison with an efficient numerical solution using a shooting method. SEL has proven that the standard analytical model produces the exact module output power if an integral averaged Seebeck coefficient is used, and also that the standard model provides a reasonably-accurate estimation of module efficiency, despite its limiting assumptions.
3D Thermoelectric Devices
SEL developed a three-dimensional, device-level multiphysics modeling technique for the purposes of designing and evaluating thermoelectric module configurations. Using the new model, several geometric parameters which are critical to module performance have been identified and explored. The impact on device performance of solder, ceramic interface and electrical contact thickness, as well as the leg spacing on a typical module has been evaluated for a standard unicouple configuration. Results have been compared to the standard one-dimensional constant property models commonly used in thermoelectric module design. See Sandoz-Rosado, E., Stevens, R. J, “Robust Finite Element Model for the Design of Thermoelectric Modules” Journal of Electronic Materials, 2010 for more details.
Heat spreading can be a significant issue when coupling thermoelectric modules with a heat sink, especially when there is a large mismatch in module and base areas. SEL has modified an analytical technique developed by G. N. Ellison in IEEE Transactions on Components and Packaging Technologies, vol. 26, no. 2, pp. 439-454, June 2003 to account for heat spreading in a thermoelectric power unit.