A Comparison Between Numerical and Simplified Thermoelectric Cooler Models

A recent investigation into thermoelectric phenomenon under large temperature differences, such as a thermoelectric cooler (TEC) at no-load, maximum- temperature-drop conditions (Delta T (max)), has raised questions about the simplified approach that assumes constant material properties. The accuracy of the simplified approach can be improved by using material properties averaged over the relevant temperature range by integration, creating a quasi-constant material property solution. A one-dimensional (1-D) numerical solution, with fully temperature-dependent material properties, of a typical Bi2Te3 TEC operating from an elevated ambient temperature under no-load, Delta T (max) conditions yielded a cold-side temperature nearly 8A degrees C lower than the quasi-constant material property solution. This same cooler was modeled in ANSYS, providing a full three-dimensional (3-D) thermoelectric solution that matched the 1-D numerical solution within 0.6A degrees C. With further investigation, it was found that more than half of the difference between the temperature-dependent numerical and quasi-constant material property solutions was due to the Thomson effect term, and most of the remaining error was due to temperature-independent electrical resistivity approximations. It was found that the error due to the temperature-independent thermal conductivity approximation was negligible. Experimental results for a 24-couple TEC further confirm the accuracy of the numerical model with temperature-dependent material properties.