Geometric conditions for minimizing entropy production in thermocouple design

This work shows a methodology for designing thermocouples of thermoelectric modules. The main quantities for design calculations are the geometric parameters: Cross-sectional area and leg length. Furthermore, the thickness of the ceramic material and the thickness of the metal bridge are considered. In addition, temperature-dependent thermoelectric properties are included in the analysis: Seebeck coefficient, thermal conductivity, electrical resistivity. An analysis of the entropy production is performed for two thermocouple geometries: Quadrangular and cylindrical. The proposed methodology allows determining the geometric conditions that the thermocouple must meet to minimize the entropy production and maximize efficiency. A conclusive result of this work is that the geometric conditions that minimize entropy production are the same that maximize the efficiency.