Analytic thermoelectric couple optimization introducing Device Design Factor and Fin Factor

An analytic solution of a thermocouple has been developed in order to gain a deeper understanding of the physics of a real device. The model is established for both rectangular and cylindrical couples and is made to account for thermal resistance of the hot and cold shoes and lateral heat transfer. A set of dimensionless parameters have been developed to determine couple behavior and serve as simplifying justifications. New dimensionless parameters, Device Design Factor and Fin Factor, are introduced to account for the thermal resistance and lateral heat transfer, respectively. Design guidelines on couple length and cross-sectional area have been established to account for conditions encountered by a realistic couple. As a result of thermal resistances a lower limit on the length of the couple can be established. In the case of a lateral heat transfer couple the efficiency is found to depend upon cross-sectional area of the leg in such a fashion as to suggest the need to design large area couples. The classic thermoelectric solution neglects the effect of thermal resistance and lateral heat transfer, leading to an over estimated conversion efficiency. The work presented provides a path to incorporate these neglected factors and offers a simplified estimation for couple performance based on analytic solutions of governing equations.