MATHEMATICAL MODELING OF A THERMOELECTRIC GENERATOR UNICOUPLE

Abstract

To ascertain the simultaneous thermal and electrical performance of a thermoelectric (TE) unicouple with interconnectors, a thermal-electric coupled iterative mathematical model is introduced. The non-linear constitutive equations describing TE phenomena within the unicouple are linked to a thermal resistance network describing the interconnectors’ behavior. Thereupon, the thermal resistance of the interconnectors, and Joule heat generated within, are considered. Temperature dependent material properties are handled by integral-averaging techniques and an iterative solution methodology. Model form uncertainty is quantified by evaluating four unique analytic models. The first, the Implicit Thomson Model (ITM), considers the Thomson effect via integral averaging of the Seebeck coefficient. The second, the Explicit Thomson Model (ETM), decouples the Thomson effect from the Peltier effect; Thomson heat is explicitly solved using the Thomson coefficient. The third, the zT model, uses the figure of merit to describe the optimum efficiency-maximizing load resistance, and quantify device efficiency under maximum power scenarios. The last, the Differential Equation Model, does not assume distributions of Joule and Thomson heats to the cold- and hot-side interfaces as do the ITM, ETM and zT model. The predictive ability of each analytic model used within the unicouple-level model is compared to high-fidelity numeric results obtained from a three-dimensional, thermal-electric coupled model implemented in ANSYS CFX. Considering a range of hot-side unicouple temperatures, each analytic model exhibits agreement with one another, and with the numeric model. With increasing load resistance values, model form uncertainty and disagreement between analytic and numeric predictions decreases to a couple of percent at optimum operating points.