Thermoelectric algebra made simple for thermoelectric generator module performance prediction under constant Seebeck coefficient approximation

Abstract

Although thermoelectric material performance can be estimated using the dimensionless figure of merit ZT, predicting the performance of thermoelectric generator modules (TGMs) is complex owing to the nonlinearity and nonlocality of the thermoelectric differential equations. Here, we present a simplified thermoelectric algebra framework for predicting TGM performance within the constant Seebeck coefficient approximation (CSA). First, we revisit the constant Seebeck coefficient model (CSM) to transform the differential equations into exact algebraic equations for thermoelectric heat flux and conversion efficiency in terms of the load resistance ratio and relative Fourier heat flux. Next, we introduce the CSA, where the Thomson term is neglected and the device parameters are assumed to be fixed. We define the average thermoelectric properties and device parameters under the zero-current condition using a simple temperature integral. Finally, we derive approximate thermoelectric algebraic equations for voltage, resistance, heat flux, and conversion efficiency as functions of current. We numerically validate that the CSA formalism is superior to other single-parameter theories, such as peak-ZT, integral-ZT, and generic engineering-ZT, in predicting efficiency. The relative standard error of the optimal efficiency is less than 11% for average ZT values not exceeding 2. By combining the CSM and CSA, TGM performance can be easily estimated without requiring calculus or solving differential equations. Therefore, this simplified thermoelectric algebra under the CSA framework has the potential to significantly enhance future TGM analysis and design, facilitating more efficient device-level research and development beyond the traditional focus on material properties.