In current research, there are excessive assumptions and simplifications in the mathematical models developed for thermoelectric generators. In this study, a comprehensive mathematical model was developed based on a plate-type thermoelectric generator divided into multiple thermoelectric units. The model takes into account temperature-dependent thermoelectric material parameters and fluid flow. The model was validated, and a maximum error of 6.4% was determined. Moreover, the model was compared and analyzed with a numerical model, with a maximum discrepancy of 7.2%. The model revealed the factors and their degree of influence on the performance of the thermoelectric generator unit. In addition, differences in temperature distribution, output power, and conversion efficiency between multiple thermoelectric units were clearly studied. This study can guide modeling and some optimization measures to improve the overall performance of thermoelectric generators.