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A hybrid analytical‐computational method for three dimensional modeling of thermoelectric generators

A hybrid analytical‐computational method is developed to calculate the temperature distribution and electrical performance of thermoelectric generators (TEG). The geometrical complexities of thermo‐elements in real modules are ignored and the TEG is assumed to be made of five distinct layers. The power output is obtained by algebraic expressions and considered as a heat sink expression in the energy equation. The coupling of thermoelectric and energy equations is handled by developing user defined functions (UDF) in the numerical solution procedure. Accordingly, the heat flow is divided into two parts accounting for the thermoelectric phenomena and the Fourier conduction in the thermoelectric layer. The model is validated and the accuracy of the results is examined against two detailed simulations as well as the available experimental data. It is shown that the model is accurate with an average deviation of 8% to 10% compared to the experiments which is only 4% to 5% higher than the detailed rigorous numerical solutions. The influence of Thomson effect is also found to be around 1%. Moreover, the effect of element numbers with a certain amount of material is investigated and it is revealed that the appropriate number of elements depends on the module temperature due to the Thomson effect.