Estimation of power output in thermoelectric generators (TEG) modules with mismatching thermal conditions

In industrial applications, thermoelectric generators (TEGs) are commonly constructed using several p-n types of thermoelectric (TE) materials interconnected in series. The TEG module is placed over the heat source to extract the maximum power output from a hot surface, with the opposite face exposed to a lower temperature. However, achieving a homogeneous temperature distribution on the module's hot side can be challenging due to many industrial heat sources' variable and non-homogeneous nature. As a result, mismatched temperature conditions are often encountered, with some TE pairs experiencing a different ${T_h}$Th temperature from others. This can significantly impact the overall performance of the TEG module, necessitating comprehensive modeling techniques to predict the behavior of these systems under the Dirichlet and Neumann boundary conditions. This work presents a mathematical model for evaluating thermoelectric generators that includes the effect of temperature-dependent TE properties and conditions of mismatch. The model also introduces a novel method for solving the strongly non-linear problem with low computational cost. The one-dimensional equations for temperature profile, electrical potential, and heat generation in the steady state are derived using radial basis functions and the homotopy method.