Approximate Analytical Solution to the Temperature Field in Annular Thermoelectric Generator Made of Temperature- Dependent Material

The conversion efficiency of annular thermoelectric generator (ATEG) is studied in consideration of temperature-dependent material parameters based on a 1-D steady model. A power series iteration approximation (PSIA) method is proposed for solving the weak nonlinear thermoelectric coupling equation in the cylindrical coordinate system. The convergence of the solution obtained by PSIA is discussed, and the numerical simulation for the 2-D finite-element model is compared with the PSIA solution. Results show that the obtained approximate solution using the PSIA method in the cylindrical coordinate system has high precision and converges rapidly, and the analytical solution and the numerical solution are in good agreement. For regular Bi
₂
Te
₃
material, when the material is independent of temperature and is homogeneous, the location of the heat source of the thermoelectric device has no effect on efficiency; when the material is dependent on temperature, the inner cooling and outer heating thermoelectric configuration has a good thermoelectric performance. The energy conversion efficiency of the temperature-dependent TEG is lower than that of the temperature-independent device at an average temperature.