Analytical analysis of temperature‐dependent thermoelectric generator and optimization based on functionally graded materials

To obtain higher output power density, an effective gradient distribution by optimizing functionally graded thermoelectric generators is determined. By deriving basic thermoelectric equations, the thermoelectric coupling governing equation considering the temperature dependence is obtained under a rectangular coordinate system. An analytical method is used to solve the governing equation in which the material parameters vary in a general law, the maximum output power density expression with gradient parameters is obtained, and then the optimal gradient parameters under certain working conditions are solved. The results show that, compared with the power series iteration approximation (PSIA) solution, the analytical solution is accurate and has fewer calculations. In our numerical example, when the volume fraction of materials varied in a power function gradient, the maximum output power density obtained using the analytical method is higher than 1.23% and 1.84% that obtained using the PSIA method when the volume fraction varied in general linear and exponential functions, respectively. Structural optimization based on the analytical solution proposed in this paper can avoid the use of numerical analysis methods for traversal calculations. Highlights Analytical solution for analyzing temperature-dependent TEG with high precision is proposed. Analytical expression of optimal electric current density for the maximum energy difference is acquired. Analytical optimization method for FG TEG is proposed and verified based on an example.