Power Series Iterative Approximation Solution to the Temperature Field in Thermoelectric Generators Made of a Functionally Graded Temperature-Dependent Material

To investigate the temperature field in and thermoelectric (TE) efficiency of TE generators made of a functionally graded temperature-dependent material, a power series iteration method is proposed for solving the weak nonlinear differential equation with variable coefficients. A homogeneous structure made of regular Bi(2)Te(3)and a gradient structure composed of regular Bi(2)Te(3)and nano-Bi(2)Te(3)are investigated. The power series iteration solution of the temperature field has good convergence and high accuracy. After four iterations, the relative error of the solution can be less than 10(-6). The numerical results obtained show that the maximum energy efficiency of a functionally graded structure composed of regular Bi(2)Te(3)and nano-Bi(2)Te(3)is larger than that of a homogeneous regular Bi(2)Te(3)structure. To reveal that the maximum energy efficiency depends on the gradient distribution, we compare the maximum energy efficiency of TE generators made of nano-Bi2Te3, nano-PbTe, and different types of functionally graded structures made of these two materials. Results indicate that the maximum energy efficiency of certain functionally graded structures is 9.9%. The effective gradient distribution can significantly enhance the maximum TE efficiency. The method and results provide theoretical guidance for the optimization of temperature-dependent materials for TE generators using functionally graded structures.