A linear thermoelectricity theory for thermoelectric materials

The governing equations of thermoelectricity are nonlinear in general. Herein, a first-order linear theory of thermoelectricity for thermoelectric (TE) materials is presented, in which the Joule heating contribution is neglected in the energy balance equation as it is usually at least one order of magnitude smaller than the total thermal energy in TE generator applications. The first-order linear theory is applied to calculate the energy conversion efficiency for homogeneous, functionally graded, and segmented TE generators under 1D heat flow conditions. Energy efficiency for a 2D example is also presented. It is found that the maximum energy efficiencies predicted by the linear theory agree well with those using the general nonlinear theory of thermoelectricity, which indicates that the linear theory is accurate in predicting the energy efficiencies of TE devices. Finally, the peak efficiency for a homogeneous leg under 1D conditions in the linear theory is also characterized by the figure of merit parameter Z as in the nonlinear theory.