A finite element computational scheme for transient and nonlinear coupling thermoelectric fields and the associated thermal stresses in thermoelectric materials

This paper proposes a finite element model for the determination of time dependent thermoelectric coupling fields. The model takes into account all thermoelectric effects, including Joule heating, Thomson effect, Peltier effect and Fourier's heat conduction. Temperature-dependent material properties are also taken into account. The method uses the finite element space discretization to obtain a first-order system of differential equations. The system is solved by employing finite difference scheme to resolve the time dependent response. A computation code is developed in commercial programming software Matlab. Once the temperature field is obtained, the thermal stress analysis can be conducted through standard thermoelasticity or finite element analysis. An equation to evaluate the stress level in the thermoelectric materials is identified. This is the first finite element scheme to deal with transient and nonlinear thermoelectric coupling fields in thermoelectric materials.