This chapter presents a numerical formulation within the finite element method in order to computationally simulate thermoelectric devices. For this purpose, a theoretical formulation based on nonequilibrium thermodynamics with historical notes is previously outlined. Then, a brief description of the finite element is reported to express the thermodynamics governing equations in an amenable form to be numerically discretized. Finally, several applications of cooling thermoelectrics are performed to highlight the benefits of the finite element method. In particular, a commercial thermoelectric device is simulated and several variables such as extracted heat, voltage drop, and temperature distributions inside the thermoelements are represented for different operating conditions. In conclusion, the present numerical tool could be used as a virtual laboratory for the design and optimization of Peltier cells.
Part of the book: Bringing Thermoelectricity into Reality