4th European Workshop on Thermoelectrics - ETS '98, Madrid (Spain). 17-18 September 1998
Summary:
Thermoelectric materials have non-linear and coupled behavior difficult to simulate, specially if the material properties have an important dependence on temperature or the problem considered is not one-dimensional. In this work, a special 3D finite element model for thermoelectricity is developed. 3D constitutive equations are introduced to relate current and heat fluxes with the gradients of voltage and temperature fields respectively. In those equations three material properties are considered: Seebeck coefficient and thermal and electric conductivities, in general temperature dependent. Equilibrium equations are obtained by electric charge and energy balance. They are transformed into weak forms, discretized and transformed into residual equations: non-linear relationships between electric voltage and temperature degrees of freedom at each node of the mesh. Then they are solved using iterative modified Newton-Raphson. An important part of this method is the construction of the residual vector and the tangent matrix, obtained from derivation of the residual equations. Finally, validation examples from non-coupled linear thermal and electrical cases to a complete 2D analysis of Peltier effect are included. The comparisons between present model results with analytical calculations show a satisfactory correlation.
Keywords: Finite Element, Non-Linear, Thermoelectric
Publication date: 1998-09-17.
Citation:
J. Pérez, D. Gavela, 3D, Non-Linear Coupled, Finite Element Model of Thermoelectricity, 4th European Workshop on Thermoelectrics - ETS '98, Madrid (Spain). 17-18 September 1998.
