Non-linear finite element formulation applied to thermoelectric materials under hyperbolic heat conduction model

摘要: In the present work, a three-dimensional, dynamic and non-linear finite element to simulate thermoelectric behavior under hyperbolic heat conduction model is presented. The transport equations, which couple electric thermal energies by Seebeck, Peltier Thomson effects, are analytically obtained through extended non-equilibrium thermodynamics, since local equilibrium hypothesis not valid model. addition, unidimensional analytical solutions validate formulation. Numerically, isoparametric eight-node elements with two degrees of freedom (voltage temperature) per node used. Non-linearities due temperature-dependence on properties Joule effects addressed Newton–Raphson algorithm. For problem, HHT Newmark-β algorithms compared obtain accurate results, numerical oscillations (Gibbs phenomena) when initial boundary conditions discontinuous. last algorithm, regularized relating time steps sizes, provides best results. Finally, implementation validated, comparing solutions, three-dimensional example