A Peridynamic Computational Scheme for Thermoelectric Fields

Abstract

Thermoelectric materials are materials that involve the coexistence of heat flux and electric current in the absence of magnetic field. In such materials, there is a coupling among electric potential and temperature gradients, causing the thermoelectric effects of Seebeck and Peltier. Those coupling effects make the design and analysis of thermoelectric materials complicated and sophisticated. The main aim of this work is dealing with thermoelectric materials with discontinuities. Since heat and electric fluxes are undefined at the crack tip and the temperature and electric fields across the crack surface are discontinuous, it is better to apply peridynamic (PD) theory to capture such details at the crack tips. Hence, we propose in this paper a PD theory which is suitable in tackling such discontinuities in thermal and electric fields. In this study, the continuum-based electrical potentials and temperature fields are written in the form of nonlocal integrals of the electrical potentials and temperature that are effective whether we have discontinuities or not. To illustrate the consistency of the peridynamic technique, a number of examples were presented and witnessed that PD results were in good agreement with those results from the literature, finite element solutions and analytical solutions.

A Review of Peridynamics (PD) Theory of Diffusion Based Problems

“…e same authors further developed an electromechanical PD model to predict the deformation and damage of explosive materials [84,85]. Zeleke et al [86][87][88] on the other hand developed a PD formulation for thermoelectric phenomena. A recent contribution of Diana and Carvell [89] employed micropolar PD (MPPD) model to solve electromechanical problems.…”

“…A recent contribution of Diana and Carvell [89] employed micropolar PD (MPPD) model to solve electromechanical problems. Very recently, Zeleke et al [88] employed PD theory to study discontinuities in electric and thermal fields. erefore, in this section, we first describe PD electrical conduction using the generalized state-based approach.…”

Analysis of Nonlinear Transient Energy Effect on Thermoelectric Energy Storage Structure

“…With the development of thermoelectric materials (TEMs) [1,2], the thermoelectric generator (TEG) began to be widely used in waste heat recovery [3,4]. The TEG is usually applied to convert thermal energy into electrical energy by exploiting the Seebeck effect [5,6].…”