Peridynamic Formulation for Coupled Thermoelectric Phenomena

Abstract

Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM). Although FEM is robust and versatile, it is not suitable to model evolving discontinuities. To avoid such shortcomings, we propose the concept of peridynamic theory to derive the balance of energy and charge equations in the coupled thermoelectric phenomena. Therefore, this paper presents the transport of heat and charge in thermoelectric material in the framework of peridynamic (PD) theory. To illustrate the reliability of the PD formulation, numerical examples are presented and results are compared with those from literature, analytical solutions, or finite element solutions.