Thermoelectric and stress distributions around a smooth cavity in thermoelectric material

Abstract

• In this paper the thermoelectric coupling problem of an infinite homogeneous isotropic thermoelectric material with a smooth cavity and exerting a uniform current density and/or uniform energy flux is studied. • New analytical solutions are completely exact, and operable for complex shapes. • New solutions have a finite form for cavity characterized by Laurent polynomial. • The curvature of the cavity contour affects the distribution of the fields. • The maximum stress concentration appears near the points with extremal curvature. Thermoelectric materials have attracted more and more attention since they are friendly to the environment and have potentials for sustainable and renewable energy applications. As typically brittle semiconductors with low mechanical strength and always subjected to defects and damages, to clarify the stress concentration is very important in the design and implement of thermoelectric devices. The two-dimensional thermoelectric coupling problem due to a cavity embedded in an infinite isotropic homogeneous thermoelectric material, subjected to uniform electric current density or uniform energy flux, is studied, where the shape of the cavity is characterized by the Laurent polynomial, and the electric insulated and adiabatic boundary around the cavity are considered. The explicit analytic solutions of Kolosov-Muskhelishvili (K-M) potentials and rigid-body translation are carried out through a novel tactic. Comparing with the reported results, the new obtained are completely exact and possess a finite form. Some results of three typical cavities are presented to analyze the electric current densities (energy fluxes) and stresses around the tips. The main conclusions include: the distribution of thermoelectric field and stress at the tip obviously depends on the curvature of the contour and load directions; for triangle and square with symmetrical tips, the thermoelectric and stress concentration reach the maximum or minimum when the load direction is parallel to or perpendicular to the symmetry axis of the tip, which is distinct to the extremum characteristics of pentagram with bimodal of curvature around the tip; the maximum thermoelectric and stress concentration appear near the maximum curvature point for most load directions, but not at the maximum curvature point.