Role of material property gradient and anisotropy in thermoelectric materials

Abstract

It was recently discovered that inclusions, fatigue damage and other types of material imperfections and defects in metals can be nondestructively detected by noncontacting magnetic measurements that sense the thermoelectric currents produced by directional heating and cooling. Since detection of small defects in thermoelectric materials is ultimately limited by intrinsic thermoelectric anisotropy and inhomogeneity of the material to be inspected, a thorough study is required on their impact on the nondestructive capability. Therefore, in this investigation the induced electric current densities and thermal fluxes are first derived for a steady line heat source in an inhomogeneous and anisotropic thermoelectric material. The exact closed-form solutions are obtained by converting the original problem into two inhomogeneous Helmholtz equations via eigenvalue/eigenvector separation. The material properties are assumed to vary exponentially in the same manner in an arbitrary direction. For the corresponding homogeneous but anisotropic material case, we also present an elegant formulation based on the complex variable method. It is shown that the induced magnetic fields can be expressed in a concise and exact closed form for a line heat source in an infinite homogeneous anisotropic material and in one of the two bonded anisotropic half-planes. Our numerical results demonstrate clearly that both property anisotropy and gradient in thermoelectric materials can significantly influence the induced thermoelectric currents and magnetic fields.