THERMOELECTRIC COUPLED ANALYTICAL SOLUTION OF THERMOELECTRIC PLATE WITH ELLIPTICAL HOLE SUBJECTED TO FAR FIELD LOAD

The two-dimensional thermoelectric coupling problem of an infinite thermoelectric plate with elliptical hole subjected to the action of uniform electric current and uniform total energy flux is studied. The analytical solutions of the electric current density and total energy flux are derived by the complex variable function method and the conformal mapping technique. The theoretical results of the degradation of elliptical hole to circular hole are compared with the results of uniform material with circular hole, and the theoretical derivation is verified. The thermal stress caused by the interference of elliptical hole in insulation with uniform heat flow is analyzed numerically by the method of complex function. The results show that the electric current density and energy flux concentration appear at the axial end of the elliptical hole. When the loaded current direction is parallel to the long axis direction, the electric current density and energy flux decrease with the increase of the axis ratio of the elliptical hole. When they are not parallel, the electric current density and energy flux increase with the increase of the axial ratio of the elliptical hole, and increase with the increase of the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole. The thermal stress caused by uniform heat flow is concentrated at the axial end of the elliptical hole. The thermal stress increases with the increase of the axial ratio of the elliptical hole and the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole.