The Distribution of the Thermal Field in an Elliptical Electric Conductor Coated with Insulation

Abstract

The paper determines the stationary thermal field in an elliptical cross-section electric conductor coated with insulation. Heat is generated by the flow of alternating current (AC) through the conducting core, and then dissipated from the insulation surface via convection and radiation. The authors have developed an original method for hybrid (analytical–numerical) modeling of a field. This method has been used to solve the relevant boundary problem of Poisson’s equation. While the eigenfunctions of the Laplace operator were determined analytically, the coefficients of the eigenfunctions were calculated by iteratively solving an appropriate system of algebraic equations. The proposed method enables the analysis of systems with an elliptical geometry and a heterogeneous layered structure (e.g., air, aluminum alloy, PCV), and does not require area discretization (grid). The developed analytical–numerical (AN) method has been positively verified using finite elements (FEs). The determined thermal field is illustrated graphically. The obtained solution has a good physical interpretation.

Keywords

• analytical–numerical method
• stationary thermal field
• insulated elliptical conductor
• steady-state current rating