Influence of the Skin and Proximity Effects on the Thermal Field in a System of Two Parallel Round Conductors

Abstract

This paper presents a semi-analytical method for determining the distribution of the thermal field in a system of two parallel round conductors, taking into account the skin and proximity effects. The method of a suitably constructed Green’s function was applied to find an analytical expression for the eigenfunctions describing the temperature distributions. In turn, the relevant integrals, which cannot be determined analytically, were calculated numerically. The foundation of the method is the knowledge of the current density distribution in the conductors. As a result, the steady-state distribution of the temperature field in the conductors for various parameter values can be determined. The obtained numerical results were positively verified using the finite element method. Using the developed method, the share of skin and proximity effects in the temperature rise and steady-state current rating was evaluated. Closed analytical formulas were obtained for the AC case with the skin effect taken into account. When the skin depth is smaller than the wire radius, the skin effect has quite a large impact on the conductor temperature. The impact of the proximity effect is much smaller but clearly noticeable when the distance between the wires is smaller than five times the wire radius. In addition, the influence of the value of the heat transfer coefficient on the thermal field of the conductors was also examined.