TY - JOUR N2 - In this article, an analytical-numerical approach to calculating a stationary thermal field in the elliptical region is presented. The eigenfunctions of the Laplace operator were determined analytically, whereas the coefficients of the eigenfunctions were obtained numerically. The cooling was modeled with 3rd kind (Hankel’s) boundary condition, where the total heat transfer coefficient was the sum of the convective and radiative components. The method was used to analyze the thermal field in an elliptical conductor and a dielectrically heated elliptical column. The basic parameters of these systems, i.e. their steady-state current rating and the maximum charge temperature, were determined. The results were verified using the finite element method and have been presented graphically. L1 - http://www.czasopisma.pan.pl/Content/119422/PDF/16_01953_Bpast.No.69(2)_26.04.21_K2_G_OK.pdf L2 - http://www.czasopisma.pan.pl/Content/119422 PY - 2021 IS - 2 EP - e136738 DO - 10.24425/bpasts.2021.136738 KW - analytical-numerical methods of field theory KW - elliptical conductors KW - Poisson’s equation A1 - Gołębiowski, Jerzy A1 - Zaręba, Marek VL - 69 DA - 10.03.2021 T1 - An analytical-numerical method for calculating the stationary thermal field in electrical systems with elliptical cross-sections SP - e136738 UR - http://www.czasopisma.pan.pl/dlibra/publication/edition/119422 T2 - Bulletin of the Polish Academy of Sciences Technical Sciences ER -