The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire.
The effect of the air boundary layer was modelled by means of changing the total heat transfer coefficient on the external perimeter of the wire. This leads to an elliptical boundary problem with Hankel’s condition dependent on the angular coordinate. The eigenfunctions of the problem were determined analytically. On the other hand, the unknown coefficients of eigenfunctions and the constants were calculated numerically by solving a respective system of algebraic equations. The steady state current rating was determined with an iterative method.
By means of the presented method, the thermal field distribution deprived of axial symmetry in the double insulated wire was determined. The obtained results have good physical interpretation and were verified with the finite element method (by means of NISA v. 16 software). The determined values of the steady-state current rating were compared with those calculated by means of the equivalent heat transfer coefficient method and the International Electrotechnical Commission (IEC) standard.
The method is applied to analyse scalar fields in layered cylindrical structures. This could be expanded to the case of a wire of any number of insulation layers. What is more, one could also consider heat sources without axial symmetry and located within the external area.
The analytical method of determining a thermal field deprived of axial symmetry in heterogeneous cylindrical system (the wire composed of three different materials) was developed.
The authors would like to thank the unknown reviewers whose precious remarks have considerably improved the article.
Golebiowski, J. and Zareba, M. (2017), "Method of analysis of asymmetrical thermal field in a double insulated wire", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 4, pp. 1075-1088. https://doi.org/10.1108/COMPEL-01-2016-0038
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