Journal of Electrical Engineering & Technology

, Volume 14, Issue 1, pp 47–53

# Application of Duhamel’s Theorem in the Analysis of the Thermal Field of a Rectangular Busbar

• Marek Zaręba
Original Article

## Abstract

The paper presents the method of thermal field analysis in a rectangular busbar taking into account the variable resistivity. The method is based on the analytical solution of the heat conduction equation. The boundary-initial problem was solved using the Duhamel’s theorem. The suitable step response of the system was determined by the separation of variables method. By means of presented method, a stationary and transient thermal field was determined in the rectangular busbar taking into account variable resistivity. The steady-state currents rating as well as the time constants of the busbar in case of variable and average resistivity were also determined. The results obtained was verified using the finite element method.

## Keywords

Analytical methods of the field theory Rectangular busbar Steady-state current rating

## Notes

### Acknowledgements

The paper was prepared at the in Bialystok University of Technology within the framework of the project S/WE/2/18 sponsored by the Ministry of Science and Higher Education.

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