Electrical Engineering

, Volume 93, Issue 4, pp 209–216

The simplified method for transient thermal field analysis in a polymeric DC cable

Open Access
Original Paper


The simplified method of analysis of the thermal field in the futuristic model of a DC cable is presented. The thermal conductivity of a non-conducting layer is very small comparing with the same parameter of conducting regions. The above causes very fast heat propagation in the core and coating, which in the consequences are approximated by inert elements of the first order. Spatial changes in the field in insulation cannot be neglected, because of the significantly slow heat transfer. For that reason, insulation is treated as an element of distributed parameters. The boundary-initial parabolic problem of a non-conducting region is solved by means of Duhamel’s theorem. The fundamental solutions of superposition integrals are determined by the separation of variables method. The maximal deviation of results obtained by the finite element method does not exceed 7.2%. The heating curves and results of verification are presented in a graphic form.


Transient heat transfer in DC cables Current transmission Asymptotic and analytical methods Duhamel’s integral 


  1. 1.
    Hammons T J (2003) Power cables in the twenty-first century. Electr Power Components Syst 31(10): 967–994CrossRefGoogle Scholar
  2. 2.
    Rengel UR (2000) Energy cables 2050—a futuristic view. IEEE Power Eng Rev 20(10): 18–21CrossRefGoogle Scholar
  3. 3.
    Gołębiowski J, Zaręba M (2009) A method of analysing the thermal field in a three-zone polymeric cable. Compel Int J Comput Math Elec Electron Eng 28(2): 320–340MATHCrossRefGoogle Scholar
  4. 4.
    Taler J, Duda P (2003) Solving of direct and reverse problem of heat conduction (in Polish). Wydawnictwa Naukowo-Techniczne, WarsawGoogle Scholar
  5. 5.
    Beck JV, Cole KD, Haji-Sheikh A, Litkouhi B (1992) Heat conduction using Green’s functions. Hemisphere Publishing Corporation, LondonGoogle Scholar
  6. 6.
    Incropera FP, de Witt DP, Bergman TL, Lavine AS (2007) Introduction to heat transfer. Wiley, New YorkGoogle Scholar
  7. 7.
    Anders GJ (1997) Rating of electric power cables. IEEE Press, New YorkGoogle Scholar
  8. 8.
    Michalski J, Eckersdorf K (1986) Measurements of temperature (in Polish). Wydawnictwa Naukowo-Techniczne, WarsawGoogle Scholar
  9. 9.
    Baehr H D, Stephan K (2006) Heat and mass transfer. Springer, BerlinCrossRefGoogle Scholar
  10. 10.
    Lehner G (1996) Elekromagnetische Feldtheorie für Ingenieure und Physiker. Springer, BerlinGoogle Scholar
  11. 11.
    Gradshteyn IS, Ryzhik IM (1996) Table of integrals, series and products. Academic Press, New YorkMATHGoogle Scholar
  12. 12.
    Wolfram S (1999) The mathematica book. Wolfram Media-University Press, CambridgeMATHGoogle Scholar
  13. 13.
    Bathe K J (1990) Finite-elemente Methoden. Springer, BerlinGoogle Scholar
  14. 14.
    Manuals for NISA (2008) NISA Suite of FEA Software (CD-ROM). Cranes Software, Inc. Troy, MIGoogle Scholar
  15. 15.
    Zienkiewicz OC, Taylor RL, Zhu IZ (2005) The finite element method: its basic and fundamentals. Elsevier, AmsterdamGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Faculty of Electrical EngineeringTechnical University of BiałystokBiałystokPoland

Personalised recommendations