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Application of boundary solution procedure in thermal field analysis

Die Anwendung der Randauflösung-Prozedur in der Analyse des Temperaturfeldes

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Contents

A new method for the thermal field analysis for the determination of the temperature distribution around a heavy-current underground cable, is given in this paper. Using finite elements in the immediate neighbourhood of the cable, it is possible to determine the temperature distribution in the whole infinite region.

The method of isoparametric elements with second order approximation is used for the numerical computations. The results obtained are more accurate than those obtained using conventional finite element methods (FEM).

The algorithm developed here can be easily adopted for the analysis of thermal field caused by underground thermal sources.

Übersicht

In diesem Aufsatz wird eine neue Methode der Feldanalyse angegeben, um die Temperaturverteilung infolge eines im Erdboden verlegen Starkstromkabels zu bestimmen. Diese Methode erlaubt die Bestimmung der Temperaturverteilung im gesamten, unendlich ausgedehnten Gebiet, obwohl die finiten Elemente nur in der unmittelbaren Umgebung des Kabels angewendet werden.

Im Programm werden die isoparametrischen Elemente gebraucht, in denen die Approximation der zweiten Ordnung angewandt wird. Die Ergebnisse sind genauer als mit der Benutzung der konventionellen Methode der finiten Elemenente. Mit dem Algorithmus, der hier dargestellt wird, kann man auch die Temperaturfelder der Heizelemente modellieren.

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Abbreviations

\(\lambda = \left\{ {\begin{array}{*{20}c} {\lambda _1 } \\ {\lambda _2 } \\ {\lambda _3 } \\ \end{array} } \right.\) :

heat permeabilty in the cable strand heat permeability in the insulation heat permeability in ground

\(q = \left\{ {\begin{array}{*{20}c} {q_1 } \\ {q_2 } \\ \end{array} } \right.\) :

power density in the cable strand power density in the insulation

p :

point in Ω

∇:

nabla

∇T :

transposition of nabla

T (p) :

temperature at pointp

T i={T i }:

vector of values of temperature at nodes inΩ i

T i ={T i }:

temperature at nodes onΓ j

α:

surface film conductance

n :

outwardly directed normal

F :

energetic functional

Ω :

infinite domain around the cable

Ω 0 :

infinite subdomain

Ω i :

subdomain solved with FEM

Ω′ i :

cable area

Г :

boundary ofΩ 0

Г 1 :

boundary ofΩ between ground and air

Г′1 :

part ofГ 1 boundingЩ 0

Г″1 :

part ofГ 1 boundingЩ i

Г 2 :

boundary of Ω along ψ-axis

Г′2 :

part ofГ 2 boundingЩ 0

Г 3 :

boundary at infinity

Г j :

boundary betweenΩ i andΩ 0

{Ψ i }:

sequence of harmonic functions

Ψ(p):

shape function in finite elementΩ 0

Ψ j ={Ψ j }:

vector of values of Ψ(P) at nodes onΓ j

S ii ,S ij ,S jj :

submatrixes of the matrix

Q i ={Q i }:

vector denoting source density

a :

depth of laying the cable

d 2 :

diameter of the insulation

d 1 :

diameter of the conductor

References

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Authors and Affiliations

  1. Institute of the Theory of Electrical Engineering and Electrical Measurements, Technical University of Warsaw, Koszykowa 75, 00-661, Warsaw, Poland

    S. Krzemiński,  J. Sikora,  J. Sroka &  S. Wincenciak

Authors
  1. S. Krzemiński
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  2. J. Sikora
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  3. J. Sroka
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  4. S. Wincenciak
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Krzemiński, S., Sikora, J., Sroka, J. et al. Application of boundary solution procedure in thermal field analysis. Archiv f. Elektrotechnik 62, 195–200 (1980). https://doi.org/10.1007/BF01570948

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  • DOI: https://doi.org/10.1007/BF01570948

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