A method of analysing the thermal field in a three‐zone polymeric cable

Abstract

Purpose

The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

Design/methodology/approach

In the method developed, the field functions are determined in the analytical way by the superposition of states and separation of variables method. The coefficients of the field functions and eigenvalues of the boundary‐initial problem are computed by the numerical method. The coefficients are the solution to the corresponding sets of equations. These sets are the result of scalar products of non‐orthogonal functions at the respective zones of the cable. The eigenvalues are determined by an algorithm, which uses the field properties and elements of the golden cut method.

Findings

The method made it possible to develop a mathematical model of the dynamics of the thermal field in a polymer DC cable. This model has good physical interpretation. The paper also presents the field distributions determined in an analytical form. Some arguments of the expressions derived are however computed numerically. The results obtained by the paper's method and by the finite elements methods were compared. The relative differences are less than 6 per cent.

Research limitations/implications

The method concerns axially‐symmetrical three‐zone systems under nominal conditions.

Practical implications

By means of the method important parameters of DC lines can be determined (e.g. spatial‐temporal heat‐up curves, admissible sustained currents, time constants).

Originality/value

An analytical‐numerical method of analysis of the thermal field in a three‐zone axially‐symmetrical system was developed. Its original element is the algorithm of determination of eigenvalues of the boundary‐initial problem and coefficients of non‐orthogonal field functions.

Citation

Gołębiowski, J. and Zaręba, M. (2009), "A method of analysing the thermal field in a three‐zone polymeric cable", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 2, pp. 320-340. https://doi.org/10.1108/03321640910929245