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Article
Publication date: 3 July 2017

Jerzy Golebiowski and Marek Zareba

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.

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 28 March 2019

Jerzy Gołębiowski and Marek Zaręba

The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

Abstract

Purpose

The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

Design/methodology/approach

The boundary-initial problem of the modified heat equation was formulated for the tubular bus. Analytical solutions were obtained by means of Green’s functions as the kernels of the integral operator inverse to the corresponding differential operator. The results were presented graphically and verified using the finite element method. The calculations were made by considering the example of the Storm Power Components tubular bus (USA).

Findings

Analytical field models were used to determine time- and space-variable heating curves, time constants and steady-state current ratings.

Research limitations/implications

This paper is related to the structure of a hollow cylinder. Other bus sections can be taken into account by using the coordinate systems of different curvilinear orthogonal symmetry.

Originality/value

Using the analytical method, the influence of the variable (temperature dependent) electrical resistivity on some important parameters and characteristics of the tubular bus was investigated. The system was considered as an element with distributed parameters.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 6 March 2009

Jerzy Gołębiowski and Marek Zaręba

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

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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