A method of analysing the thermal field in a three-zone polymeric cable
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.
dc cables heat transfer numerical analysis electrical components thermal testing