Parallel analysis of thermal field in a layered DC cable part I: The model, discretization, time decomposition, minimization of perturbations. Issue 1 (2014)

• Record Type: Journal Article
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 24:Issue 1(2014)
• Page Start: 58
• Page End: 72
• Publication Date: 2014
• Subjects: DC cable -- FDM -- Parallel computations -- Parallel modelling -- Thermal field dynamics; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-02-2012-0044
• Languages: English
• ISSNs: 0961-5539

Abstract

Abstract : Purpose – The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables.Design/methodology/approach – Initial‐boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two‐stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously.Findings – A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non‐linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model.Research limitations/implications – The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter.Practical implications – The time‐spatial distribution of thermal field in the cross‐section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system.Originality/value – A parallel algorithm of solving initial‐boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed. Acknowledgements : The paper was prepared at Bialystok Technical University within a framework of the S/WE/3/08 project sponsored by the Ministry of Science and Higher Education, Poland.