Thermal Analysis of Electrical Wires by Finite Volume Method

Abstract

In this paper is proposed the algorithm to calculate thermo-electrical characteristics of round insulated wire, considering temperaturedistribution in radial direction. However, non-linear phenomena require iterative calculation processes, which consume large computertime resources. Therefore, having numerical calculation results approximated by simplified mathematic expressions helps to speed upthe analysis of thermo – electrical characteristics. The procedure of obtaining polynomial coefficients from thermo-electricalcharacteristics is the major emphasis of this paper. In order to illustrate the procedure for implementation, only a single round wire withconvection and radiation at the boundaries is treated. The mathematical model is obtained from energy conservation law and is appliedto the round wire. The energy balance equation, which describes heat transfer in a round wire, is a homogenous partial derivativesequation (PDE), where non-linear electrical resistance and specific heat capacity are considered. Finite Volume Method (FVM) isapplied for the development of finite-difference equations, thus to solve iterative problem, which is caused by non-linear phenomena inelectrical resistance, convection and radiation. The PDE is solved by semi-implicit method. Finally, least-square algorithm is used toobtain polynomial coefficients I0, a, b, c, d, τ. Ill. 6, bibl. 5 (in Lithuanian; summaries in Lithuanian, English, Russian).