Transient heat conduction in wires with heat sources; lumped and distributed solution techniques

The aim of this study is to test the approximate lumped analysis against the more rigorous distributed parameter approach in the solution of 1D and 2D nonlinear heat conduction problems associated with electrical cables under a current load. The system of partial differential equations governing the distributed parameter model is replaced by a system of ordinary differential equations with total derivatives with respect to time. The number of temperature unknowns is highly reduced and the numerical solution, even though approximate, can be very fast. Furthermore, with the use of the thermal-electrical analogy, the lumped system can be described as an equivalent electric circuit composed of thermal resistances and capacitances properly connected and solved with dedicated software. In this work, the lumped approach is applied to the overheating effect of insulated electric cables under a current load both in a steady and a transient regime. For this application, the lumped methodology can be very useful owing to the presence of several regions of solution domain having negligible internal conductive resistance. The approximate solutions are compared with the distributed parameter approach obtained with a commercial FEM code. An empirical methodology is described for modeling single cables and composite flat cables in such a way as to minimize the difference between the approximate and the more rigorous solution, both in a steady state and in a dynamic regime. The difference can be limited to less than few percent and can be considered fully adequate for industrial design.