Benchmarking 0D, 1D, and 2D Analytical Thermal Models for Cylindrical Inductors in Power Electronic Systems

Inductors are critical components in power electronic systems, yet their thermal behavior is often approximated using simplified lumped models that neglect internal gradients and transient spatial effects. This paper presents a benchmarking study of analytical thermal modeling approaches for cylindrical inductors, including 0D lumped, 1D radial, and 2D radial-axial transient formulations. Starting from the general heat conduction equation in cylindrical coordinates, closed-form or semi-analytical solutions are discussed under uniform internal heat generation and convective boundary conditions. The proposed framework provides a benchmark-oriented analytical reference for selecting the appropriate thermal model complexity in reliability-oriented design of inductive components in power electronic systems. The models are applied to a representative two-layer cylindrical inductor composed of a ferrite core and a copper winding, under identical loss and cooling assumptions, considering two axial lengths in order to assess geometric influence. Steady-state temperature levels, transient responses, modal time constants, and axial gradient indicators are extracted to quantify the differences among modeling levels. The results show that the dominant thermal behavior is governed by a single slow mode with a time constant on the order of one hour. The spatially averaged temperature predicted by the 0D model deviates by less than 2.5% from the 2D solution in steady-state conditions, with the 1D model providing accurate predictions when axial gradients remain weak.