Induction heating

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Induction heating

Induction heating is a common industrial process in which an electrically conducting object is heated electromagnetically via an applied alternating magnetic field. This is a two-way coupled problem where temperature-dependent conductivity affects electromagnetic solution.

Skin and proximity effects make current and heating distributions very complex while large differences in temporal and spatial scales can make numerical 3D simulations even more challenging.

Other important models used in FEM electromagnetic simulation software are

– Hysteresis loss (Pv depends on B and f)
– Temperature-dependent conductivity
– Massive, foil and stranded winding models
– Circuits
– Core material models – electrical laminated steel, ferrite and soft magnetic composite

Fortunately, we have experience modeling large 3D models (more than 5M elements) in a wide frequency range. In addition, doing so fast using iterative (contrary to direct) numerical methods.

Current trends indicate that researchers and engineers are more inclined to work with open-source software.

In particular, we find that Elmer FEM is very versatile and suitable for industry problems. Multi-physics problems, i.e. simulations involving coupled structural mechanics, electromagnetics, heat transfer, etc., can be solved out-of-the-box. To assess the performance of Elmer FEM, a simple example case of induction heating is considered. Results are compared with COMSOL Multiphysics, one of the most advanced and popular commercial simulation packages. The geometry used in this study was taken from a blog article “Hardware requirements for CENOS”. The geometry consists of three domains – a workpiece, a coil and surrounding air. 

Currents computed by Elmer FEM

Currents computed by COMSOL

Joule heat computed by Elmer

Joule heat computed by COMSOL

Our experience has shown that Elmer FEM results are in good agreement with a reference solution computed in COMSOL Multiphysics.

In most cases, the temperature distribution in the part is the most useful information we can get from simulation, but the accuracy of the solution can be affected by many factors, including external ones. For example, heat transfer from work-piece to air can be solved in many ways. The simplest one is to apply the heat transfer coefficient on surfaces with or without radiation term. Alternatively, a more accurate approach is using the coupling capabilities of our software EOF-Library and adding CFD software for Conjugate Heat Transfer analysis.

All computer modelling involving COMSOL Multiphysics was performed by a third party for Academic purpose only. EOF Consulting specializes in open-source software and does not provide consulting services for commercial software packages. 

SIA EOF Consulting ir noslēdzis 28.02.2020 līgumu Nr. VP-L-2020/12 ar Latvijas Investīciju un Attīstības Aģentūru par atbalsta saņemšanu vaučera programmas ietvaros. Pētījuma mērķis ir veikt eksperimentālo izstrādi, lai atrisinātu 3 industriālu problēmu modeļuzdevumus. EOF Consulting LLC signed contracts BIZIN-I-2019/731 and SKV-L-2019/115 with LIAA for recieving support from ERAF projects ( and

We received a grant from Olaine municipality as part of the Iedvesma competition: