A transient volumetric heat source model for stationary induction heating of thin plates: Case study with experimental validation and industrial application

Stationary induction heating is critical for forming and straightening thin-walled structures, where the transient temperature field governs the process outcome. While fully coupled electro-magneto-thermal (CEMT) simulations offer high accuracy, their computational cost limits engineering utility. Existing equivalent heat source models are efficient but rely on time-invariant heat generation rate (HGR) assumptions, which lead to significant errors for stationary processes where the HGR evolves substantially over time. This study quantifies the HGR evolution through high-fidelity CEMT analysis, identifying two resolved transient stages—surface concentration and thickness diffusion—followed by the onset of a quasi-steady trend near the end of the heating interval, driven by the skin effect and the Curie temperature transition. Based on this understanding, an equivalent transient volumetric heat source (ETVHS) model is proposed, employing cross-stage analytical functions to capture the HGR evolution. The model is validated against CEMT simulations across five current settings, and coefficient transfer is examined for two additional coil lengths. An AH32 literature case assesses the framework after configuration-specific recalibration. Experimental comparisons at the heating-center and coil-edge measurement locations show good agreement in temperature history. After calibration, the thermal-solver speed-up relative to CEMT ranges from approximately 540 to 650. A full-scale ship-panel example demonstrates the feasibility of using the model as thermal input for multi-step straightening simulation. The approach provides an efficient tool for thermal analysis within the calibrated conditions and the tested transfer range.