Modelling of induction heating of carbon steel tubes: Mathematical analysis, numerical simulation and validation

► Numerical simulations of the heating by induction in steel tubes were performed. ► Finite element method was employed in this electromagnetic-heat transfer coupled problem. ► The outside temperature evolution of the steel tubes was determined experimentally and numerically. ► Temperatures in the inner and outer tube surface and the heat affected zone were determined. The transient liquid phase bonding process is been performed to join carbon steel tubes. Fe96.2B3.8 wt% amorphous ribbons of thickness a ≈20μm have been employed as filler material. The tubes are aligned with their butted surfaces in contact with the amorphous layer. The joint is heated into a high frequency induction coil under Argon atmosphere. The temperature is raised at the highest possible rate to the process temperature (at about ≈1250°C) and then held for a predetermined time. In this paper, the numerical simulations of the heating stage of the bonding process have been made using the finite element method. This method had shown of being able to deal with these kind of coupled problems: electromagnetic field generated by alternating currents, eddy currents generated on the steel tube, heating of the steel tube due to joule effect and heat transfer by conduction, convection and radiation. The experimental heating stage, for its further simulation, was done with carbon steel tubes. In particular, we are interested in the temperature evolution of the tube upon heating: time to reach the process temperature at the joint, temperature differences between the inner and outer surface of the tube and the extension of the heat affected zone, taking into account the ferromagnetic–paramagnetic transition. The numerical simulations are validated by comparison with infrared radiation thermometer measurements of the outer surface of the tube at remarkable positions (e.g.: the joint, the zone at the end of the joint, etc.).