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As far as the authors know, no sufficiently complete model of continual induction hardening was developed and solved so far. The paper presents both mathematical model of the process and algorithm of its solution in the quasi‐coupled formulation.

Computation of electromagnetic and temperature fields is based on the finite element method, while time variable boundary conditions are determined by means of an original theoretically‐empirical procedure.

Substantial are backgrounds for design of the inductor and parameters of the field current as well as parameters of the cooling medium.

The model reached a good level of accuracy validated by suitable experiments. Nevertheless, next work in the field will also have to respect history of the heating before cooling itself (the austenitizing temperature is a function of the velocity of heating). Very important is also appropriate meshing of the investigated region to suppress numerical instabilities appearing during the computation process. Finally, acceleration of numerical schemes is a must, because modelling of one common task (on very fast PCs) takes about 4 h.

The results and conclusions may be used for designing devices for continual induction hardening of axisymmetric bodies.

Complete mathematical and computer model of the process, original methodology for finding the coefficient of convective heat transfer from the cooled part of the heated workpiece to ambient water spray.

Impedance of long direct massive conductors carrying time‐variable currents is a complex function of time. Its evolution is affected not only by the skin effect but also by the temperature rise. This paper presents a numerical method that allows one to compute the resistance and internal inductance of a non‐ferromagnetic conductor of any cross‐section from values of the total Joule losses and magnetic energy within the conductor, and also illustrates the theoretical analysis based on the field approach on a typical example and discusses the results.

The purpose of this paper is to investigate the parameters and operation characteristics of an actuator working on the principle of thermoelasticity whose structure was designed by the authors.

The mathematical model of the system describes the effects of three physical fields (electromagnetic field, temperature field, and field of mechanical strains and stresses due to thermoelasticity). While the electromagnetic field was solved independently, the thermomechanical task in common with the contact problem was solved in the hard‐coupled formulation. The computations were mostly carried out by own codes.

This type of actuator is characterized by extremely high forces acting in its dilatation element.

The parameters of the system may still be improved using a longer field coil and dilatation element. Attention has to be paid, however to the mechanical stability of the system. Another improvement could be achieved by suitably designed cooling of the coil that would allow increasing parameters of the field current (its frequency or amplitude).

The device is promising for various fixing tasks in the industrial environment.

Although the methods of numerical processing of particular fields are known, the paper provides an algorithm for their simultaneous solution while respecting the temperature dependencies of the material properties and continuous change of the contact surfaces.