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The heating of flat workpieces of different materials and geometrical characteristics (width, thickness) is often required in the metal industry. The temperature requirements depend on the process to which the workpiece should undergo and the mechanical and chemical characteristics which must be obtained by the heat treatment. For certain applications in which the electrical resistivity of the workpiece material is low or the ratio between the width and thickness of the body is high, the classical longitudinal flux induction heating is efficient only if high frequencies are used. A good alternative is the travelling wave induction heating (TWIH) which has a structure similar to the linear induction machines (LIM).

In this paper an analytical method, based on Fourier's series, which allows to determine the eddy currents distribution in travelling wave induction heaters with cylindrical symmetry is described. The method is particularly suitable for parametric analyses of heating systems with magnetic or non‐magnetic, solid, bimetallic or hollow loads, with inductors (with or without external magnetic yoke) of the transverse flux or travelling wave type. Useful results can be obtained also for the heating of “flat” metal loads, by inductors facing one side of the load.

Low electrical resistivity metal billets can be heated by the currents induced by the rotation of the billet itself inside a transverse DC magnetic field produced by a superconductive coil. The main drawback of this approach is related to cost of installation that requires an adequate refrigerating system. The purpose of this paper is to propose a more convenient solution, which allows the same high efficiency to be achieved at lower cost. In this solution, the billet is kept still and a series of permanent magnets, positioned in the inner part of a ferromagnetic frame, is rotated.

Some results of the new induction system are shown. These results are obtained applying for the electromagnetic solution both an FE commercial code and an analytical method. The analytical code is developed because several parameters of the system need to be optimized.

The performance of the solution presented is comparable with those of the system with superconductive coils. The results of the two methods applied are in good agreement; thus the analytical code is validated.

A new solution for the induction heating of aluminum billets is presented. The analytical code developed requires a very short computational time, also because it gives directly the steady‐state condition of the system and, for this reason, it can be conveniently applied to an automatic design process.

The paper aims to deal with the induction heating of metal billets rotating in a DC magnetic field.

The induced power distributions are analysed and the main heating parameters are estimated with reference to an infinitely long Al billet 200 mm diameter. The paper refers to the activity developed in the frame of a National Italian Project carried out by research groups of the Universities of Bologna, Padua and Roma “La Sapienza.”

The main process parameters have been evaluated for the heating up to 500°C of an Al billet 200 mm diameter.

This innovative technology appears to be very promising for improving the efficiency of the through heating of high‐conductivity metals (e.g. copper, aluminum) before hot working, by using superconducting magnets.

The paper analyses the induction heating of a infinitely long billet rotating in a uniform DC magnetic field.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.

The purpose of the paper is to propose a cost‐effective method of non‐parametric optimisation in order to explore shapes of a magnetic pole, in the search for the optimal one fulfilling a prescribed objective function.

The boundary of the magnetic field region to synthesize is considered as a moving boundary separating two materials (air and ferrite). An objective‐function dependent velocity field is defined, in order to update the position of nodes located along the unknown boundary. Specifically, a uniform magnetic field within the controlled region is aimed at.

The application of the proposed method to the design of a magnet for magnetic‐fluid hyperthermia made it possible to reduce the field deviation with a little computational effort.

Instead of using a standard algorithm of numerical minimisation to find the optimal search direction, a field‐dependent velocity proportional to the objective function value is exploited. This way, the motion of the boundary towards the optimal shape is automatically driven: in principle, in fact, the velocity reaches the zero value at the optimum.

Thanks to the kinematic law governing the movement of the boundary to synthesize, the overall computational cost is low. Moreover, the non‐parametric approach to the shape synthesis preserves the advantage of a broad search space.

The purpose of this paper is to present the synthesis of magnetic fluid characteristics, like diameter of nanoparticles (NPs) and their concentration, in order to obtain a prescribed temperature rate. An evolution strategy algorithm is used in the optimization procedure, while three‐dimensional finite‐element (FE) modelling is used for magnetic field and thermal field analysis in transient conditions.

FE analysis has been used in order to compute the magnetic and thermal field in a suitable model of the tumor region. The power density due to NP has been accordingly derived.

The NP distribution, giving a prescribed thermal response, is synthesized.

The proposed method can be used to design a therapeutic treatment based on magnetic fluid hyperthermia.

The paper belongs to a streamline of innovative studies on computational hyperthermia.

Magnetic fluid hyperthermia experiment requires a uniform magnetic field in order to control the heating rate of a magnetic nanoparticle fluid for laboratory tests. The automated optimal design of a real-life device able to generate a uniform magnetic field suitable to heat cells in a Petri dish is presented. The paper aims to discuss these issues.

The inductor for tests has been designed using finite element analysis and evolutionary computing coupled to design of experiments technique in order to take into account sensitivity of solutions.

The geometry of the inductor has been designed and a laboratory prototype has been built. Results of preliminary tests, using a previously synthesized and characterized magneto fluid, are presented.

Design of experiment approach combined with evolutionary computing has been used to compute the solution sensitivity and approximate a 3D Pareto front. The designed inductor has been tested in an experimental set-up.

Transverse flux induction heating (TFH) is a process advantageously applied for the heat treatment of thin non‐ferrous metal strips. In comparison with the better known longitudinal flux heating the design of TFH inductors is more complex. In fact both the prediction of power density distribution in the strip and the calculation of the thermal transient during the heating process require a solution of 3D electromagnetic and thermal problems. Moreover the requirements for a good inductor design are in conflict with each other. In the paper a code for the solution of 3D electromagnetic and thermal problems suitable for the design of TFH systems is presented. The analytical‐numerical approach (analytical for the electromagnetic problem, numerical for the thermal one) is suitable for coupling with optimisation algorithms. Both evolutionary strategy and simplex methods and their combination have been used in order to obtain an optimal design for a particular application of TFH.