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The paper deals with the problem of induction hardening of long prismatic ferromagnetic bodies. The body is first heated to the austenitizing temperature typically in a cylindrical inductor fed from a source of harmonic current and then merged into a cooling medium. In specific cases, equalisation of temperatures within the body before its cooling may also be required. The mathematical model of the induction heating consists of two non‐linear second order differential equations of the parabolic type describing the distribution of the electromagnetic and non‐stationary temperature fields while the cooling is described by the heat equation and a theoretically empirical algorithm for mapping the process of hardening. The suggested methodology partially takes into account the temperature dependencies of all material parameters. The theoretical analysis is supplemented with an illustrative example and discussion of the results. Computations have been performed by means of professional codes and single‐purpose user programs developed by the authors.

The heating of flat metal products has an increasing importance in different technical applications. One of the most advanatageous heating methods is induction heating. The heat is generated within the workpiece itself. It provides high power densities and high productivity. For induction heating of flat metal products two methods are applied: the longitudinal and the tranverse magnetic flux heating. In our case we have applied tranverse flux heating. This paper presents certain results of electromagnetic field obtained by means of finite element method and transient thermal field obtained by finite difference method. The analysis is made by simulating the heating phenomenon while the sophisticated software has been employed.

Modeling of induction surface hardening strongly depends on accuracy of material properties data and their temperature characteristics. However, it is especially complicated in case of the magnetic permeability dependent not only on temperature but also on the magnetic strength. This paper aims to estimate the influence of the magnetic permeability on modeling of coupled physical fields describing the process. Investigations are provided for the gear wheels made of the steel C45E.

Computation of coupled electromagnetic temperature and hardness fields is based on FEM methods. The Flux 3D software is applied for the numerical simulation of coupled electromagnetic and temperature fields. The QT Steel software is applied for a determination of the hardness and microstructure distributions.

Obtained results may be used as a kind of background for the design of induction surface hardening systems.

The presented calculation model provided quite a good accuracy of hardness distribution validated by the experiments. Next work in the field should be aimed at taking into account a dependence of the magnetic permeability on the field current frequency.

Mathematical model of induction surface hardening with taking into account time dependence on the magnetic permeability on temperature and magnetic strength is elaborated. Experimental validation of hardness distribution is provided. A quite reasonable convergence between simulations and measurements was achieved.

As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and simultaneous hardening processes and exemplary results of computations and measurements. The upper critical temperature A_c3 is determined from the Time Temperature Austenization diagram for investigated steel.

Computation of coupled electromagnetic, thermal and hardness fields is based on the finite element methods, while the hardness distribution is determined by means of experimental dependence derived from the continuous cooling temperature diagram for investigated steel.

The presented results may be used as a theoretical background for design of inductor-sprayer systems in continual and simultaneous arrangements and a proper selection of their electromagnetic and thermal parameters.

The both models reached a quite good accuracy validated by the experiments. Next work in the field should be aimed at further improvement of numerical models in order to shorten the computation time.

The results may be used for designing induction hardening systems and proper selection of field current and cooling parameters.

Complete mathematical and numerical models for continuous and simultaneous surface induction hardening including dual frequency induction heating of gear wheels. Experimental validation of achieved results. Taking into account dependence of the upper critical temperature A_c3 on speed of heating.

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.

The purpose of this paper is to enable the correct selection of the radiofrequency thermal ablation (RFTA) process parameters for an individual patient by applying a computer modelling of RFTA.

The model is based on the X‐ray computer tomography images of the primary and metastatic hepatic tumours. The authors used the professional package of FLUX3D to generate the geometric models, assign materials properties, assign boundary conditions, perform mesh, carry out coupled thermo‐electromagnetic analysis and for post processing. The distribution of temperature and electric potential in the tissues of tumour and liver had been obtained as main results of the calculations.

The computational results show that the RFTA algorithm is effective in solving this practical problem. The computational results show that the selection of the type of electrodes used in the RFTA process is as important as the correct selection of the process parameters, i.e. voltage and frequency.

The paper presents a method to simulate the RFTA process and to select the process parameters.

This paper aims to create mathematical models and control algorithms allowing the authors to study and form effective modes of operation of multi-inductor system of electrical heating of moving hollow cylindrical blanks.

The developed mathematical models were based on the finite-difference method, the control volume method and their combination. The reliability of the results obtained was verified by comparing the calculated results with the experimental ones. The temperature control system was synthesized using methods of the object management theory with distributed parameters.

A set of mathematical instruments has been created that allow modelling the operation modes of installation for induction heating of moving hollow cylindrical blanks. Recommendations were given on the formation of an automatic control system that provides heating of a moving hollow cylindrical billet to the required temperature with simultaneous equalization of temperature along the length of the billet in case of highly uneven initial temperature along the length of the billet.

Part of the paper will be used by the industrial plant for the purpose of heat treatment of iron alloys workpiece. Particularly, a control system will be basically formed based on the models.

The scientific novelty of the paper is to create control algorithms and mathematical models for the induction heating system of tubular workpieces allowing to explore interrelated electromagnetic and thermal processes taking into account nonlinearities and design features of the system, as well as to form effective modes of its operation based on transfer functions and methods of the object management theory with distributed parameters.

Induction heating processes need to adapt to complex geometries or variable processes that require a high degree of flexibility in the induction heating setup. This is usually done using complex inductors or adaptable resonant tanks, which leads to costly and constrained implementations. This paper aims to propose a multi-level, versatile power supply able to adapt the output to the required induction heating process.

This paper proposes a versatile multilevel topology able to generate versatile output waveforms. The methodology followed includes simulation of the proposed architecture, design of the power electronics, control and magnetic elements and laboratory tests after building a 10-level prototype.

The proposed converter has been designed and tested using an experimental prototype. The designed generator is able to operate at 1 kVpp and 100 A at 250 kHz, proving the feasibility of the proposed approach.

The proposed converter enables versatile waveform generation, enabling advanced tests and processes on induction heating system. The proposed system allows for multifrequency generation using a single inductor and converter, or advanced tests for inductive and capacitive components used on induction heating systems. Unlike previous multifrequency proposals, the proposed generator enables a significantly improved versatility in terms of operational frequency and amplitude in a single converter.

This paper aims to propose a new 3D electromagnetic model to compute translational motion eddy current in the conducting plate of a novel linear permanent magnet (PM) induction heater. The movement of the plate in a DC magnetic field created by a PM inductor generates induced currents that are at the origin of a heating power by Joule effect. These topologies have strong magnetic end effects. The analytical model developed in this work takes into account the finite length extremity effects of the conducting plate and the reaction field because of induced currents.

The developed model is based on the combination of the sub-domain’s method and the image’s theory. First, the magnetic field expressions because of the PMs are obtained by solving the three-dimensional Maxwell equations by the method of separation of variables, using a magnetic scalar potential formulation and a magnetic field strength formulation. Then, the motional eddy currents are computed using the Ampere law, and the finite length extremity effects of the conducting plate are taken into account using the image’s method. To analyze the accuracy of the proposed model, the obtained results are compared to those obtained from 3D finite element model (FEM) and from experimental tests performed on a prototype.

The results show that the developed analytical model is very accurate, even for geometries where the edge effects are very strong. It allows directly taking into account the finite length extremity effects (the transverse edge effects) of the conducting plate and the reaction field because of induced currents without the need of any correction factor. The proposed model also presents an important reduction in computation time compared to 3D finite element simulation, allowing fast analysis of linear PM induction heater.

The proposed electromagnetic analytical model can be used as a quick and accurate design tool for translational motion PM induction heater devices.

A new 3D analytical electromagnetic model, to find the induced power in the conducting plate of a novel translational motion induction heater has been developed. The studied heating device has a finite length and a finite width, which create edge effects that are not easily considered in calculation. The novelty of the presented method is the accurate 3D analytical model, which allows finding the real power heating and real distribution of the induced currents in the conducting plate without the need to use correction factor. The proposed model also takes into account the reaction field because of induced currents. In addition, the developed model improves an important reduction in the computation time compared with 3D FEM simulation.

To provide a suitable linkage of a computational fluid dynamics code and a shape optimization code for the augmentation of local heat transfer coefficients in forced convection channels normally used in the cooling of electronic equipment.

A parallel‐plate channel with a discrete array of heat sources embedded in one wall, while the other wall is insulated, constitutes the starting model. Using water as coolant, the objective is to optimize the shape of the channel employing a computerized design loop. The two‐part optimization problem is constrained to allow only the unheated wall to deform, while keeping the same inlet shape and observing a maximum pressure drop constraint.

First, the results for the linearly deformed unheated wall show significant decrease compared with the wall temperatures of the heated wall, with the maximum wall temperature occurring slightly upstream of the outlet. Second, when the unheated wall is allowed to deform nonlinearly, a parabolic‐like shaped wall is achieved where the maximum wall temperature is further reduced, with a corresponding intensification in the local heat transfer coefficient. The effectiveness of the computerized design loop is demonstrated in complete detail.

This paper offers a simple technique for optimizing the shapes of forced convection channels subjected to pre‐set design constraints.