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This paper aims to exhibit a numerical study to analyze the influence of a periodic magnetic source on free convection flow and entropy generation of a ferrofluid in a baffled cavity. In this study, ferrofluid nanofluid was selected due to its ability to image magnetic domain structures within the cavity. The non-uniform magnetic source is considered as a sinusoidal distribution in the vertical direction.

The finite volume technique is used to evaluate the steady two-dimensional partial differential equations that govern the flow with its corresponding boundary conditions.

The obtained results indicate that a significant increase in the average Nusselt number can be achieved with the use of the periodic magnetic source instead of a uniform case. In addition, the effectiveness of the adiabatic baffle notably depends on its position and Rayleigh number. Regardless of the values of period and Hartmann numbers, the periodic magnetic source has a higher entropy generation and lower Bejan number than the uniform magnetic source.

The novelty of this research lies in applying a periodic magnetic source on the natural convection of ferrofluids in a baffled cavity.

This paper aims to present a new iterative procedure for the 3D representation of focusing magnetic fields in TWTs generated by PPMs, by using equivalent sources and optimisation algorithms.

In the integrated optimisation strategy general models for magnetic sources are employed and local and global inverse problems are iteratively solved for the minimization of the representation error.

The results obtained show that the target accuracy is reached with a low computational effort, employing a minimum number of equivalent sources.

The procedure is robust and converges for all the examined magnetic field configurations.

Different from other approaches, the procedure presented here can be directly applied to a variety of different models for magnetic sources.

This study aims to analyze entropy generation and magnetohydrodynamic (MHD) natural convection of hybrid nanofluid in a square cavity, with a heated elliptical block placed at the center, in presence of a periodic-variable magnetic field.

In this paper, simulations were performed with a FORTRAN home code. The numerical methodology used to solve Navier–Stokes, energy and entropy generation equations with corresponding boundary conditions, is essentially based on the finite volume method and full multigrid acceleration.

The cavity is filled with Ag–Tio₂/Water hybrid nanofluid. The main objective of this investigation is to predict the effects of body’s size (6 cases), type of applied magnetic field (variable or uniform), the non-dimensional period number of the variable magnetic field (VMF) (0.2 ≤ Λ ≤ 0.8), the inclination angle of the VMF (0 ≤ χ ≤ 90), Rayleigh number (5 × 103 ≤ Ra ≥ 105) and Hartmann number (5 ≤ Ha ≥ 100) on thermal performance, heat transfer rate, entropy generation and flow patterns.

To the authors’ best knowledge, this paper is the first numerical investigation deals with the entropy generation and natural convection of hybrid nanofluid in a two-dimensional cavity, with specific thermal boundary conditions, containing an elliptical block under periodic-variable magnetic field. Different combinations between flow-governing parameters were made to find optimal thermal performance.

The purpose of this paper is to simulate the flow of a conducting fluid past a circular cylinder placed centrally in a channel subjected to an imposed transverse magnetic field to study the effect of a magnetic field on vortex shedding at different Reynolds numbers varying from 50 to 250.

The two‐dimensional incompressible laminar viscous flow equations are solved using a second‐order implicit unstructured collocated grid finite volume method.

An imposed transverse magnetic field markedly reduces the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It is observed that the periodic vortex shedding at the higher Reynolds numbers can be completely suppressed if a sufficiently strong magnetic field is imposed. The required magnetic field strength to suppress shedding increases with Reynolds number. The simulation shows that the separated zone behind the cylinder in a steady flow is reduced as the magnetic field strength is increased.

In this paper, due attention is given to resolve and study the unsteady cylinder wake and its interaction with the shear‐layer on the channel wall in the presence of a magnetic field. A critical value of the Hartmann number for complete suppression of the shedding at a given Reynolds number is found.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The definition of a simple model of low frequency magnetic field created by power industrial installations can be approached by using an equivalent source system (ESS). Given a set of measured magnetic field points, the ESS, made by a limited set of current carrying wires or turns, must be placed and supplied in order to fit the measured magnetic field values. An optimisation procedure can be used to define the current values and the location of the ESS which minimize the error between the measured and computed magnetic field values.

A two‐step optimal procedure is defined: in the outer step a stochastic optimisation routine is used to drive the geometric control parameters of the ESS while, in the inner step, the current values flowing through the sources are computed to find the minimization of the error with respect to a set of measured magnetic field values. The optimisation procedure is based on an artificial immune system algorithm which focuses on a deep exploration of the search space and gave interesting results both in terms of accuracy and computational efficiency.

The results show that the proposed approach is able to reconstruct the magnetic field created by complex source system and give some accuracy measure on the reconstruction error. The optimisation process carried out also on conductor positions has allowed to find out the location of the real sources in an accurate way, also in presence of measurement errors.

The approach proposed uses optimisation procedures to solve the inverse problem of source reconstruction starting by a set of measured magnetic field values. The definition of a simple equivalent source structure, together with an optimisation procedure to set its control parameters, allows to simulate complex magnetic field sources, like power substations or cable systems, in a very efficient and compact way.

The purpose of this paper is to supply a numerical analysis tool to solve eddy currents induced in nonlinear materials such as steel by boundary element method (BEM), and then apply it to design and analysis of power devices.

Utilizing integral formulas derived on the basis of rapid attenuation of the electromagnetic fields, the paper formulates eddy currents in steel. In the formulation, nonlinear terms are regarded as virtual sources, which are improved iteratively with the electromagnetic fields on the surface. The periodic electromagnetic fields are expanded in Fourier series and each harmonic is analyzed by BEM. The surface and internal electromagnetic fields are obtained numerically one after the other until convergence by the Newton‐Raphson method.

It is confirmed that this approach gives accurate solutions with meshes much larger than the skin depth and therefore is adequate to apply to a large‐scale application.

The eddy current is formulated by utilizing the impedance boundary condition in order to meet a large‐scale application, and so solutions near the edge are poor. In the case of better solutions being required, some modifications are necessary.

To lessen computer memory consumption, the parallel component of the currents to the steel surface is analyzed as a 2D problem and the normal component is obtained from the parallel component. One 2D equation for one analyzing region is discretized by dividing the region into layers adaptively and then solved. Next, another is solved sequentially. This method gives a compatible numerical analysis tool with finite element method.

Effect of unstable “wavy” temperature distribution on the part surface during the process of induction heating of ferromagnetic materials was observed and reported by two Russian scientists in 1940 (Babat and Lozinskii, 1940). They reported that under certain conditions, one can observe periodical or quasi-periodical bright stripes on the part surface when its temperature passes through the Curie point. In time, these stripes expand and merge, forming a normal temperature pattern. They called this phenomenon “polosatiy nagrev” (striation heating). Let us call it the “zebra effect” for simplicity. It can exist for a relatively long time, from several seconds to several tens of seconds. Several explanations of the zebra effect were proposed with not very convincing arguments. The purpose of this study is to improve the understanding of this effect.

Wider spreading of induction technology and use of computer simulation of induction processes create a demand and open new possibilities for study of the zebra effect. This study provides an overview of the available information about the zebra effect and gives new explanation of this phenomenon based on existing experimental data and new results of simulation. Conditions for zebra occurrence and its technological importance or limitations are discussed.

Computer simulation using the Flux 2D program allows to demonstrate the striation (zebra) effect that can appear in the process of heating magnetic materials and reproduce main experimental findings related to this effect. Simulation provides a great opportunity to investigate the zebra phenomenon in virtual reality, providing qualitatively correct results. Results of simulation show that the zebra effect can appear in a relatively narrow range of material properties and operating conditions. The main factor is a big enough gradient of permeability near the Curie point. At present, it is difficult to expect high quantitative accuracy of simulation due to multiple assumptions in simulation algorithms and insufficient or inaccurate information about the material properties near the Curie point.

Several explanations of the zebra effect were proposed with not very convincing arguments. There were concerns that the zebra effect could set significant limits on the use of induction heating for surface hardening due to non-uniform temperature distribution along the part (Babat and Lozinskii, 1940; Babat, 1965; Lozinskii, 1949, 1969). However, it did not happen. There were no complaints from scientists or practitioners regarding any negative effect of the zebra phenomenon. Moreover, the authors of this paper did not find any original publications on this issue for more than half a century. Only few old induction experts confirm that they observed the zebra effect or something similar, whereas a great majority of induction community members never heard about it.

The paper aims to improve convergence characteristics of the Newton–Raphson (NR) method applied to time-periodic finite element method using various line searches, as time-periodic finite element method causes deterioration of convergence characteristic of nonlinear analysis based on NR method. The study also aims to accelerate and improve accuracy of electromagnetic field analysis for improvement of the performance of electrical machine.

The paper proposes new type line searches that set approximate step size for NR method. The line search evaluated step size using higher-order interpolation of functional derivative. In addition, two criteria for applying these line search were proposed. First method set one scalar value for every NR iteration that is named constant step size. Second method define different step size in each time step of time-periodic finite element method to update solution vector that is named different step size.

The paper provides efficient line searches to improve convergence characteristics for NR method. Nonlinear magnetic field analysis of two transformer models is demonstrated. The proposed methods achieve the following results: higher-order functional NR is efficient in improving convergence characteristics, and the proposed methods succeeded about twice faster in both models.

The paper fulfills improvement of convergence characteristics of the NR method applied to time-periodic finite element method using proposed line searches and accelerate electromagnetic field analysis.

The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.

In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.

The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.

Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.

Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.

With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.