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This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems.

The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility.

This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor.

Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study.

This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications.

Most of the linear encoders are based on optics. The accuracy and reliability of these encoders are greatly reduced in polluted and noisy environments. Moreover, these encoders have a complex structure and large sensor volume and are thus not suited to small application scenarios and do not have universality. This paper aims to present a new absolute magnetic linear encoder, which has a simple structure, small size and wide application range.

The effect of swing error is analyzed for the sensor structural arrangement. A double-threshold interval algorithm is then proposed to synthesize multiple interval electrical angles into absolute angles and convert them into actual displacement distances.

The final linear encoder measurement range is 15.57 mm, and the resolution reaches ± 2 µm. The effectiveness of the algorithm is demonstrated experimentally.

The linear encoder has good robustness, and high measurement accuracy, which is suitable for industrial production. The linear encoder has been mass-produced and used in an electric power-assisted braking system.

This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

Detecting the orientation of cracks is a major challenge in the development of eddy current nondestructive testing probes. Eddy current-based techniques are limited in their ability to detect cracks that are not perpendicular to induced current flows. This study aims to investigate the application of the rotating electromagnetic field method to detect arbitrary orientation defects in conductive nonferrous parts. This method significantly improves the detection of cracks of any orientation.

A new rotating uniform eddy current (RUEC) probe is presented. Two exciting pairs consisting of similar square-shaped coils are arranged orthogonally at the same lifting point, thus avoiding further adjustment of the excitation system to generate a rotating electromagnetic field, eliminating any need for mechanical rotation and focusing this field with high density. A circular detection coil serving as a receiver is mounted in the middle of the excitation system.

A simulation model of the rotating electromagnetic field system is performed to determine the rules and characteristics of the electromagnetic signal distribution in the defect area. Referring to the experimental results aimed to detect artificial cracks at arbitrary angles in underwater structures using the rotating alternating current field measurement (RACFM) system in Li et al. (2016), the model proposed in this paper is validated.

CEDRAT FLUX 3D simulation results showed that the proposed probe can detect cracks with any orientation, maintaining the same sensitivity, which demonstrates its effectiveness. Furthermore, the proposed RUEC probe, associated with the exploitation procedure, allows us to provide a full characterization of the crack, namely, its length, depth and orientation in a one-pass scan, by analyzing the magnetic induction signal.

High resolution simulations of body-internal electric field strengths induced by magneto-quasistatic fields from wireless power transfer systems are computationally expensive. The exposure simulation can be split into two separate simulation steps allowing the calculation of the magnetic flux density distribution, which serves as input into the second simulation step to calculate the body-internal electric fields. In this work, the magnetic flux density is interpolated from in situ measurements in combination with the scalar-potential finite difference scheme to calculate the resulting body-internal field. These calculations are supposed to take less than 5 s to achieve a near real-time visualization of these fields on mobile devices. The purpose of this work is to present an implementation of the simulation on graphics processing units (GPUs), allowing for the calculation of the body-internal field strength in about 3 s.

This work uses the co-simulation scalar-potential finite difference scheme to determine the body-internal electric field strength of human models with a voxel resolution of 2 × 2 × 2 mm³. The scheme is implemented on GPUs. This simulation scheme requires the magnetic flux density distribution as input, determined from radial basis functions.

Using NVIDIA A100 GPUs, the body-internal electric field strength with high-resolution models and 8.9 million degrees of freedom can be determined in about 2.3 s.

This paper describes in detail the used scheme and its implementation to make use of the computational performance of modern GPUs.

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.

Calculating the stator end-winding leakage inductance, taking into account the rotor, is difficult due to the irregular shape of the end-winding. The end-winding leakage may distribute at the end of the active part and the fringing flux of the air gap. The fringing flux belongs to the main flux but goes into the end-winding region. Then, not all the magnetic flux occurring in the end region is the end-winding leakage flux. The purpose of this paper was to find a method to accurately separate the leakage from the total flux, taking into account the rotor.

In this paper, two methods based on energy calculation are presented. Both methods require the assumption that the machine is symmetrical. The first method depends on the total leakage inductance and the machine’s active region length. The second method is based on the energy stored in the end region of the machine. In this case, removing the energy produced by the fringing flux of the air gap is necessary. The model should have a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap.

The method presented in the paper does not require rotor removal. The values of the end-winding leakage inductance computed based on the proposed method were compared with values computed using the method with the removed rotor. The computations show that the proposed method is closest to the results from the method presented in the literature. Results obtained in the first method present that rotor influence on the value of end-winding leakage inductance exists. The model of the stator end-winding described in the paper is general. Therefore, the proposed methods are suitable for calculating the end-winding leakage inductance of other electric machines.

The method presented in the paper considers the rotor in end-winding leakage inductance calculation. It is not necessary to remove the rotor as in the similar method presented in the literature. The authors elaborated a parametric model with a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. The authors also elaborated their 3D model of the machine winding for calculations in Opera 3D.

The purpose of this paper is to use the corresponding magnetic sensor and detection method to detect and image the defects of small diameter pipelines. Urban gas pipeline is an energy transportation tool for urban industrial production and social life, which is closely related to urban safety. Preventing the occurrence of urban gas pipeline transportation accidents and carrying out pipeline defect detection are of great significance for the urban economic and social stability. To perform pipeline defect detection, the magnetic flux leakage internal detection method is generally used in the detection of large-diameter long-distance oil and gas pipelines. However, in terms of the internal detection of small-diameter pipelines, due to the heavy weight, large structure of the detection device and small pipe diameter, the detection is more difficult.

In order to solve the above matters, self-made three-dimensional magnetic sensor and three-dimensional magnetic flux leakage imaging direct method are proposed for studying the defect identification. Firstly, for adapting to the diameter range of small-diameter pipelines, and containing the complete information of the defect, a self-made three-dimensional magnetic sensor is made in this paper to improve the accuracy of magnetic flux leakage detection. And on the basis of it, a small diameter pipeline defect detection system is built. Secondly, as detection signal may be affected by background magnetic field interference and the jitter interference, the complete ensemble empirical mode decomposition with adaptive noise method is utilized to screen the detected signal. As a result, the useful signal is reconstructed and the interference signal is removed. Finally, the defect contour inversion imaging of detection is realized based on the direct method of three-dimensional magnetic flux leakage imaging, which includes three-dimensional magnetic flux leakage detection data and data segmentation recognition.

The three-dimensional magnetic flux leakage imaging experimental results shown that, compared to the actual defects, the typical defects, irregular defects and crack groove defects can be analyzed by the magnetic flux leakage defect contour imaging method in qualitative and quantitative way respectively, which provides a new idea for the research of defect recognition.

A three-dimensional magnetic sensor is made to adapt the diameter range of small diameter pipeline, and based on it, a small-diameter pipeline defect detection system is built to collect and display the magnetic flux leakage signal.

This paper aims to examine the thermal transmission and entropy generation of hybrid nanofluid filled containers with solid body inside. The solid body is seen as being both isothermal and capable of producing heat. A time-dependent non-linear partial differential equation is used to represent the transfer of heat through a solid body. The current study’s objective is to investigate the key properties of nanoparticles, external forces and particular attention paid to the impact of hybrid nanoparticles on entropy formation. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates. Hybrid nanofluid has been proven to have useful qualities, making it an attractive coolant for an electrical device. The findings would help scientists and engineers better understand how to analyse convective heat transmission and how to forecast better heat transfer rates in cutting-edge technological systems used in industries such as heat transportation, power generation, chemical production and passive cooling systems for electronic devices.

Thermal transmission and entropy generation of hybrid nanofluid are analysed within the enclosure. The domain of interest is a square chamber of size L, including a square solid block. The solid body is considered to be isothermal and generating heat. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the SIMPLE algorithm on a uniformly staggered mesh. QUICK and central difference schemes were used to handle convective and diffusive elements. In-house code is developed using FORTRAN programming to visualize the isotherms, streamlines, heatlines and entropy contours, which are handled by Tecplot software. The influence of nanoparticles volume fraction, heat generation factor, external magnetic forces and an irreversibility ratio on energy transport and flow patterns is examined.

The results show that the hybrid nanoparticles concentration augments the thermal transmission and the entropy production increases also while the augmentation of temperature difference results in a diminution of entropy production. Finally, magnetic force has the significant impact on heat transfer, isotherms, streamlines and entropy. It has been observed that the external magnetic force plays a good role in thermal regulations.

Hybrid nanofluid is a desirable coolant for an electrical device. Various nanoparticles and their combinations can be analysed. Ferro-copper hybrid nanofluid considered with the help of prevailing literature review. The research would benefit scientists and engineers by improving their comprehension of how to analyses convective heat transmission and forecast more accurate heat transfer rates in various fields.

Due to its helpful characteristics, ferrous-copper hybrid nanofluid is a desirable coolant for an electrical device. The research would benefit scientists and engineers by improving their comprehension of how to analyse convective heat transmission and forecast more accurate heat transfer rates in cutting-edge technological systems used in sectors like thermal transportation, cooling systems for electronic devices, etc.

Entropy generation is used for an evaluation of the system’s performance, which is an indicator of optimal design. Hence, in recent times, it does a good engineering sense to draw attention to irreversibility under magnetic force, and it has an indispensable impact on investigation of electronic devices.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyse convective energy transport and entropy generation in a chamber with internal block, which is capable of maintaining heat and producing heat. Effects of irreversibility ratio are scrutinized for the first time. Analysis of convective heat transfer and entropy production in an enclosure with internal isothermal/heat generating blocks gives the way to predict enhanced heat transfer rate and avoid the failure of advanced technical systems in industrial sectors.

The accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.

The different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.

The paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.

The Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.