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Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

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.

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

The obtained results are new and presented for the first time in the literature.

The bodies of aircraft structures have a lot of fastener holes and under different situations these holes bear external forces, which cause a tensile stress on the surface that leads to the failure of materials. Cold expansion process is one of the widely‐used methods to improve the fatigue behavior of materials used in aerospace industry, and such improvement is due to the compressive residual stress around cold expanded hole. The induced residual stress distribution around cold expanded hole is affected by several parameters such as, diametrical interfaces, surface finish of fastener holes, temperature, mandrel speed, i.e. the speed of inserting mandrel into the hole, and so on. In previous studies, most of effective parameters were investigated, whereas, the effect of mandrel speed on the residual stress distribution has not been considered. The present study, seeks to simulate cold expansion process on aluminum alloy 2A12TA using ABAQUS finite element (FE) package and to consider the effect of different mandrel speeds on residual stress distribution around cold expanded hole. It aims to verify the results of FE simulation by experimental data.

There are two kinds of data in this paper; experimental and FE results. The experimental results for cold expansion process have been extracted from the literature and ABAQUS finite element package was employed in order to simulate the above‐mentioned process. Moreover, FE results were validated by the experiments.

The results presented here show the influence of mandrel speed on residual stress distribution around cold expanded hole using a new analytical‐numerical method. The results gained by FE simulation show relative differences between the diagrams of residual stress distribution corresponding different mandrel speeds. It is shown in the paper; the residual stress around cold expanded hole rises by the increase of mandrel speed and consequently the improvement of fatigue life will be achieved.

The present study is part of Abbas Hosseini's MSc. dissertation, an original research work.

The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

In the method developed, the field functions are determined in the analytical way by the superposition of states and separation of variables method. The coefficients of the field functions and eigenvalues of the boundary‐initial problem are computed by the numerical method. The coefficients are the solution to the corresponding sets of equations. These sets are the result of scalar products of non‐orthogonal functions at the respective zones of the cable. The eigenvalues are determined by an algorithm, which uses the field properties and elements of the golden cut method.

The method made it possible to develop a mathematical model of the dynamics of the thermal field in a polymer DC cable. This model has good physical interpretation. The paper also presents the field distributions determined in an analytical form. Some arguments of the expressions derived are however computed numerically. The results obtained by the paper's method and by the finite elements methods were compared. The relative differences are less than 6 per cent.

The method concerns axially‐symmetrical three‐zone systems under nominal conditions.

By means of the method important parameters of DC lines can be determined (e.g. spatial‐temporal heat‐up curves, admissible sustained currents, time constants).

An analytical‐numerical method of analysis of the thermal field in a three‐zone axially‐symmetrical system was developed. Its original element is the algorithm of determination of eigenvalues of the boundary‐initial problem and coefficients of non‐orthogonal field functions.

The purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.

GITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.

The effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.

The strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.

The purpose of this paper is to determine and evaluate resource allocation algorithms for mixed‐structure operation systems with unknown parameters characterized by experts using the formalism of C‐uncertain variables.

Aggregation and decomposition of mathematical models of operations, performed using analytical‐numerical optimization methods, lead to serial and parallel structures for which allocation algorithms are known. Evaluation of allocations carried out by means of a computer simulation.

Resource allocation problems for mixed‐structure operation systems may be solved by applying aggregation, decomposition and allocation algorithms determined for simple structures. Allocation algorithms based on C‐uncertain variables outperform these based on basic uncertain variables.

Application of the presented algorithms is limited to some mixed structures, however, the methodology used appears general enough to allow developing algorithms for other mixed structures.

The algorithms developed may be embedded into a knowledge‐based system supporting management‐level decisions concerning optimal distribution of limited financial resources.

Originally determined rules for aggregation and decomposition, as well as resulting allocation algorithms. The presented methodology seems promising for developing a general resource allocation algorithm – valid for any mixed structure of an operation system.

According to the method of moment, an effective electromagnetic approach for the substation's grounding grid in high frequency domain is presented. An efficient method based on the generalized pencil‐of‐function method is developed to calculate the generalized Sommerfeld integral. With the method, the value of Green's function in a two‐layer medium can be obtained quickly and accurately. The number of unknown variables of the moment method is small. As the dipole antenna theory is introduced, the frequency of the injected current to the grounding grid can vary in a large scale. The method can be used to analyze not only the performance of the grounding grid, but also other grids located under the earth, in the air or penetrating a lossy interface. The computational results are in good agreement with those obtained by other method.

The purpose of this paper is to compare the methods of calculating the parameters of air-cored stator flux permanent magnet generator and to compare these results with the measurements of the designed and manufactured generator. The generator is to be designed for operation in a wind power plant.

An analytical method and 2D and 3D finite element methods (FEMs) were used to calculate the parameters of the coreless permanent magnet axial generator. The analytical method and 2D FEM were applied to individual cross-sections through the air gap of the machine. After the design and construction of the generator and measuring station, the results of calculations and measurements were compared.

The results of investigated calculation methods and measurements were found to be mutually compatible. Analytical methods and 2D FEM required proper interpretation of the results when comparing them with the 3D FEM. The results of the measurements and calculations showed the usefulness of the generator for operation in a wind power plant.

Full comparison of results of 2D and 3D calculations with the results of the measurements on the machine model confirmed the usefulness of fast 2D methods for the analysis of coreless generators. The results differed by the effects of leakage inductance of windings’ front connections. The application of an axial generator designed with the described methods in a wind turbine showed its proper operation.