• Title/Summary/Keyword: Maxwell Equations

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Thermally-Expandable Molding Process for Thermoset Composite Materials (열팽창 치공구를 이용한 열경화성 복합재료의 성형연구)

  • 이준호;금성우;장원영;남재도
    • Polymer(Korea)
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    • v.24 no.5
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    • pp.690-700
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    • 2000
  • In this study, an elastomer-assistered compression molding process was investigated by experiments as well as modeling for the long-fiber reinforced thermoset composites. The consolidation pressure generated by fixed-volume and variable-volume conditions was thermodynamically derived for both elastomer and curing prepregs, and was compared with the pressure measured during curing of epoxy matrix. Exhibiting non-linear viscoelastic characteristics in the compressive stress-strain tests, the measured stress was well compared with a modifed KWW (Kohlrausch-Williame-Watts) equation, which is based on the Maxwell viscoelastic model. Using the developed model equations, the consolidation pressure generated by the elastomer was successfully predicted for the compression molding process of thermoset composite materials in tile closed mold system.

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Analysis of Switched Reluctance Motors Characteristics using FEM (유한요소법을 이용한 SRM의 특성해석)

  • Lee, Joon-Ho;Lee, Hyang-Beom;Lee, Ki-Sik
    • Proceedings of the KIEE Conference
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    • 1996.07a
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    • pp.139-141
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    • 1996
  • The switched reluctance motors(SRM) are simple and robust in structure. Because the wide range of power and speed, their application field is increasing. In order to design the motors and to evaluate the performance of them properly, an accurate study about the analysis of motor characteristics is required. In this paper, for the analysis of SRM characteristics, the finite element method which is based on the solution of combined equations both the electromagnetic field equations and the circuit equations of stator is adopted. The analysis model is to he assumed two-dimensional and the nonlinear property of magnetic materials is considered by Newton-Raphson method. To verify the usefulness of the proposed algorithm, commercial SRM is chosen and simulated. The computed torques obtained by Maxwell Stress Tensor are compared with the experimental data and it is found that they are in good agreement. By applying the proposed algorithm to two cases, currents of stator and torques at every angular positions of rotor are obtained step by step. Comparing them, one can recognize that torque ripple of SRM can he improved by controlling the switching sequences of driving circuits.

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Mathematical approach for optimization of magnetohydrodynamic circulation system

  • Lee, Geun Hyeong;Kim, Hee Reyoung
    • Nuclear Engineering and Technology
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    • v.51 no.3
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    • pp.654-664
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    • 2019
  • The geometrical and electromagnetic variables of a rectangular-type magnetohydrodynamic (MHD) circulation system are optimized to solve MHD equations for the active decay heat removal system of a prototype Gen-IV sodium fast reactor. Decay heat must be actively removed from the reactor coolant to prevent the reactor system from exceeding its temperature limit. A rectangular-type MHD circulation system is adopted to remove this heat via an active system that produces developed pressure through the Lorentz force of the circulating sodium. Thus, the rectangular-type MHD circulation system for a circulating loop is modeled with the following specifications: a developed pressure of 2 kPa and flow rate of $0.02m^3/s$ at a temperature of 499 K. The MHD equations, which consist of momentum and Maxwell's equations, are solved to find the minimum input current satisfying the nominal developed pressure and flow rate according to the change of variables including the magnetic flux density and geometrical variables. The optimization shows that the rectangular-type MHD circulation system requires a current of 3976 A and a magnetic flux density of 0.037 T under the conditions of the active decay heat removal system.

An Anisotropic Perfectly Matched Layer(APML) for Mesh Truncation in The Finite Difference Time Domain Method (유한차분시간영역(FDTD)법에 있어 Mesh Truncation을 위한 비등방성 완전정합층에 관한 연구)

  • 박동희;김정기
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.9 no.5
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    • pp.678-686
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    • 1998
  • This paper describes an anisotropic perfectly matched layer (APML) for mesh truncation of the Finite Difference Time Domain(FDTD) method. The APML method can classified by a split type and an unsplit type, in case of the split type be made up 12 equations or 8 equations largely, and in case of the unsplit type be made of 6 equations. Therefore the latter is more simple as compare with the former. For the APML method presented in this paper is the latter, is directly derived from the time domain equations of Maxwell and extend to the three dimensional problem for the method suggested by Chen. Especially, in the edge and corner parts except the planes, the APML method effectively treated as compound with the Chen's method and Gedney's method newly. The results of the numerical method in this paper show the radiation patterns and the time responses of electromagnetic fields of the wire antennas according to wavelengths and the APML results are compared with Mur's first order absorbing boundary condition and Kraus's analytical results. Eventually, Mur's first order condition have many errors at the edge and corner. On the other hand, in comparison with Kraus's analytical results, it is quite good agreement, and the validity of present method is confirmed.

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Molecular Theory of Plastic Deformation (I). Theory (소성변형의 분자론 (제1보). 이론)

  • Kim Chang Hong;Ree Taikyue
    • Journal of the Korean Chemical Society
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    • v.21 no.5
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    • pp.330-338
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    • 1977
  • In order to elucidate the plastic deformation of solids, the following assumptions were made: (1) the plastic deformation of solids is classified into two main types, the one which is caused by dislocation movement and the other caused by grain boundary movement, each movement being restricted on a different shear surface, (2) the dislocation movement is expressed by a mechanical model of a parallel connection of various kinds of Maxwell dislocation flow units whereas the grain boundary movement is also expressed by a parallel connection of various kinds of Maxwell grain boundary flow units; the parallel connection in each type of movements indicates that all the flow units on each shear surface flow with the same shear rate, (3) the latter model for grain boundary movement is connected in series to the former for dislocation movement, this means physically that the applied stress distributes homogeneously in the flow system while the total strain rate distributes heterogeneously on the two types of shear planes (dislocation or grain boundary shear plane), (4) the movement of dislocation flow units and grain boundary units becomes possible when the atoms or molecules near the obstacles, which hinder the movement of flow units, diffuse away from the obstacles.Using the above assumptions in conjunction with the theory of rate processes, generalized equations of shear stress and shear rate for plastic deformation were derived. In this paper, four cases important in practice were considered.ted N${\cdot}{\cdot}{\cdot}$O hydrogen bond and the second of two normal N${\cdot}{\cdot}{\cdot}$O hydrogen bonds, both of which exist between the amino group and the perchlorate, groups. A p-phenylenediamine group is approximately planar within an experimental error and bonded to twelve perchlorates: ten perchlorates forming hydrogen bonds and two being contacted with the van der Waals forces. A perchlorate group is surrounded by six p-phenylenediamines and four perchlorates; among the six p-phenylenediamines, five of them are hydrogen-bonded, and the rest contacted with the van der Waals force.

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Physical Properties of Microencapsulated Phase Change Material Slurries (미립잠열슬러리의 물성에 관한 실험적 연구)

  • 이효진;홍재창;이재구
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.12 no.9
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    • pp.860-869
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    • 2000
  • The thermal conductivity and density of slurries entrained with the particles of Micro-PCM are measured with respect to its temperatures as well as concentrations. For the thermal conductivity of slurries, a device made from P.A. Hilton (Model No. H470) is adopted. There is a well-scaled 0.3 mm gap between shells into which the slurry is injected. The temperatures of the slurry are changed to $5~25^{\circ}C$ , for which it is controled by the supplied voltage and cooling water circulated around the outer shell. The concentrations of Micro-PCM slurries are varied from 5 wt% to 50 wt%. Some general equations such as Maxwell's equation, are evaluated for their applicability with Micro-PCM slurry. As a result, it happens to be some 20% discrepancy between the experiment and the applied equations. The density measurements of Micro-PCM slurry to its temperature and concentration are peformed by hydrometer. For the experiment, tetradecane encapsulated slurry (($t_m≒6^{\circ}C$) and a mixed wax ($t_m≒50^{\circ}C$) are tested. The temperature changes of tetradecane are applied for $0^{\circ}C\;to\;$20^{\circ}C$and a mixed wax for $20^{\circ}C\;to\;$60^{\circ}C$ and its concentrations are changed from 5 wt% to 30 wt%. The results are compared with a general equation and the referenced data. For the conclusion, the experimental result and a general equation are well agreed.

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A NUMERICAL ANALYSIS OF CZOCHRALSKI SINGLE CRYSTAL GROWTH OF SILICON WITH MISALIGNED CUSP MAGNETIC FIELDS (Misaligned된 비균일자장이 인가된 초크랄스키 실리콘 단결정성장에 대한 수치적 해석)

  • Kim, Chang Nyung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.1
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    • pp.121-131
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    • 2000
  • Melt flow, heat and mass transfer of oxygen have been analyzed numerically in the process of Czochralski single crystal growth of silicon under the influence of misaligned cusp magnetic fields. Since the silicon melt in a crucible for crystal growth is of high temperature and of highly electrical-conducting, experimentation method has difficulty in analyzing the behavior of the melt flow. A set of simultaneous nonlinear equations including Navier-Stokes and Maxwell equations has been used for the modelling of the melt flow which can be regarded as a liquid metal. Together with the melt flow which forms the Marangoni convection, a flow circulation is observed near the comer close both to the crucible wall and the free surface. The melt flow tends to follow the magnetic lines instead of traversing the lines. These flow characteristics helps the flow circulation exist. Mass transfer characteristics influenced by the melt flow has been analyzed and the oxygen absorption rate to the crystal has been calculated and turned out to be rather uniform than in the case of an aligned magnetic field.

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Magneto-thermo-elastic response of a rotating functionally graded cylinder

  • Hosseini, Mohammad;Dini, Ali
    • Structural Engineering and Mechanics
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    • v.56 no.1
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    • pp.137-156
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    • 2015
  • In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

Numerical Visualization of the Unsteady Shock Wave Flow Field in Micro Shock Tube

  • Arun, Kumar R.;Kim, Heuy-Dong
    • Journal of the Korean Society of Visualization
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    • v.10 no.1
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    • pp.40-46
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    • 2012
  • Recently micro shock tube is extensively being used in many diverse fields of engineering applications but the detailed flow physics involved in it is hardly known due to high Knudsen number and strong compressibility effects. Unlike the macro shock tube, the surface area to volume ratio for a micro shock tube is very large. This unique effect brings many complexities into the flow physics that makes the micro shock tube different compared with the macro shock tube. In micro shock tube, the inter- molecular forces of working gas can play an important role in specifying the flow characteristics of the unsteady shock wave flow which is essentially generated in all kinds of shock tubes. In the present study, a CFD method was used to predict and visualize the unsteady shock wave flows using the unsteady compressible Navier-Stokes equations, furnished with the no-slip and slip wall boundary conditions. Maxwell's slip equations were used to mathematically model the shock movement at high Knudsen number. The present CFD results show that the propagation speed of the shock wave is directly proportional to the initial pressure and diameter of micro shock tube.

Analytical solution for buckling analysis of micro sandwich hollow circular plate

  • Mousavi, Mohammad;Mohammadimehr, Mehdi;Rostami, Rasoul
    • Computers and Concrete
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    • v.24 no.3
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    • pp.185-192
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    • 2019
  • In this paper, the buckling of micro sandwich hollow circular plate is investigated with the consideration of the porous core and piezoelectric layer reinforced by functionally graded (FG)carbon nano-tube. For modeling the displacement field of sandwich hollow circular plate, the high-order shear deformation theory (HSDT) of plate and modified couple stress theory (MCST) are used. The governing differential equations of the system can be derived using the principle of minimum potential energy and Maxwell's equation that for solving these equations, the Ritz method is employed. The results of this research indicate the influence of various parameters such as porous coefficients, small length scale parameter, distribution of carbon nano-tube in piezoelectric layers and temperature on critical buckling load. The purpose of this research is to show the effect of physical parameters on the critical buckling load of micro sandwich plate and then optimize these parameters to design structures with the best efficiency. The results of this research can be used for optimization of micro-structures and manufacturing different structure in aircraft and aerospace.