• Title/Summary/Keyword: heat equation

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The formation mechanism of grown-in defects in CZ silicon crystals based on thermal gradients measured by thermocouples near growth interfaces

  • Abe, Takao
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.9 no.4
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    • pp.402-416
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    • 1999
  • The thermal distributions near the growth interface of 150nm CZ crystals were measured by three thermocouples installed at the center, middle (half radius) and edge (10nm from surface) of the crystals. The results show that larger growth rates produced smaller thermal gradients. This contradicts the widely used heat flux balance equation. Using this fact, it is confirmed in CZ crystals that the type of point defects created is determined by the value of the thermal gradient(G) near the interface during growth, as already reported for FZ crystals. Although depending on the growth systems the effective length of the thermal gradient for defect generation are varied, we defined the effective length as 10n,\m from th interface in this experiment. If the G is roughly smaller than 20C/cm, vacancy rich CZ crystals are produced. If G is larger than 25C/cm, the species of point defects changes dramatically from vacancies to interstitials. The experimental results after detaching FZ and CZ crystals from the melt show that growth interfaces are filled with vacancies. We propose that large G produces shrunk lattice spacing and in order to relax such lattice excess interstitials are necessary. Such interstitials recombine with vacancies which were generated at the growth interface, nest occupy interstitial sites and residuals aggregate themselves to make stacking faults and dislocation loops during cooling. The shape of the growth interface is also determined by te distributions of G across the interface. That is, the small G and the large G in the center induce concave and convex interfaces to the melts, respectively.

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Two dimensional time-dependent creep analysis of a thick-walled FG cylinder based on first order shear deformation theory

  • Loghman, Abbas;Faegh, Reza K.;Arefi, Mohammad
    • Steel and Composite Structures
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    • v.26 no.5
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    • pp.533-547
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    • 2018
  • In this paper the time-dependent creep analysis of a thick-walled FG cylinder with finite length subjected to axisymmetric mechanical and thermal loads are presented. First order shear deformation theory (FSDT) is used for description of displacement components. Inner and outer temperatures and outer pressure are considered as thermo-mechanical loadings. Both thermal and mechanical loadings are assumed variable along the axial direction using the sinusoidal distribution. To find temperature distribution, two dimensional heat transfer equation is solved using the required boundary conditions. The energy method and Euler equations are employed to reach final governing equations of the cylinder. After determination of elastic stresses and strains, the creep analysis can be performed based on the Yang method. The results of this research indicate that the boundaries have important effects on the responses of the cylinder. The effect of important parameters of this analysis such as variable loading, non-homogeneous index of functionally graded materials and time of creep is studied on the behaviors of the cylinder.

Numerical Analysis of Laminar Flows in the Two Dimensional Sector Cavity by Finite Analytic Method in Polar Coordinate System (極座標系 有限解析法 에 의한 2次元 부채꼴 캐비티 의 層流流動 解析)

  • 배주찬;강신영
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.8 no.3
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    • pp.185-194
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    • 1984
  • The finite analytic method is extended to solve the steady two dimensional Navier-Stokes equation of stream functions and vorticity in polar coordinate system. The method is applied to calculate laminar flows in a sector cavity where the motion is induced by the rotation of the outer wall. Numerical solutions are obtained in the range of Reynolds number 0 to 5000 and aspect ratios 0.50, 1.20, 1.60 and 1.92. The finite analytic method is verfied to be accurate and fast convergent at high Reynolds numbers. It is promising as a numerical method of viscous flows and heat transfer. Flows in sector cavities show different flow structures and formation of secondary vortex with aspect ratios and Reynolds numbers in comparison with rectangular cavities.

Numerical Analyses to Simulate Thermal Stratification Phenomenon in a Piping System (배관계통에서의 열성층 현상 모사를 위한 수치해석)

  • Jeong, Jae-Uk;Kim, Sun-Hye;Chang, Yoon-Suk;Choi, Jae-Boong;Kim, Young-Jin;Kim, Jin-Su;Chung, Hae-Dong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.33 no.5
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    • pp.381-388
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    • 2009
  • In some portions of nuclear piping systems, stratification phenomena may occur due to the density difference between hot and cold stream. When the temperature difference is large, the stratified flow under diverse operating conditions can produce high thermal stress, which leads to unanticipated piping integrity issues. The objectives of this research are to examine controvertible numerical factors such as model size, grid resolution, turbulent parameters, governing equation, inflow direction and pipe wall. Parametric three-dimensional computational fluid dynamics analyses were carried out to quantify effects of these parameters on the accuracy of temperature profiles in a typical nuclear piping with complex geometries. Then, as a key finding, it was recommended to use optimized mesh of real piping with the conjugated heat transfer condition for accurate thermal stratification analyses.

Analysis of Compressive Characteristics of Wire-woven Bulk Kagome (Wire-woven Bulk Kagome의 압축 특성 분석)

  • Lee, Byung-Kon;Choi, Ji-Eun;Kang, Ki-Ju;Jeon, In-Su
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.1
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    • pp.70-76
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    • 2008
  • Periodic cellular metals (PCMs) are actively being investigated because of their excellent specific strength and stiffness, and multi-functionality such as a heat disperse structure bearing external loading. The Kagome truss PCM has been proved that it has higher resistance to plastic buckling and lower anisotropy than other truss PCMs. In this paper, the out-of-plane compressive responses of the WBK specimens have been measured, theoretically predicted and numerically analyzed. Three specimens of two-layered WBK are fabricated and tested for measuring the responses. The peak stress of compressive behavior and effective elastic modulus are predicted based on the equilibrium equation and elastic energy conservation. Moreover, the structure of the specimen is modeled using the commercial mesh generation code, PATRAN and the finite element analysis for the model under the compression is carried out using the commercial FE code, ABAQUS. Finally, the obtained results are compared with each other to analyze the compressive characteristics of Wire-woven Bulk Kagome (WBK).

Modeling and Simulation of the Pneumatic Part in a Cold Gas Blow-Down Type Hydraulic Actuation System for a Missile (상온기체 블로우다운 방식을 사용한 유도무기용 유압식 구동장치의 공압부에 대한 모델링 및 시뮬레이션)

  • Park, Hee Seung
    • Journal of Drive and Control
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    • v.13 no.3
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    • pp.1-7
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    • 2016
  • A cold gas blow-down hydraulic actuation system is widely used in missiles that require an actuation system with a fast response time under a limited space with a short operating time and large loads on the actuators. The system consists of a pneumatic part that supplies the regulated high-pressure gas to a reservoir, and a hydraulic part that supplies pressurized hydraulic oil to the actuators by the pressurized gas in the reservoir. This paper proposes a mathematical model to analyze and simulate the pneumatic part of an actuation system that supplies the operating power to the actuators. The mathematical model is based on the ideal gas equation and also considers the models for heat transfer. The model is applied to the pressure vessel and the gas part of the reservoir, and the model for the pneumatic part is established by connecting the two models for the parts. The model is validated through a comparison of the simulation results with the experimental results. The comparison shows that the suggested model could be useful in the design of the pneumatic part of a cold gas blow-down type hydraulic actuation system.

Prediction of Laminar Burning Velocity and Flame Thickness in Methane-Air Pre-Mixture (메탄-공기 예혼합기에서의 층류 화염속도 및 화염두께 예측)

  • Kwon, Soon-Ik;Bowen, Philip J.
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.9
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    • pp.1201-1208
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    • 2003
  • The thickness of flame and preheat zone from burning velocity which was computed by using Premix code of Chemkin program for methane-air mixture. Also the thickness was evaluated from temperature profile which is also obtained from Premix code for the equivalence ratio of 0.5 to 1.6. The computations were carried out for the laminar flame thickness and burning velocity under the unburned gas temperature 0.5bat-30bar and temperature of 300K-700K at ${\Phi}=l.0$. Comparison of the results showed no difference between these two methods. The flame thickness was decreased by increasing the pressure and temperature, but, the affect of pressure is more significant than the effect of temperature on the flame thickness. The thickness of preheat zone was about 66.5% of the flame thickness, and flame thickness and burning velocity were also predicted by using empirical equation.

A SIMPLIFIED METHOD TO PREDICT FRETTING-WEAR DAMAGE IN DOUBLE $90^{\circ}$ U-BEND TUBES

  • Choi, Seog-Nam;Yoon, Ki-Seok;Choi, Taek-Sang
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.616-621
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    • 2003
  • Fluid-elastic instability is believed to be a cause of the large-amplitude vibration and resulting rapid wear of heat exchanger tubes when the flow velocity exceeds a critical value. For sub-critical flow velocities, the random turbulence excitation is the main mechanism to be considered in predicting the long-term wear of steam generator tubes. Since flow-induced interactions of the tubes with tube supports in the sub-critical flow velocity can cause a localized tube wear, tube movement in the clearance between the tube and tube support as well as the normal contact force on the tubes by fluid should be maintained as low as possible. A simplified method is used for predicting fretting-wear damage of the double $90^{\circ}$U-bend tubes. The approach employed is based on the straight single-span tube analytical model proposed by Connors, the linear structural dynamic theory of Appendix N-1300 to ASME Section III and the Archard's equation for adhesive wear. Results from the presented method show a similar trend compared with the field data. This method can be utilized to predict the fretting-wear of the double $90^{\circ}$U-bend tubes in steam generators.

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Cover Layer Design and Temperature Analysis in Pseudo NFR System Using SIL Head (SIL 헤드유사 근접장 시스템 개발을 위한 보호막 설계 및 열해석)

  • Kim Kyungho;Kim Sookyung;Lee Sung-Q;Park Kang-Ho;Lee Seung-Yop
    • Transactions of the Society of Information Storage Systems
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    • v.1 no.1
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    • pp.58-66
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    • 2005
  • Pseudo-Near Field Recording (Pseudo-NFR) system is proposed to prevent contamination and oxidation of media surface occurred in conventional NFR systems. To solve these critical problems of the NFR systems, we investigate the optimal thickness of cover layer for Pseudo NFR. This paper presents the theoretical analysis for cover layer thickness based on the measured length of dust particle and numerical simulation for the temperature distribution using Finite Difference Time Domain (FDTD) method and heat conduction equation. To verify the simulation results, we conduct and compare simulation results in case of far field MO recording and near field MO recording. A measured dust particle length in general environment was mostly less than $20{\mu}m$, and the optimal thickness of cover layer is $30{\mu}m$ in this case. Based on the designed optimal cover layer thickness, temperature distribution is simulated to have $800{\~}850^{\circ}C$.

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Oscillation of Microbeam Structure with Irregular Mass Distribution

  • Kang, Seok-Joo;Kim, Jung-Hwan;Kim, Ji-Hwan
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2013.04a
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    • pp.528-532
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    • 2013
  • In this study, an analytical model of micro-beam structure including thermoelastic damping with irregularly distributed masses is investigated. The significance of thermoelastic damping for micro-scale mechanical resonators is evaluated to design -with high quality factor(Q-factor). The beam model of this work is based on Euler-Bernoulli beam theory. In order to determine the natural frequency of the model, energy method is applied. Also, the thermoelatic damping effects are considered by using heat conduction equations, and the Q-factor can be determined. To derive the equation of motion, non-dimensionalization is employed for systematic analysis. Results of the model are verified, and present mode shapes and Q-factors for the micro-beam with thermoelastic damping including random point masses.

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