• East Asian mathematical journal
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• v.30 no.1
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• pp.79-91
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• 2014

We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.1-16
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• 2017

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1649-1661
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• 2005

We consider. a horizontal static liquid layer on a planar solid boundary. The layer is evaporating when the plate is heated. Vapor recoil and thermo-capillary are discussed along with the effect of mass loss and vapor convection due to evaporating liquid and non-equilibrium thermodynamic effects. These coupled systems of equations are reduced to a single evolution equation for the local thickness of the liquid layer by using a long-wave asymptotics. The partial differential equation is solved numerically.

• Proceedings of the KWS Conference
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• 2002.10a
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• pp.205-210
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• 2002

This article presents an integrated modeling approach for coupled analysis of heat transfer and microstructure evolution in welding carbon steel. The modeling procedure utilizes commercial [mite element code ABAQUS/Standard as the platform for solving the equation of heat conduction. User subroutines that implement computational thermodynamics and kinetics models are integrated with the FEA code to compute the transient microstructure evolution. In this study, the integrated models are applied to simulate the hot-tap repair welding of carbon steel pipeline. Microstructural components are treated as user output variables. Based on the predicted microstructure and cooling rates, hardness distributions in the welds were also predicted. The predicted microstructure and hardness distribution were found in good agreement with metallographic examinations and hardness measurements. This study demonstrates the applicability of computational models for the development of welding procedure for in-service pipeline repair.

• International Journal of Korean Welding Society
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• v.2 no.2
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• pp.1-6
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• 2002

This article presents an integrated modeling approach for coupled analysis of heat transfer and microstructure evolution in welding carbon steel. The modeling procedure utilizes commercial finite element code ABAQUS/Standard as the platform for solving the equation of heat conduction. User subroutines that Implement computational thermodynamics and kinetics models are integrated with the FEA code to compute the transient microstructure evolution. In this study, the integrated models are applied to simulate the hot-tap repair welding of carbon steel pipeline. Microstructural components are treated as user output variables. Based on the predicted microstructure and cooling rates, hardness distributions in the welds were also predicted. The predicted microstructure and hardness distribution were found in good agreement with metallographic examinations and hardness measurements. This study demonstrates the applicability of computational models for the development of welding procedure for in-service pipeline repair.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.3
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• pp.79-84
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• 1998

It is very difficult to analyze the transient temperature distribution during quenching of the steel because of coupled effects among temperature, structures and stresses. In this paper, using Inoue's equation of evolution and mixture rule, transient temperature distribution is calculated by the finite element method considering latent heat of transformation structure and temperature dependence of physical and mechanical prperties for the 0.45% carbon cylindrical steel bar with 40mm diameter and 20mm height during end-quenching.

• Magazine of the Korea Concrete Institute
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• v.7 no.6
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• pp.186-196
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• 1995

In this study, parameters such as unit cement weight and placing temperature which influence on temperature rise and temperature rise velocity are investigated through adiabatic tests for the domestic ordinary portland cement(0PC). Adiabatic temperature rise suggested by Korean Concrete Spec. are compared with that from this experimental results. As a result of this study, adiabatic temperature rise of OPC suggested spec. is overestimated. Also it is shown that 2-parameter equation suggested in the spec. overestimate heat evolution at early age and reasonable prediction of heat evolution can be obtained by using 3-parameter equation. Results of numerical analysis by using the input data from this test and the suggested values from spec. shows similar temperatures. However thermal stresses pridicted using input value from spec. may result 20% more than that from this test in case of externally restricted state.

• Journal of the korean Society of Automotive Engineers
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• v.6 no.4
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• pp.46-53
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• 1984

The analysis of temperature distribution and change of metallic structures during water quench were presented by finite element method. In temperature calculation the equation of unsteady state hear conduction problem considering latent heat due to phase transformation was applied to finite solid cylinder, SM 45C of 40mm diameter and 40mm height. In metallic structure analysis iso-thermal transformation curve and the equations of evolution in pearlite-martensite transformation were applied. The calculated results upon temperature and metallic structures were agreed with those of experimental observations.

• Fire Science and Engineering
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• v.10 no.2
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• pp.28-39
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• 1996

A recently developed electro-thermal simulation methodology is used to analyze the behavior of a PWM(Pulse-Width-Modulated) voltage source inverter which uses IGBT(Insulated Gate Bipolar Transistor) as the switching devices. In the electro-thermal network simulation methdology, the simulator solves for the temperature distribution within the power semiconductor devices(IGBT electro-thermal model), control logic circuitry, the IGBT gate drivers, the thermal network component models for the power silicon chips, package, and heat sinks as well as the current and voltage within the electrical network. The thermal network describes the flow of heat form the chip surface through the package and heat sink and thus determines the evolution of the chip surface temperature used by the power semiconductor device models. The thermal component model for the device silicon chip, packages, and heat sink are developed by discretizing the nonlinear heat diffusion equation and are represented in component from so that the thermal component models for various package and heat sink can be readily connected to on another to form the thermal network.