• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.308-313
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• 2009

본 논문은 확장된 이동최소제곱 유한차분법을 이용하여 1차원 Stefan 문제를 해석할 수 있는 수치기법이 제시한다. 이동하는 경계의 자유로운 묘사를 위해 요소망이나 그리드 없이 절점만을 사용하는 이동최소제곱 유한차분법을 사용하였으며, 계면경계의 특이성을 모형화하기 위해 Taylor 다항식에 쐐기함수를 도입했다. 지배방정식은 안정성이 높은 음해법(implicit method)을 이용하여 차분하였다. 미분의 특이성을 갖는 이동경계를 포함한 반무한 융해문제의 수치해석을 통해 확장된 이동최소제곱 유한차분법이 높은 정확성과 효율성을 갖는 것을 보였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.39-48
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• 2013

This paper develops a 2-D moving least squares(MLS) difference method for Stefan problem by extending the 1-D version of the conventional method. Unlike to 1-D interfacial modeling, the complex topology change in 2-D domain due to arbitrarily moving boundary is successfully modelled. The MLS derivative approximation that drives the kinetics of moving boundary is derived while the strong merit of MLS Difference Method that utilizes only nodal computation is effectively conserved. The governing equations are differentiated by an implicit scheme for achieving numerical stability and the moving boundary is updated by an explicit scheme for maximizing numerical efficiency. Numerical experiments prove that the MLS Difference Method shows very good accuracy and efficiency in solving complex 2-D Stefan problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.348-355
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• 1992

Casting structures and properties are determined by the solidification speed in the metal mold. The heat transfer characteristics of the interface between the mold and the casting is one of the major factors that control the solidification speed. According to Sully's research, the thermal resistance exists due to the air-gap formation at the mold-casting interface during the freezing process and the interface heat transfer coefficient is used to describe the degree of it. In this study, one-dimensional Stefan problem with air-gap resistance in the cylindrical geometry is considered and heat transfer characteristics is numerically examined. The temperature distribution and solidification speed are obtained by using the modified variable time step method. And the effects of the major parameters such as mold geometry, thermal conductivity, heat transfer coefficient and initial temperature of casting on the thermal characteristics are investigated.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.3
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• pp.162-170
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• 1996

A numerical study on the Stefan problem occurred in cryosurgery is performed. Crank-Nicholson type finite difference algorithm based on the enthaly method is adapted to solve the phase change problem in this study. As it is a moving boundary problem, special emphasis is put on the estimation of the freezing front location. Two cases selected here are freezings of human tissue by disk type cryoprobe and by hemispherical one. In both cases, the heat flows are considered to be one dimensional. The calculated results using enthalpy method are compared with those using the program TRUMP and with Neumann's solution. These results agree guite well with each other. While it is pretty difficult to get accurate freezing front location by TRUMP due to the so- called "phase change knee" occured during the phase change, the algorithm based on the enthalpy method is proved to be very powerful to cope with this kind of problem.f problem.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.6
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• pp.891-897
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• 1999

The heat transfer characteristics at the interface between the mold and the casting is one of the major factors for the solidification speed which determines the casting structures. The thermal resistance exists due to air gap formation at the mold/casting interface during the freezing process. In this study one dimensional Stefan problem with the air-gap resistance in the cylindrical mold is considered and the heat transfer characteristics is numerically examined by using the enthalpy method which is convenient in solving the Stefan problem with mushy zone. The present results agreed very well with those of previous papers. The effects of major parameters such as thermal conductivity, heat transfer coefficient of mold, on the thermal characteristics are investigated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1205-1215
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• 1992

The solidification rate is of special importance in determining the casting structures and properties. The heat transfer characteristics at the interface between the mold and the casting is one of the major factors that control the solidification rate. The thermal resistance exists due to the air-gap formation at the mold/casting interface during the freezing process. In this study two-dimensional Stefan problem with air-gap resistance in the rectangular mold is considered and the heat transfer characteristics is numerically examined by using the enthalpy method. The effects of the major parameters, such as mold geometry, thermal conductivity, heat transfer coefficient, and initial temperature of casting, on the thermal characteristics are investigated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.2
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• pp.67-77
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• 1994

In this study, one-dimensional Stefan problem with air-gap resistance in the rectangular mold is considered and the thermal characteristics are examined by using the enthalpy-based simple implicit finite-difference scheme. The enthalpy and temperature are nondimensionalized to obtain general solutions. The temperature distribution and the locations of solidus and liquidus line are obtained and the effects of major parameters on the thermal characteristics are investigated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.10 no.3
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• pp.260-270
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• 1998

The viscous plane stagnation-flow solidification problem is theoretically investigated. An analytic solution at the beginning of solidification is obtained by expanding the temperature and thickness of solidified layer in powers of time. An exact expression for the steady-state thickness of solidified layer is also obtained. The .fluid flow toward the cold substrate inhibits the solidification process. As Stefan number becomes larger, or Prandtl number becomes smaller, the solidification is more strongly inhibited by the fluid flow. The transient heat flux at the liquid side of solid-liquid interface is increased, as Stefan number or Prandtl number is increased.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.1
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• pp.1-11
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• 2000

This study investigates the problem of phase change from liquid to solid in the inviscid stagnation flow. The solution of dimensionless governing equations is determined by the three dimensionless parameters of (temperature ratio/conductivity ratio), Stefan number, and diffusi-vity ratio. The solution at the initial stage of freezing is obtained by expanding it in powers of time, and the final equilibrium state is determined from the steady-state governing equations. The equilibrium state is dependent on (temperature ratio/conductivity ratio), but is independent of Stefan number and diffusivity ratio. The effect of fluid flow on the pure conduction problem can be clearly seen from the solution of the initial stage and the final equilibrium state, and the characteristics of the solidification process for all the dimensionless parameters are elucidated.