• 한국자기학회지
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• 제13권1호
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• pp.41-46
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• 2003

본 연구에서는 높이와 길이의 비가 1:4인 장방형 케버티에서 바닥을 가열하고 좌우측 및 상부를 냉각할 경우 나타나는 베나드 유동을 다루었다. 자성유체는 미시적인 견지에서 자장의 영향에 의해 내부입자가 회전을 하고, 그 영향이 거시적인 열유동에 미치게 된다. 본 연구에서는 수치해석방법으로 비전도성 자성유체의 지배방정식계에 GSMAC algorithm을 적용하였다. 그 결과 베나드 유동은 외부자장의 방향 및 세기에 따라 제어할 수 있었고, H=-7000에서 임계점이 존재함을 알 수 있었다.

• 한국결정성장학회:학술대회논문집
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• 한국결정성장학회 1997년도 Proceedings of the 12th KACG Technical Meeting and the 4th Korea-Japan EMGS (Electronic Materials Growth Symposium)
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• pp.187-196
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• 1997

Oxygen transfer in silicon melts during crystal growth under vertical magnetic fields is investigated numeriaclly and experimentally. A three-dimensional numerical simulation, including melt convection and oxygen transport, is carried out to understand how oxygen transfers in the melt under magnetic fields. Oxygen concentrations in single silicon crystals grown from the melt under these magnetic fields are experimentally measured by using an infrared absoption technique. The rusults obtained are compared to results from a numerical simualtion. An anomalous increase is observed in the oxygen concentration of the grown crystals under a magnetic field of about 0/03 tesla. The cause of this anomaly is identified as Benard instability, since the temperature at the bottom of the crucible is higher than that at interface. When the temperature at the bottom is decreased, the Benard cell can be removed, and a monotonical decrease in the oxygen concentration in the single crystals can be observed.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 12th Asian Congress of Fluid Mechanics
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• pp.80.3-80.3
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• 2008

• Nuclear Engineering and Technology
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• 제54권9호
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• pp.3540-3550
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• 2022

The supercritical carbon dioxide (S-CO₂) Brayton cycle is an important energy conversion technology for the fourth generation of nuclear energy. Since the printed circuit heat exchanger (PCHE) used in the S-CO₂ Brayton cycle has narrow channels, Rayleigh-Bénard (RB) convection is likely to exist in the tiny channels. However, there are very few studies on RB convection in supercritical fluids. Current research on RB convection mainly focuses on conventional fluids such as water and air that meet the Boussinesq assumption. It is necessary to study non-Boussinesq fluids. PRB convection refers to RB convection that is affected by horizontal incoming flow. In this paper, the computational fluid dynamics simulation method is used to study the PRB convection phenomenon of non-Boussinesq fluid-supercritical carbon dioxide. The result shows that the inlet Reynolds number (Re) of the horizontal incoming flow significantly affects the PRB convection. When the inlet Re remains unchanged, with the increase of Rayleigh number (Ra), the steady-state convective pattern of the fluid layer is shown in order: horizontal flow, local traveling wave, traveling wave convection. If Ra remains unchanged, as the inlet Re increases, three convection patterns of traveling wave convection, local traveling wave, and horizontal flow will appear in sequence. To characterize the relationship between traveling wave convection and horizontal incoming flow, this paper proposes the relationship between critical Reynolds number and relative Rayleigh number (r).

• 대한기계학회논문집
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• 제16권1호
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• pp.132-141
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• 1992

본 연구에서는 실제적으로 베나트 대류의 발생시 유체층의 상하면은 적당한 대류 열전달 계수를 가지고 있게 되는데, 이와 같은 경계 조건을 가진 가변 점성 유 체의 안정성은 연구된 바가 없다. 이에 따라 본 연구를 수행하게 되었으며 유체의 점성이 지수 함수적으로 (.nu.=.nu.o exp(-CT)) 변화할 경우를 관찰하였다. Fig.1은 대 상이 된 유체층을 보인 것으로 하부는 고정되어 있고 상부는 고정되어 있거나 자유 표 면 상태이다. 유체층의 하부는 상부보다 더 뜨겁게 되어 있는데, 이것은 유체층의 상부는 차가운 주위로 열을 빼앗기며 하부는 뜨거운 주위로부터 가열되기 때문이다. 이때 상하부의 냉각 및 가열 경계 조건은 대류경계 조건으로 주어진다. 열팽창 계수 는 양이며 온도의 증가에 따라 점성은 감소한다.이와 같은 온도-점성 관계, 수력학 적 경계조건, 열적 조건등은 프란틀 수가 큰 유체에서 표본적으로 나타나는 것들로서 선형적 안정 이론을 적용하여 옳은 결과를 얻을 수 있다.

• 대한수학회보
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• 제29권1호
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].

• 에너지공학
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• 제24권1호
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• pp.78-87
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• 2015

중대사고시 금속용융물층의 열속 집중 현상(Focusig effect)에 대해 상부와 측면벽의 냉각 조건과 높이를 변화시키면서 실험과 수치해석을 수행하였다. 상사성(Analogy) 원리를 이용해 열전달 실험 대신 물질전달 실험을 수행하였으며 황산-황산구리 수용액의 전기도금계를 물질전달계로 채택하였다. $Ra_H$ 수 $8.49{\times}10^7{\sim}5.43{\times}10^9$ 범위에서 상부와 측면벽의 냉각 조건을 세 가지로, 높이를 네 가지로 변화시키면서 열전달을 측정하였다. 상부만 냉각인 경우의 실험결과를 동일한 조건인 Rayleigh-Benard 자연대류 상관식과 비교한 바 Dropkin과 Somerscales, Globe와 Dropkin의 상관식과 매우 일치하였다. 측면벽만 냉각인 경우, 상부와 측면벽 모두 냉각인 경우, 상부만 냉각인 경우 순으로 열전달이 감소하였고, 냉각 조건을 고정한 상태에서 높이를 감소시킬수록 측면 열전달이 향상되었다.

• 대한기계학회논문집B
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• 제20권6호
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• pp.2046-2056
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• 1996

The constrained melting inside an isothermally heated horizontal cylinder has been repeatedly investigated in many studies only for the moderate Rayleigh numbers. This study extends the range of Rayleigh numbers to systematically investigate the transition during melting processes, especially focusing on the complex multi-cellular flow pattern and thermal instability. The enthalpy-porosity formulation, with appropriate source terms to account for the phase change, is employed. For low Rayleigh numbers, initially developed single-cell base flow keeps the flow stable. For moderate Rayleigh numbers, even small disturbances in balance between thermal buoyance force and viscous force result in branched flow structure. For high Rayleight numbers, Benard type convection is found to develop within a narrow gap between thee wall and the unmelted solid. The marginal Rayleigh number and the corresponding wave number are in excellent agreement with those from linear stability theory.