• Journal of the Korean Magnetics Society
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• v.13 no.1
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• pp.41-46
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• 2003

This study deals with the Benard flow of magnetic fluids in a rectangular cavity. The ratio of height to length of the cavity is 1 : 4 and the bottom of the cavity is assumed to be a heating face while the other sides are to be cooling faces. When magnetic field was equally impressed, considering the internal rotation of the elementary ferromagnetic particle, we found the following result from the numerical analysis of the GSMAC algorithm applied to the equations for the magnetic fluid. Benard flow was controled by the intensity and the direction of magnetic fields, and a critical point was appeared when the magnetic field near H=-7000 was applied.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.06a
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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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• 2008.08a
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• pp.80.3-80.3
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• 2008

• Nuclear Engineering and Technology
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• v.54 no.9
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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).

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.1
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• pp.132-141
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• 1992

The critical condition for onset of Benard convection with variable viscosity .nu.=.nu.$_{0}$exp(-CT) has been obtained using a linear stability theory. The bottom wall is rigid while the upper surface may be either free or rigid. The two boundaries are subject to convective heat transfer. The critical Rayleigh numbers are presented up to maximum viscosity ratio of 3000. It is greater for smaller upper and/or lower surface Biot numbers. Its dependence on the viscosity ratio is complicated. However, a simple sublayer theory is found to be applicable for extremely large viscosity ratio. In such cases, the critical Rayleigh number and the critical wave number are functions of viscosity ratio and lower surface Biot number.r.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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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].

• Journal of Energy Engineering
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• v.24 no.1
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• pp.78-87
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• 2015

Focusing effect of a metallic layer in a severe accident depending on the aspect ratios and cooling conditions of top plate and side wall was investigated. Experiments were carried out for Rayleigh numbers and aspect ratio in the range of $8.49{\times}10^7{\sim}5.43{\times}10^9$, 0.135~0.541 respectively. In order to achieve high Rayleigh numbers, the heat transfer experiments were replaced by mass transfer experiments based on the heat and mass transfer analogy. A sulfuric acid-copper sulfate ($H_2SO4-CuSO_4$) electroplating system was adopted as the mass transfer system. The experimental results agreed well with the Rayleigh-Benard natural convection correlations of Dropkin and Somerscales and Globe and Dropkin. When compared with the standard Rayleigh-Benard problem, the cooling by the side wall is even higher than the top. For a shorter height, the interaction between the heated and cooled plumes increases due to decrease of the height. Thus, the heat transfer increases.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.6
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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.