• Proceedings of the KSME Conference
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• 2000.04b
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• pp.282-289
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• 2000

Direct numerical solution for flow and heat transfer for Benard convection with a body is obtained using an accurate and efficient Fourier-Chebyshev collocation and multi-domain method. The flow and temperature fields are obtained fur different Rayleigh numbers and thermal boundary conditions of body. The body has adiabatic and constant temperature conditions. The existence of a body gives different flow and heat transfer fields in the system, compared to pure Benard convection. The flow and temperature fields are also affected by the thermal boundary condition of a body.

• The KSFM Journal of Fluid Machinery
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• v.7 no.4 s.25
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• pp.32-39
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• 2004

This study deals with the Benard Flow of Magnetic Fluids in a rectangular cavity which the ratio between height and width is 1 : 4 and the base side or left side is a heating face while 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 equation of the magnetic fluid. Benard flow is controlled by intensity and direction of magnetic fields, and critical point appears when especially magnetic field with a heating base and side area near H=-7000 and H=-10000 is applied.

• 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.

• Journal of ILASS-Korea
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• v.26 no.2
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• pp.67-72
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• 2021

Rayleigh-Benard-Marangoni (RBM) convection have been artificially made for application of various engineering fields. For a relatively larger circular container, natural convection experiments were carried out to reveal and show the flow characteristics with engine oil (SAE30) using IR camera. IR camera has captured the temperature distribution on the free surface. From these experiments, it was confirmed that it was possible to quantitatively analyze the occurrence characteristics of RBM flow clearly from the thermal images taken with IR camera. As the aspect ratio increased, both the number of internal and external cavities increased. And found that the criteria of RBM flow generation proposed through previous experiments performed for small-sized containers are also very effective with the results on larger circular container.

• 대한공업교육학회지
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• v.30 no.2
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• pp.123-129
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• 2005

A Rayleigh-Benard problem with non-uniform wall temperatures of the form, $T_L=T_1+{\delta}{\Delta}T{\sin}kx$ and $T_U=T_2-{\delta}{\Delta}{\sin (kx)$, is numerically investigated. In the conduction-dominated regime with small a Rayleigh number, a two-tier structure appears with two counter-rotating rolls stacked on the top of each other. The flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximetely square-shape cells. Four multiple flows and dual flows classified by the number of cells are found at k=0.5 and k=1, respectively.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.80.3-80.3
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• 2008

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2744-2749
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• 2008

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder for Rayleigh number of $Ra=10^7$. This study investigates the effect of the inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder ($\delta$) is changed vertically along the center-line of square enclosure. The natural convection bifurcates from unsteady to steady state according to $\delta$. Two critical positions of ${\delta}_{C,L}$ and ${\delta}_{C,U}$ as a lower bound and an upper bound are ${\delta}_{C,L}=0.05$ and ${\delta}_{C,U}=0.18$, respectively. Within the defined bounds, the thermal and flow fields are steady state. When the inner cylinder locates at ${\delta}{\geq}{\delta}_{C,U}$, the space between the upper surface of inner cylinder and the top surface of the enclosure forms a relatively shallow layer where the natural convection characterized as the pure Rayleigh-Benard convection forms alternately the upwelling and downwelling plums, as a result that a series of cells known as Benard cells is derived.

• 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.

• 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).

• 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].