• 대한공업교육학회지
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• v.33 no.2
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• pp.300-311
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• 2008

This study investigates the natural convection of air(Pr=0.7) between two walls having a small- wave- number sinusoidal temperature distributions with a phase difference. The wave number and the phase difference of wall temperatures are k=0.5 and ㄱ/2, respectively. In the conduction-dominated regime at small Rayleigh number, two slightly inclined cells are formed over one wave length. At higher Rayleigh number, however, multicellular convection occurs in thermally unstable region. A spatial symmetry is intermittently broken in the transient period at the Rayleigh number near the critical value. The steady-state flows always satisfy the spatial symmetry. A steep increase of Nusselt number occurs near the Rayleigh number at which transition of flow pattern occurs.

• 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.

• Journal of computational fluids engineering
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• v.9 no.4
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• pp.1-6
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• 2004

This study investigates the transition of flows in a natural convection problem with periodic wall temperatures of the form, T/sub L/=T₁＋δ Tsinκχ and T/sub L/=T₂＋δ Tsinκχ .The fluid considered is air with P/sub γ/=0.7. In the conduction-dominated regime with a small Rayleigh number, two large cells are formed over one wave length, for all wave numbers. When k≤1.8, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The flow patterns are classified by the number of eddies over one wave length, and several kinds of transition phenomena, such as 2→3→4, 4→3→2, and 2→4 eddy flow, occur with increase( or decrease) of the Rayleigh number. Dual solutions are found above a critical Rayleigh number, and an anomalous bifurcation is observed.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.4
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• pp.285-294
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• 1993

An oscillatory motion of natural convection in a two-dimensional square enclosure fitted with a horizontal partition is investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was positioned perpendicularly at the mid-height of one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were carried out with the variations of the partition length and Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height with water(Pr=4.95). As the results, an oscillatory motion of natural convection has perfectly shown the periodicity with the decrease of Rayleigh number, and the stability was reduced to a chaotic state with the increase of Rayleigh number. The period of oscillation gets shorten with the decrease of the partition length and the increase of Rayleigh number. The frequency of oscillation obtained by the variations of stream function is more similar to the experimental results than that of the average Nusselt number. The stability of oscillation grows worse with the increase of Rayleigh number. The transition Rayleigh number for the chaos is gradually decreased with the increase of the partition length.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.12 no.4
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• pp.234-239
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• 1983

The natural free convection in a vertical tube with uniform heat flux and temperature has been studied by the theoretical analysis is of governing equations and experimental measurements. In order to determine the Characteristics of Convective heat transfer in the tube, a dimensionless Rayleigh number is introduced. The relationship between Nusselt and Rayleigh number is compared with the numerical analysis of finite difference method and experiment. Nusselt number obtained from the experimental measurements are in a good agreement with the calculated values, and the relationship equations between Nusselt and Rayleigh number are obtained.

• Advances in aircraft and spacecraft science
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• v.5 no.4
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• pp.411-430
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• 2018

This computational study examines the augmentation of classic 2-D Rayleigh-$B{\acute{e}}nard$ convection by the addition of periodically-spaced transverse fins. The fins are attached to the heated base of the cavity and serve to partition the cavity into 'units' with different aspect ratios. The respective impacts upon heat transfer of the fin configuration parameters - including spacing, height, thickness and thermal conductivity - are systematically examined through numerical simulations for a range of laminar Rayleigh numbers (0 < Ra < $2{\times}10^5$) and reported in terms of an average Nusselt number. The selection of the low Rayleigh number regime is linked to likely scenarios within aerospace applications (e.g. avionics cooling) where the cavity length scale and/or gravitational acceleration is small. The net heat transfer augmentation is found to result from a combination of competing fin effects, most of which are hydrodynamic in nature. Heat transfer enhancement of up to $1.2{\times}$ that for a Rayleigh-$B{\acute{e}}nard$ cavity without fins was found to occur under favorable fin configurations. Such configurations are generally characterized by short, thin fins with half-spacings somewhat less than the convection cell diameter from classic Rayleigh-$B{\acute{e}}nard$ theory. In contrast, for unfavorable configurations, it is found that the introduction of fins can result in a significant reduction in the heat transfer performance.

• Journal of computational fluids engineering
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• v.21 no.3
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1440-1448
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• 2004

Multiple solutions in natural convection of air (Pr=0.7) between two horizontal walls with mean temperature difference and the same periodic nob-uniformities are investigated. An analytical solution is found for small Rayleigh number, and the general solution is investigated by using a numerical method. In the conduction-dominated regime, two upright cells are formed between two walls over one wave length. When the wave number is small, 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 approximately square-shape cells. And several kinds of multiple flows classified by the number of cells are found.

• 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).

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.3
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• pp.145-152
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• 2001

Low Rayleigh number thermal convection in a fluid layer confined between two-infinite horizontal walls kept at spatially sinusoidal temperature distributions, T_L=T_m+\Delta T\sin \kappax,\;T_U=T_m+\Delta T\sin(\kappax-\beta)$, is theoretically investigated by a regular perturbation expansion method. For small wave numbers, an upright cell is formed between the two walls at $\beta$=0. The cell is tilted, as the phase difference increases, and a flow with tow counter-rotating eddies occurs at $\beta=\pi$. when the wave number is large, isolated eddies are formed near the lower and upper walls, for all the phase differences. There exists a wave number at which maximum heat transfer rate at the walls occurs, at each of the phase differences. And the wave number increases with increase of the phase difference. for a fixed wave number, the heat transfer rate decrease with increase of the phase difference.