• Nuclear Engineering and Technology
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• 제44권3호
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• pp.283-296
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• 2012

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body in the center is studied. Three different Prandtl numbers (0.01, 0.7 and 7) are considered for the investigation of the effect of the Prandtl number on natural convection. Adiabatic boundary conditions are employed for the side walls. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10_3$ to $10_6$. It had been experimentally reported that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. It was found that when Ra=$10_6$, only the case for intermediate Pr (=0.7) reached a non-changing steady state and the low and high Pr number cases (Pr=0.01 and 7) showed a periodically oscillatory fashion hydrodynamically and thermally. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers are presented to show the overall heat transfer characteristics in the system. Further, the isotherms and streamline distributions are presented in detail to compare the physics related to their thermal behavior.

• 대한기계학회논문집
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• 제19권7호
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• pp.1731-1740
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• 1995

Experimental investigations have been made to study the double-diffusive nature of convection of an initially stratified salt-water solution due to heating from below in a rotating cylindrical cavity. The objective is to examine the flow phenomena and the heat transfer characteristics according to the changes in temperature gradient, concentration gradient and rotating velocity of cavity. Thermal and solutal boundary conditions at side wall are adiabatic and impermeable, respectively. The top and bottom plate are maintained each at constant temperature and concentration. The cavity is put into a state of solid body rotation. Like the stationary case, the types of initially-formed flow pattern are classified into three regimes depending on the effective Rayleigh number and Taylor number; stagnant flow regime, single mixed-layer flow regime and successively formed multi-mixed layer flow regime. At the same effective Rayleigh number, the number of initially-formed mixed layer and its growth rate decrease as the effect of rotation increases. The temperature and concentration profiles are both uniform in each layer due to convective mixing in the layered-flow regime, but look both liner in stagnant flow regime and single mixed-layer flow regime. At the interface between adjacent layers, the temperature changes smoothly but the concentration changes rapidly.

• 설비공학논문집
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• 제16권11호
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• pp.999-1005
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• 2004

Thermal convection between two horizontal walls kept at small amplitude nonuniform temperatures of the form, $T_L=T_1+a{\Delta}T$ sin kx and $T_U=T_2+b{\Delta}T\;sin(kx-{\beta})$ with a, $b{\ll}1$, is numerically investigated. When the Rayleigh number is small, an upright cell is formed between two walls at ${\beta}=0$; the cell is tilted at ${\beta}={\pi}/2$, and a flow with two-tier-structure cells occurs at ${\beta}={\pi}$. As the Rayleigh number is increased, Nusselt number increases smoothly for ${\beta}=0\;and\;{\pi}/2$, but increases rather steeply for ${\beta}={\pi}$ near the critical Rayleigh number ($Ra_c=1708$). When the wave number is small (k=0.5), multicellular convection occurs over one wave length, for all phase differences, and multiple solutions are found.

• 태양에너지
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• 제18권2호
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• pp.123-135
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• 1998

자연대류에서 정사각형 밀폐공간의 중앙에 고립된 전도성 장애물이 들어 있을 때 열전도도의 효과를 수치해석적으로 연구하였다. Pr=0.17, $Ra=1.0{\times}10^4,\;1.0{\times}10^5,\;1.0{\times}10^6$, 유체와 전도체의 열전도율비인 $K^*$=1.0, 6.6, 34.0 그리고 전도성 장애물의 비 ${\zeta}$=0.5,1.0,2.0에서 수치연구를 수행하였다. 그 결과들은 유선, 등온선 그리고 Nusselt수로 나타내었다. Ra and $K^*$ 값이 일정한 상태에서 평균 Nusselt수가 증가함에 따라 ${\zeta}$ 가 증가하였다. ${\zeta}=1.0$(장애물의 형상비)일 경우 Rayleigh수에 관계없이 $K^*$(장애물의 열전도율비)가 증가할수록 평균 Nusselt수는 감소한다. 장애물의 크기와 열전도율비가 동일할 때 대류열전달 효과는 ${\zeta}=0.5$인 경우보다 ${\zeta}=2.0$일 때 더 향상되었다.

• 한국가시화정보학회:학술대회논문집
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• 한국가시화정보학회 2005년도 추계학술대회 논문집
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• pp.117-120
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• 2005

This study of thermal convection uses the following geometry: a horizontal layer of fluid heated from below of solid lid at bottom and cooled from above. A variety range of thermal conductivity ratio, $\kappa$ is considered to investigate the interface temperature, $\theta_{i}$ between solid and fluid region. Periodic boundary conditions are employed in the horizontal direction to allow for lateral freedom for the convection cells. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral multi-domain methodology, for different effective Rayleigh numbers, $Ra_{eff}$ varying over the range of $10^{4}\;to\;10^{7}$ in which the effective Rayleigh number is defined as $Ra{\times}<\overline{T}_{i}>$.

• 대한기계학회논문집B
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• 제38권11호
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• pp.943-950
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• 2014

본 연구는 다양한 위치의 원형 실린더가 존재하는 사각 밀폐계에서 Prandtl 수 변화에 따른 밀폐계 내부의 자연대류 현상에 대한 수치해석을 수행하였다. Rayleigh 수가 $10^3$, $10^4$, $10^5$ 그리고 다양한 위치의 내부 원형 실린더에 대해서 Prandtl 수를 0.1, 0.7, 7 로 변화시키며 Prandtl 수의 영향을 분석하였다. 내부 원형 실린더의 위치는 -0.2 에서 0.2 까지 0.1 간격으로 변화시켰다. Prandtl 수의 변화에 따른 밀폐계 내부의 자연대류 현상은 밀폐계 내부의 온도장과 유동장 및 표면 평균 Nusselt 수의 분포를 바탕으로 분석하였다. Rayleigh 수가 $10^5$ 일 때 내부 실린더의 위치에 상관없이 Prandtl 수가 증가할수록 평균 Nusselt 수는 증가하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.83-88
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• 2006

Natural convection flows in a cubical air-filled cavity that has one pair of opposing faces isothermal at different temperatures, $T_h\;and\;T_c$ respectively, the remaining four faces having a linear variation from $T_c\;to\;T_h$ are numerically simulated by a solution code(PowerCFD) using unstructured cell-centered method. An extension to a previously published work, special attention of this work is paid to three-dimensional flow and thermal characteristics in nature convection according to new orientation at Ra= $1{\times}105$. Comparisons of the average Nusselt number at the cold face are made with benchmark solutions and experimental results found in the literature. It is demonstrated that the average Nusselt number on the cold face has a maximum value around the diamond-type inclination angle of $43.2^{\circ}\;at\;Ra=1{\times}105$. We also report the effect of new orientation on the type of flow and temperature structure in a cubical-cavity.

• 설비공학논문집
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• 제1권4호
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• pp.305-312
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• 1989

Laminal natural convection heat transfer in the annulus between isothermal horizontal non-circular cylinders is studied by solving the Navier-Stokes and energy equation using an elliptic numerical procedure. Results are obtained to determine the effects of the diameter ratio($D_o/D_i$) and Rayleigh number on heat transfer. The diameter ratio is varied from 1.5 to 13.0 at Pr=0.7, H/L=1.5 and $10^3{\leqslant}Ra_L{\leqslant}4{\times}10^4$. It is found that the diameter ratio causes a more significant on the local heat transfer coefficient of lower semi-circular cylinder and plate than upper semi-circular cylinder. The mean Nusselt number increases as the diameter ratio and Rayleigh number increase, and is higher than that of the circular annulus with a same wetted perimeter.

• 대한기계학회논문집B
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• 제21권12호
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• pp.1595-1607
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• 1997

The natural convection of a horizontal layer heated from below in a three-dimensional rectangular enclosure was dealt with both numerically and experimentally. The aspect ratios are 1:2:3.5 and Boussinesq fluid is water with the Prandtl number of 5.0. This experimental study showed how to measure the variation of temperature field in a 3-D rectangular enclosure with small aspect ratios by using TLC(Thermochromic Liquid Crystal) and color capturing technique. The experimental temperature field had periodic characteristics of 75 sec at Ra=2.37*10$^{5}$ . But the numerical convection flow had periodic characteristics of 79 sec at the same Rayleigh number. In three dimensional computation it was found that the convection roll structure bifurcated from four rolls to two rolls as the Rayleigh number is increased.

• 전기화학회지
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• 제2권2호
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• pp.98-105
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• 1999

본 연구에서는 전기장에 의하여 유발되는 자연대류의 영향을 줄이기 위하여 수평 다공성 유체층에 열적 성충화를 유지하여 부력과 유체층의 안정화 효과를 체계적으로 조사하였다. 이를 위하여 수평 다공성 유체층에서 이중확산대류에 의한 물질전달 상관식을 이론적으로 유도하고, 전기화학 실험을 통하여 이론에 의한 모델을 보완하였다. 물질전달 상관식은 다공성 매질층에 대한 유동 방정식으로 Forchheimer모델을 사용하고 미세 난류 모델을 적용하여, 용질 및 열 Darcy-Rayleigh수와 Lewis 수로 유도하였다. 실험에서는 다공성매질에 포화된 황산구리황산용액내의 구리이온을 전기 화학적 방법을 통하여 확산 또는 자연대류에 의한 물질전달 실험을 수행하였다. 이론 및 실험적 해석 결과를 종합하면 다공성 매질 내에서 구리이온의 이중확산대류에 의한 물질전달 상관식은 다음과 같다. $$Sh=\frac{0.03054(Rs_D-LeRa_D)^{1/2}}{1-3.8788(Rs_D-LeRa_D)^{-1/10}}$$ 본 연구의 결과는 실험치와 잘 부합되었으며, 모델식의 원형은 열 및 물질전달계에서 자연대류의 영향을 효과적으로 제어할 수 있는 방안으로 활용될 수 있을 것이다.