• Title/Summary/Keyword: Rayleigh Number(Ra)

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Natural Convection Heat Transfer from a Horizontal Annulus with Spacers (격판을 가진 수평환상공간에서의 자연대류 열전달)

  • 이범철;정한식;권순석
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.1
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    • pp.153-160
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    • 1989
  • A numerical and experimental study has been performed on natural convection heat transfer from a horizontal annulus with spacers. The mode of heat transfer in the annulus is changed from conduction to convection at Ra = 10$^{3}$. By increasing wall conductivity, mean Nusselt number is apparently increased at $K_{w}$/K$_{f}$ .leg. 48, but at /K$_{w}$/K$_{f}$ > 48, slightly increased for no spacers, and decreased for vertical spacers and horizontal spacers. The mean Nusselt number can be represented in an exponential function of Grashof number at all conditions. The characterics of natural convection heat transfer show similiarity for no spacers and vertical spacers but show difference for horizontal spacers. The presence of the horizontal spacers increased the convective heat transfer by an average 6 percent over that for the no forced cooling to outer cylinder. The maximum local Nusselt number appears at .theta. = 150.deg. in a conducting tube and .theta. = 30.deg. in an outer cylinder for vertical spacers, and appears at .theta. = 180.deg. in a conducting tube and .theta. = 0.deg. in an outer cylinder for horizontal spacers.spacers.

Natural Convection from a Vertical Flat Plate with Horizontal Rectangular Fins (수직평판(垂直平板)에 부착(附着)된 수평(水平)핀에서의 자연대류(自然對流))

  • Kim, S.J.;Lee, J.C.;Seo, L.S.;Kwon, S.S.
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.17 no.4
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    • pp.448-455
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    • 1988
  • A study has been conducted experimentally on natural convection heat transfer characteristics of a vertical flat plate with horizontal rectangular fins in air. The effects of fin heights and Rayleigh numbers are mainly investigated. The experimental results are as follows; 1. The mean fin, plate and total Nusselt numbers decrease as dimensionless fin heights H/S increase at $0.50{\leq}H/S{\leq}2.00$. 2. The mean fin surface Nusselt number in case of H/S = 0.50 and $Ra_c=4.33{\times}10^3$ shows its maximum at $X_1$, surface where there is no interference with other fins. 3. Owing to the interference of fins the mean plate Nusselt numbers at H/S=0.50 and 2.00 for $Ra_S=6.57{\times}10^3$ are 35% and 80% respectively less than the mean fin Nusselt numbers. 4. The mean fin, plate and total Nusselt numbers of horizontal rectangular fins show higher values at short fins, but lower values at long fins than those of upward vertical fins.

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Unsteady Free Convection Flow in Horizontal Channels with Arbitrary Wall Temperatures (임의의 벽면온도에 따른 수평채널에서의 비정상 자연대류운동)

  • Im, Goeng
    • The Journal of Engineering Research
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    • v.1 no.1
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    • pp.23-30
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    • 1997
  • Energy transfer by free convection arises in many engineering applications, such as a hot steam radiator for heating a room, refrigeration coils, electric transformers, heating elements and electronic equipments. Generally unsteady natural convection flow in a horizontal channel with arbitrary wall temperatures and the mathematical and physical basis of convection transport has been considered in general. A physically meaningful exact solution of the problem has been obtained in a closed form by the application of the standard finite sine transform technique. Influences of the governing parameters, the Prandtl number and the Rayleigh number, to bring the flow and heat transfer to final steady states have been discussed separately. For constant values of the arbitray wall temperatures and of the function, determining the average axial velocity, the final steady state is approached in different times respectively for the cases when the Prandtl number Pr>1 and Pr<1. It is also seen that the function, representing the axial temperature gradient, is influenced by none of the governing parameters : but the steady state flow is influenced only by the Rayleigh number. There are, of course, many applications. Free convection strongly influences heat transfer from pipes and transmission lines, as well as from various electronic devices. It is also relevant to the environmental sciences, where it is responsible for oceanic and atmospheric motions, as well as related heat transfer processes.

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Free Convection due to Vertical Isothermal Wires Immersed in Water near its Density Extremum (최대밀도점 부근의 물 속에 잠겨있는 수직 등온 강선에 의한 자연대류)

  • Eom, Y.K.;Riu, K.J.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.8 no.3
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    • pp.338-350
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    • 1996
  • A numerical analysis is carried out to study the two-dimensional steady state natural convection from vertical wires immersed in cold pure water. The surface of the wire is $0^{\circ}C$ unifrom temperature. Results of the analysis are presented for free stream temperature from $0^{\circ}C$ to $25^{\circ}C$ and the aspect ratio N from $5.26{\times}10^{-3}$ to $1.0{\times}10^{-3}$. The effects of the density extremum and aspect ratio on the flow pattern and the heat transfer characteristics are discussed As the aspect ratio N becomes larger, in the range of $1.0^{\circ}C{\leq}T_{\infty}{\leq}4.4^{\circ}C$ and $6{^{\circ}C}{\leq}T_{\infty}{\leq}17^{\circ}C$, the effect of Pr number on the heat transfer is shown to be more significant than the aspect ratio. Investigating into the effect of the density extremum on the heat transfer from wires, the new heat transfer correlations are suggested with the relation of average Nu mumber vs. modified Ra number. Here, the coefficient values C of correlations are presented as the function of density extremum parameter $R^*$. The effects of the density extremum parameter are also discussed.

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Numerical Study on Natural Convectionin a Doubly-Inclined Cubical-Cavity (이중으로 경사진 3차원 캐비티내 자연대류 열전달현상에 관한 수치해석적 연구)

  • Myong, Hyon-Kook
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.31 no.12
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    • pp.1002-1008
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    • 2007
  • Natural convection flows in a doubly-inclined cubical air-filled cavity are numerically simulated by a solution code(PowerCFD) using unstructured cell-centered method. For a physical realizability, the cavity has one pair of opposing isothermal faces at different temperatures, $T_h\;and\;T_c$, respectively, the remaining four faces having a linear variation from $T_c\;to\;T_h$. The paper redefines a new doubly-inclined orientation for the cubical-cavity benchmark problem. Special attention is paid to three-dimensional thermal characteristics in natural convection according to the new orientation at $Ra=4\times10^4$. Comparisons of the average Nusselt number at the cold face are made with benchmark solutions and experimental results found in the literature. It is found that the average Nusselt number at the cold face has a maximum value at the doubly-inclined angle ranging from $40^{\circ}\;to\; 45^{\circ}$ We also report the effect of new orientation on the type of temperature structure in a doubly-inclined cubical-cavity.

Thermal Instability of Natural Convection in a Glass Melting Furnace (유리 용융로에서 자연대류의 열적 불안정성)

  • Lim, Kwang-Ok;Lee, Kwan-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.12
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    • pp.1774-1783
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    • 1998
  • The transition from steady laminar to chaotic convection in a glass melting furnace specified by upper surface temperature distribution has been studied by the direct numerical analysis of the two and three-dimensional time dependent Navier-Stokes equations. The thermal instability of convection roll may take place when modified Rayleigh number($Ra_m$) is larger than $9.71{\times}10^4$. It is shown that the basic flows in a glass melting furnace are steady laminar, unsteady periodic, quasi-periodic or chaotic flow. The dimensionless time scale of unsteady period is about the viscous diffusion time, ${\tau}_d=H^2/{\nu}_0$. Through primary and secondary instability analyses the fundamental unsteady feature in a glass melting furnace is well defined as the unsteady periodic or weak chaotic flow.

Natural Convection Heat Transfer of an Inclined Helical Coil in a Duct (기울어진 덕트 내 헬리컬 코일의 자연대류 열전달)

  • Park, Joo-Hyun;Chung, Bum-Jin
    • Journal of Energy Engineering
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    • v.23 no.2
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    • pp.13-20
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    • 2014
  • The natural convection heat transfers of a helical coil in a duct were measured experimentally varying the inclination. To achieve high Rayleigh number, mass transfer experiments instead of heat transfer experiments were performed based upon the analogy. The $Ra_D$ was fixed to $4.55{\times}10^6$. The turn numbers were 1~10. the pitch to diameter ratio were 1.3~5, and the inclination of the helical coil $0^{\circ}{\sim}90^{\circ}$. The measured $Nu_D$ for a single turn of the helical coil was very close to that from McAdams heat transfer correlation for a horizontal cylinder. The heat transfers of the helical coil were varied by the pith, number of turns, and duct height in a complex manner showing the velocity, chimney, and pre-heating effects. The results of the study contributes to the phenomenological analyses of the natural convection heat transfer of a compact heat exchanger.

The Thermocapillary Effect on Pure Conduction Mechanism in a Closed Square Cavity (수평 사각밀폐공간내의 전도열전달 기구에서 열모세관효과)

  • Yu, Jae-Bong;An, Do-Won;Yoo, Joo-Sik;Eom, Yong-Kyoon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.11 s.242
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    • pp.1209-1219
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    • 2005
  • In a closed square cavity filled with a liquid, a cooling horizontal upper wall and a heating lower wall, the flow isn't generated under the ground-based condition when Rayleigh number is lower than 1700. In this mechanism, Ra=1534, Temperature and velocity fields near an air-bubble in silicon-oil under a cooled upper wall were investigated. Temperature and velocity fields is visualized using the thermo-sensitive liquid-crystal and light sheet visualization technique. The quantitative analysis fer the temperature and the flow fields were carried out by applying the image processing technique to the original data. The symmetry shape of two vortexes near an air bubble was observed. As the bubble size increased, the size of vortex and the magnitude of velocity increased. In spite of elapsed time, a pair of vortexes was the unique and steady-state flow in a square cavity and wasn't induced to the other flow in the surround region.

Conjugate Heat Transfer in Cylindrical Annulus for an Insulated Tube (단열관을 위한 원통 환상공간 내에서의 복합 열전달)

  • Kang, B.H.;Yang, S.H.;Kwon, S.S.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.7 no.4
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    • pp.633-641
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    • 1995
  • The effect of the gap width on conjugate heat transfer in the cylindrical annulus for an insulated tube has been studied numerically by the finite difference method. The parameters considered here are the Rayleigh number, Ra, the dimensionless insulated wall thickness, $W/D_i$ and the dimensionless gap width, S/W. As S/W increases, the mean wall temperature increases at the inside wall of annulus and decreases at the outside walls of annulus and the insulated tube at $S/W{\leq}0.5$, and then slightly increases at $Re=10^4$, $W/D_i=1.47$. The heat transfer rate decreases at $S/W{\leq}0.5$ and then increases apparently as S/W increases at $Re=10^4$, W/Df=1.47. Therefore, it is considered that $$S/W{\sim_=}0.5$$ is the optimum gap width for the effect of insulation at $Re=10^4$, $W/D_f=1.47$.

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Experimental Study on Effect of Inclination Angle on Natural Convection from Cylindrical Heatsinks with Plate Fins (평판-휜을 갖는 기울어진 원통형 히트 싱크의 자연 대류에 경사각이 미치는 영향에 대한 실험적 연구)

  • Park, Kuen Tae;Kim, Hyun Jung;Yoo, Jaisuk;Lee, Moon Gu;Kim, Dong-Kwon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.39 no.4
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    • pp.343-350
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    • 2015
  • The natural convection heatsink is the most commonly used cooling device, especially for high-power LED lights, because of its reliability and low long-term cost. High power LED lights are generally used in an inclined configuration for street lamps and security lamps. However, it was difficult to estimate the thermal performance of an inclined heatsink, because the results from previous studies are not applicable to the inclined configuration. In this study, we measured the thermal performance of an inclined cylindrical heatsink with plate fins. Various fin numbers, fin heights, base temperatures, and inclination angles ($30^{\circ}$ and $60^{\circ}$) were examined. Based on the experimental results, the Nusselt number correlation is presented. This correlation is applicable when the Rayleigh number, ratio of the fin height to cylinder diameter, and fin number are in the ranges 100,000-600,000, 1/6-1/2, and 9-72, respectively.