• Title/Summary/Keyword: Prandtl number

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A Numerical Analysis of Characteristics of Combined Heat Transfer in Laminar Layer Along Cylinderical Periphery by P-N Method (P-N 근사법을 이용한 원관주위 층류 경계층내 조합 열전달 전달 특성 해석)

  • 이종원;이창수
    • Journal of Advanced Marine Engineering and Technology
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    • v.19 no.2
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    • pp.10-19
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    • 1995
  • Heat trnasfer for absorbing and emitting media in laminar layer along the cylinders has been analyzed. Governing equation are transformed to local nonsimilarity equations by the dimensional analysis. The effects of the Stark number, Prandtl number, Optical radius and wall emissivity are mainly investigated. For the formal solution a numerical integration is performed and the results are compared with those obtained by P-1 and P-3 approximation. The results show that boundary layers consist of conduction-convection-radiation layer near the wall and convection-radiation layer far from the wall. As the Stark number of wall emissivity increases the local radiative heat flux is increased. The Pradtl number or curvature variations do not affect the radiative heat flux from the wall, but The Prandtl number or wall emissivity variations affect the conduction heat flux. Consequently the total heat flux from the wall are affected by the Prandtl number or wall emissivity variation.

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Conjugate Natural Convection in Double Enclosed Annuli Between Horizontal Concentric Cylinders (水平 同心圓二重 環狀密閉 空間에서의 Conjugate 自然對流 熱傳達)

  • 손병진;강희영
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.9 no.4
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    • pp.430-439
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    • 1985
  • Conjugate natural convection in double enclosed annuli between horizontal concentric cylinders has been studied by the numerical analysis and experimental measurements. The interface conditions between the liquid and the solid of middle shell are obtained through the correlation factor based on the ratio of solid to fluid thermal conductivities and the Prandtl number. The characteristics of conjugate heat transfer are discussed under various dimensionless parameters such as conductivity ratios, shell thickness, diameter ratios, Prandtl number, and Rayleigh number. It is found that the average equivalent conductivity K over var $_{eq}$ does not depend on the conductivity ratios and shell thickness. The K over bar $_{eq}$ however, depends on the Prandtl number and the Rayleigh number.

Transient Buoyant Flows of a Stratified Fluid in a Vertical Channel

  • Park, Jun-Sang
    • Journal of Mechanical Science and Technology
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    • v.15 no.5
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    • pp.656-664
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    • 2001
  • A theoretical analysis is performed to describe the qualitative behavior of transient buoyant flows in a vertical channel. Consideration is given to the case of a fluid with a pre-existing stratification. The fluid motion is generated by giving impulsive anti-symmetric step-changes in temperature at the vertical left ad right sidewalls. The qualitative character of the flow is shown to be classified in the Rayleigh number (Ra)-Prandtl number ($sigma$) diagram. The transitory approach to the steady state can be monotonic or oscillatory, depending on ($sigma$-1)$^2$$pi$$^4$ 4$sigma$$R_a$. The prominent characteristics of time-dependent flow are discussed for large $R_a$. The profiles of temperature and velocity in the transient phase are depicted, which disclose distinctive time scales of motion. The transient process is shown to be sensitive to the Prandtl number. The detailed evolutions of flow and temperature fields are illustrated for large $R_a$.

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The Coupling of Conduction with Free Convection Flow Along a Vertical Flat Plate in Presence of Heat Generation

  • Taher, M.A.;Lee, Yeon-Won
    • Journal of Advanced Marine Engineering and Technology
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    • v.31 no.7
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    • pp.833-841
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    • 2007
  • The aim of this paper is to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flow adjacent to a vertical flat plate under boundary layer approximation. Using the similarity transformations the governing boundary layer equations for momentum and energy are reduced to a system of partial differential equations and then solved numerically using Finite Difference Method(FDM) known as the Keller-box scheme. Computed solutions to the governing equations are obtained for a wide range of non-dimensional parameters that are present in this problem, namely the coupling parameter P. the Prandtl number Pr and the heat generation parameter Q. The variations of the local heat transfer rate as well as the interface temperature and the friction along the plate and typical velocity and temperature profiles in the boundary layer are shown graphically. Numerical solutions have been consider for the Prandtl number Pr=0.70

Thermo-Flow Analysis of Offset-strip fins according to Prandtl Number (Plandtl 수에 따른 옵셋 스트립핀에서의 열 및 유동 분석)

  • Joo, Youn-Sik;Kim, Min-Soo;Lee, Kwan-Soo
    • Proceedings of the SAREK Conference
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    • 2008.11a
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    • pp.233-238
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    • 2008
  • This paper numerically investigates thermo-flow characteristics of offset strip fins to obtain a correlation between heat transfer and pressure drop. The flow was divided into three regimes, i.e. laminar, transition and turbulent. The predicted j and f values from the SST k-$\omega$ turbulence model agreed with previous correlations with the error less than 20% in transition and turbulent regimes. Heat transfer and pressure drop were predicted by varying Prandtl number from 0.5 to 40. The Prandtl number showed little effects on pressure drop but had great effect on the heat transfer characteristics. An overall correlation to predict j was suggested by incorporating the effect of Pr and a new j correlation was suggested for each Pr.

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Natural Convection in Shallow Cavities

  • Bae, Dae-Seok
    • International Journal of Air-Conditioning and Refrigeration
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    • v.6
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    • pp.158-167
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    • 1998
  • Natural convection heat transfer in a rectangular enclosure is investigated numerically for low aspect ratio(height/width) cavities. Numerical results are obtained for aspect ratios between ${10}^{-2}$ and ${10}^0$, Rayleight numbers from ${10}^3$ to ${10}^7$ and Prandtl numbers from 10$^{-2}$ to 10$^3$. Results are compared with existing analytical and experimental results. A heat transfer correlation is developed to predict the mean Nusselt number as a function of the three governing dimensionless parameters: Rayleigh number, aspect ratio and Prandtl number.

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Numerical Study of Laminar Flow and Heat Transfer in Curved Pipe Flow (곡관에서의 층류 유동 및 열전달에 관한 수치해석 연구)

  • Kang, Changwoo;Yang, Kyung-Soo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.37 no.10
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    • pp.941-951
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    • 2013
  • A three dimensional numerical simulation of laminar flow and heat transfer in fully developed curved pipe flow has been performed to study the effects of Dean number and pipe curvature on the flow and temperature fields under the thermal boundary condition of axially uniform wall heat flux. The Reynolds number under consideration ranges from 100 to 4000, and the Prandtl number is 0.71. The curvature ratios are 0.01, 0.025, 0.05 and 0.1. The axial velocity and temperature profiles and the local Nusselt number obtained from the present study are in good agreement with the previous numerical and experimental results currently available. To show the effects of pipe curvature on the flow and heat transfer, the resistance coefficients and heat transfer coefficients are computed and compared with the results of the previous theoretical and experimental studies. The averaged Nusselt number is correlated with Dean and Prandtl numbers. Furthermore, the critical Reynolds number for transition to turbulent flow is observed to depend upon the curvature ratio.

DESIGN ANALYSIS OF OFFSET STRIP FIN HEAT EXCHANGER

  • Bhowmik, Himangshu;Lee, Kwan-Soo
    • Proceedings of the KSME Conference
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    • 2008.11b
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    • pp.2131-2136
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    • 2008
  • The characteristics of heat transfer and pressure drop in an offset strip fin heat exchanger was studied with a steady-state three dimensional numerical model. Flow Reynolds number $Re_{dh}$ ranged from 10 to 3500 and Prandtl number Pr ranged from 0.7 to 50. The dimensionless performance factors, i.e. 'the pumping power factor F' and 'the heat transfer performance factor J' were analyzed and obtained a relationship between them. Finally, the prediction of F and J factors was generalized for different Prandtl numbers.

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Natural Convection of Low-Prandtl-Number Fluids in a Narrow Horizontal Annulus (좁은 수평 환형공간에서의 낮은 Prandtl 수 유체의 자연 대류)

  • Yoo, Joo-Sik
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.12
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    • pp.1784-1795
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    • 1998
  • Natural convection of low Prandtl number fluids with $Pr{\leq}0.2$ in a narrow horizontal annulus is numerically investigated. For $Pr{\leq}0.2$, hydrodynamic instability induces oscillatory multicellular flows consisting of multiple like-rotating cells. For a fluid with $Pr{\approx}0$, the region in which instability of conduction regime first forms is near the vertical section of annulus, and the multiple cells are distributed uniformly in the lower and upper regions of annulus. As Pr increases, however, the cells are shifted upwards. The like-rotating cells drift downward, as time goes on, and the speed of travel increases with increase of Pr. For a fluid with Pr=0.1, a flow with period-4 solution is observed between chaotic states.

Effect of axial rotation on oscillatory thermocapillary flow in half-zone of high Prandtl number fluid (높은 Prandtl 수 유체에서 축회전이 열모세관 유동의 진동에 미치는 영향)

  • Jeon, Seung-Won;Lee, Kyu-Jung
    • Proceedings of the KSME Conference
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    • 2008.11b
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    • pp.2248-2253
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    • 2008
  • A numerical study on oscillatory thermocapillary flow in half-zone has performed to understand the effect of axial rotation. 2d unsteady code is developed to observe the onset of oscillation. 2cs Silicone oil with Prandtl number of 26.5 is used as a working fluid. The critical temperature difference at onset of oscillation is investigated under the different aspect ratios and rotation modes. It is shown that the onset of oscillation is delayed when aspect ratio reduces and rotating speed increases. The oscillatory flow is strongly reduced under top rotation and co-rotation modes, while it is augmented under bottom rotation and counter-rotation modes. It is thought that interaction between return flow and bottom wall is important to explain the oscillatory flow.

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