• Journal of Energy Engineering
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• v.7 no.2
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• pp.187-193
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• 1998

The turbulent heat transfer to low Prandtl number fluid flow through rod bundles is analyzed using k-$\varepsilon$ two-equation model. For the prediction of the turbulent flow field, an anisotropic eddy viscosity model is used. In the analysis of the temperature field, the effects of various parameters such as geometry, Reynolds and Prandtl numbers are considered. The calculation in made for Prandtl numbers from 0.001 to 0.1 in order to analyze the heat transfer to low Prandtl number fluid such as liquid metals. The numerical results show that for small P/D (Pitch/Diameter) geometries low Prandtl number makes severe changes of the rod surface temperature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.541-550
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• 1988

Natural convection in a square enclosure was investigated numerically for low prandtl number fluids using Finite Element Method. In case of Ra=10$^{4}$, 10$^{5}$ and 10$^{6}$ the temperature gradient decreases gradually at the lower end of the hot wall(or at the upper end of the cold wall) as prandtl number decreases in the range of 0.01 .leq. Pr .leq. 10. Maximum heat transfer occurs at a somewhat higher point from the lower end of hot wall(or at somewhat lower point from the upper end of the cold wall) and it draws near to the lower end of the hot wall(or draws near to the upper end of the cold wall) with increasing prandtl number. The flow in the enclosure appears as an Unicell Pattern for Ra .leq. 10$^{4}$ and secondarily flows(or tertiary flows) appears in the core region for Ra .geq. 10$^{5}$ . The line joining the center of secondary cells skewes in a clockwise direction as the Prandtl number decreases.

• Nuclear Engineering and Technology
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• v.44 no.3
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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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.4
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• pp.325-336
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• 1994

A numerical simulation of velocity and temperature fields and Nusselt number distributions is performed by using the algebraic stress model (ASM) for the velocity profiles and low Reynolds number ${\kappa}-{\varepsilon}$ model and the algebraic heat flux model(AHFM) for turbulent heat transfer in a $180^{\circ}$ bend with a constant wall heat flux. In the low Reynolds number ${\kappa}-{\varepsilon}$ model, turbulent Prandtl number is modified by considering the streamline curvature effect and the non-equilibrium effect between turbulent kinetic energy production and dissipation rate. Every heat flux term presented in the transport equation of turbulent heat flux is reduced to algebraic expressions in a way similar to algebraic stress model. Also. in the wall region, low Reynods number algebraic heat flux model(AHFM) is applied.

• 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.5 no.4
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• pp.284-292
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• 1981

The flow of fluid with low prandtl number in the entrance region of a circular pipe has been considered, where the wall temperature is maintained to be constant. A finite difference method is used for the integral form of the governing equations in order that they satisfy the conservative properties of the numerical solutions. It is confirmed that the hydrodynamic entrance length and be divided into growing boundary layer region and fully viscous region, which is compared with existing results obtained by using boundary layer approximations. By assuning the developing velocity profile in the entrance region, the thermal entrance length is estimated and the local Nusselt number is obtained at various locations along the axial dirction.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.06a
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• pp.210-215
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• 2005

A three-dimensional numerical simulation is performed to investigate on a low Reynolds number mixed convection in a horizontal rectangular channel with the upper part cooled and the lower part heated uniformly. The three-dimensional governing equations are solved using a finite volume method. For convective term, the central differencing scheme is used and for the pressure correction, the PISO algorithm is used. Solutions are obtained for A=4, Pr=0.72, 10, 909, the Reynolds number ranging from $2.1{\times}10^{-2}$ to $1.2{\times}10^{-1}$, the Rayleigh number is $3.5{\times}10^4$. It is found that vortex roll structures of mixed convection in horizontal rectangular channel can be classified into three roll structures which affected by Prandtl number and Reynolds number.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.6
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• pp.750-756
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• 1985

Experimental investigation was carried out to study the natural convection of water and silicon oil due to end temperature differences in a horizontally insulated rectangular enclosure of aspect ratio 0.1 with a special attention on the core configuration in the laminar boundary-layer flow regime. Rayleigh number ranges covered herein are Ra=4.40 * 10$^{6}$ -9.64 * 10$^{7}$ for water and Ra=1.69*10$^{5}$ -3.80*10$^{6}$ for silicon oil, respectively. In the case of water, for Ra.geq.2.21 * 10$^{7}$ there appeared distinct horizontal thermal layers adjacent to the horizontal boundaries in the core and the temperature distribution outside the horizontal thermal layers, i.e., in the mid-core region, is vertically stratified. The core flow pattern was shown to be nonparallel with a weak back flow in the mid-core for Ra.geq.3.63 *10$^{7}$ . In the case of silicon oil, distinct horizontal thermal layers appeared along the core horizontal boundaries for Ra.geq.1.27 * 10$^{6}$ with a stratified temperature distribution in the mid-core, but the core flow pattern in this case was shown to be parallel. In addition, secondary flow appeared near the hot wall for Ra.geq.3.80 * 10$^{6}$ . Nusselt number, Nu, was found to be proportional to R $a^{0.3}$ for water and R $a^{0.28}$ for silicon oil in the boundary-layer flow regime. There also in an indication from the comparison with other results that Nu is independent of aspect ratio for water in the boundary-layer flow regime in low aspect ratio enclosures.res.

• Journal of Power System Engineering
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• v.13 no.5
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• pp.11-17
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• 2009

A numerical study of unsteady mixed convection in a cavity with high viscous fluid is presented. Finite volume method was employed for the discretization and PISO algorithm was used for calculating pressure term. The parameters governing the problem are the Rayleigh number ($10^3\;{\leq}\;Ra\;{\leq}\;10^5$), the Reynolds number (0 < Re $\leq$ 1), and the aspect ratio (0.5 $\leq$ AR $\leq$ 2). The fluid used is silicon oil, a high prandtl number fluid, Pr = 909.1. The results show velocity vectors and temperature distributions. It is found that the periodic flows in a cavity are observed at very low Reynolds numbers, and the period of periodic flow decreases with increasing Reynolds and Rayleigh numbers, and increases with increasing aspect ratio. Also, the Reynolds number range of periodic flow increases with increasing Rayleigh numbers and aspect ratio.