• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.11
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• pp.943-950
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• 2014

This paper presents a numerical study conducted for analyzing the effect of the Prandtl number on natural convection in a square enclosure with an inner circular cylinder in various positons. Several Prandtl numbers (Pr = 0.1, 0.7, and 7) and Rayleigh numbers (Ra = $10^3$, $10^4$ and $10^5$) are considered in the numerical study, along with different positions of the inner circular cylinder. The position of the inner circular cylinder is changed in steps of 0.1 in the range of -0.2 to 0.2. The effect of the Prandtl number on natural convection in the enclosure is analyzed on the basis of the thermal and flow fields and the distribution of the Nusselt number. Regardless of the position of the cylinder, when the Rayleigh number is $10^5$, the surface-averaged Nusselt number of the inner cylinder and the enclosure increases as the Prandtl number increases.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.11
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• pp.935-942
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• 2014

A numerical analysis of the effect of the Prandtl number on the natural convection in a cold outer tilted square enclosure with an inner hot circular cylinder is presented. Several Prandtl numbers (Pr=0.1, 0.7, 7) are considered, with different angles($0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$) for the enclosure and Rayleigh numbers ($Ra=10^3$, $10^4$, $10^5$). The effect of the Prandtl number on the natural convection is analyzed using isotherms and streamline and surface-averaged Nusselt numbers. The flow and heat transfer characteristics are found to be dependent on the time for $Ra=10^5$ and Pr=0.1 at angles of $0^{\circ}$ and $45^{\circ}$. However, in the other cases, the flow and heat transfer characteristics are independent of the time.The surfaceaveraged Nusselt number increases with an increase in the Prandtl number. As the Prandtl number increases, the Nusselt number becomes larger regardless of the angle for $Ra=10^5$. In particular, the Nusselt number steeply increases when the angle is $45^{\circ}$ for $Ra=10^5$ and Pr=0.1.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.2
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• pp.345-353
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• 1987

An analysis is performed to study flow and heat transfer characteristics of mixed free and forced convection about a sphere. Nonsimilar boundary layer equations which are valid over the entire regime of mixed convection are derived in terms of the mixed convection parameter, Gr/Re$^{2}$, through a dimensional analysis. The transformed conservation equations are solved by a finite difference method for the whole range of mixed convection regime. Numerical results for fluids having the Prandtl number 0.7 and 7 are presented. As the mixed convection parameter increases, the local friction coefficient and local heat transfer coefficient increases as well. For small Prandtl number, the friction coefficient is larger, while for large Prandtl number, the heat transfer coefficient is larger. Natural convection effect on the forced flow is more sensitive for small Prandtl number fluid. Flow separation migrates rearward as an increase in the mixed convection parameter. For small Prandtl number, the buoyancy effect is relatively small so that the flow separation occurs earlier.

• Journal of computational fluids engineering
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• v.16 no.3
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• pp.29-36
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• 2011

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body at its centered area was studied. Three different Prandtl numbers (0.01, 0.7 and 7) were considered for an effect of the Prandtl number on natural convection. A two-dimensional solution for unsteady natural convection was obtained, using Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10^4$ to $10^6$. It had been experimentally and numerically reported [1,2] 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. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers was presented to show the overall heat transfer characteristics in the system. And also, the isotherms and streamline distributions were presented in detail to compare the physics related to their thermal behavior.

• 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.

• Journal of Mechanical Science and Technology
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• v.19 no.3
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• pp.913-923
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• 2005

The dynamic mixed model (DMM) combined with a box filter of Zang et. al. (1993) has been generalized for passive scalar transport and applied to large eddy simulation of turbulent channel flows with Prandtl number up to 10. Results from a priori test showed that DMM is capable of predicting both subgrid-scale (SGS) scalar flux and dissipation rather accurately for the Prandtl numbers considered. This would suggest that the favorable feature of DMM, originally developed for the velocity field, works equally well for scalar transport problem. The validity of the DMM has also been tested a posteriori. The results of the large eddy simulation showed that DMM is superior to the dynamic Smagorinsky model in the prediction of scalar field and the model performance of DMM depends to a lesser degree on the ratio of test to grid filter widths, unlike in the a priori test.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.21 no.6
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• pp.340-346
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• 2009

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.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.11a
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• pp.29-30
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• 2005

A three-dimensional numerical calculation has been performed to investigate mixed convective vortex flow in rectangular channels(width/height=4) with the upper part cooled and the lower part heated uniformly. In this study, the Prandtl number was 909, the Reynolds number was varied from 0 to $9.6{\times}10^{-2}$ and the Rayleigh number from $10^3$ to $5{\times}10^4$. The governing equations were discretized using the finite volume method. From a parametric study, velocity and temperature distributions were obtained and discussed. It is found that vortex flow of mixed convection in rectangular channels can be classified into three flow patterns which depend on Reynolds and Rayleigh numbers, and the regular vortex structure disappears around Rayleigh number $5{\times}10^4$.