• Solar Energy
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• v.7 no.1
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• pp.53-60
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• 1987

Natural convection in the annulus between concentric inclined cylinders has been studied by the numerical analysis. Governing equations are numerically solved by means of successive over-relaxation methods for a range in orientation from horizontal to vertical. It is found that flow patterns can also be observed the co-axial double spiral. As the angle of inclination is increased, the center of the eddy is shifted into the lower part of annulus and flow structure is apparently changed. In the present study, the maximum local Nusselt numbers for the inner and outer walls at the vertical cylinder increase more than those at the horizontal cylinder by 71%, 42% respectively. Consequently the effect of inclination on the heat transfer is considerably large.

• Solar Energy
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• v.8 no.1
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• pp.33-40
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• 1988

The characteristics of thermal instabilities of natural convection in a horizontal fluid layer bounded below by a rigid plate and above by an interface with a passive gas is presented. The critical Grashof number decreases as the surface tension gradient effect (Marangoni effect) at the interface increases and the flow remains unstable for a critical Marangoni number depending on Prandtl numbers. These results are in substantial agreement with those of Smith and Davis.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.65.4-65.4
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• 2008

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.1-2
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• 2007

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.252-263
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• 1997

Steady-state two-dimensional natural convective heat transfer in horizontal cylindrical annuli was studied by solving the governing equations based on the primitive variables. Emphasis was put on the occurrence of the multiple solutions at a given set of parameter values, and on the determination of the bifurcation points at which those multiple solutions begin to branch out. The multicellular flow pattern from the results of melting process in an isothermally heated horizontal cylinder for high Rayleigh numbers, was used as initial guesses for the field variables. This was succeeded in new bifurcation point to tetracellular solutions for an identical set of parameter variables of previous works. The close examination of flow pattern transition around bifurcation point was also conducted. It was found that the mechanisms of flow transition are different depending on the critical Rayleigh number of bifurcation point.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.10
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• pp.2595-2606
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• 1995

Buoyancy-assisted melting of an unconstrained ice in an isothermally heated horizontal enclosure was numerically analyzed in a range of wall temperatures encompassing the density inversion point. The problem as posed here involves two physically distinct domains each of which has its own scales and respective heat transfer mode. These two domains join at the junction where the liquid squeezed out of the film region flushes into the lower melt pool. Both of these domains have been treated separately in the literature by a patching technique which invokes several, otherwise unnecessary, assumptions. The present study eliminates successfully such a superfluous procedure by treating the film and lower melt pool regions as a single domain. As a result of this efficient solution procedure, the interaction of the water stream ejected at the junction and the natural convection in the melt pool could be clarified for different wall temperatures. Though limited by two-dimensionality, the present results conformed indirectly the earlier reported transition of the flow pattern, as the wall temperature was increased over the density inversion point. The transient evolution of the melting surface, the time rate of change in melt volume fraction, the local and temporal variation of the heat transfer coefficients are analyzed and presented.

• Nuclear Engineering and Technology
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• v.30 no.6
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• pp.581-591
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• 1998

Numerical analysis was peformed for the two-dimensional turbulent natural convection for a long horizontal line with different end temperatures. The turbulent model has been applied a standard k-$\varepsilon$ two equation model of turbulence similar to that the proposed by the Launder and Spalding. The dimensionless governing equations are solved by using SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which is developed using control volumes and staggered grids. The numerical results are verified by comparison with the operating PWR test data. The analysis focuses on the effects of variation of the heat transfer rates at the pipe surface, the thermal conductivities of the pipe material and the thickness of the pipe wall on the thermal stratification. The results show that the heat transfer rate at the pipe surface is the controlling parameter for mitigating of thermal stratification in the long horizontal pipe. A significant reduction and disappearance of the thermal stratification phenomenon is observed at the Biot number of 4.82$\times$10$^{-1}$ . The results also show that the increment of the thermal conductivity and thickness of the wall weakens a little the thermal stratification and somewhat reduces temperature gradient of y-direction in the pipe wall. These effects are however minor, when compared with those due to the variation of the heat transfer rates at the surface of the pipe wall.

• 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.

• 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 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.