• Journal of computational fluids engineering
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• v.9 no.4
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• pp.1-6
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• 2004

This study investigates the transition of flows in a natural convection problem with periodic wall temperatures of the form, T/sub L/=T₁＋δ Tsinκχ and T/sub L/=T₂＋δ Tsinκχ .The fluid considered is air with P/sub γ/=0.7. In the conduction-dominated regime with a small Rayleigh number, two large cells are formed over one wave length, for all wave numbers. When k≤1.8, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The flow patterns are classified by the number of eddies over one wave length, and several kinds of transition phenomena, such as 2→3→4, 4→3→2, and 2→4 eddy flow, occur with increase( or decrease) of the Rayleigh number. Dual solutions are found above a critical Rayleigh number, and an anomalous bifurcation is observed.

• 대한공업교육학회지
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• v.30 no.2
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• pp.123-129
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• 2005

A Rayleigh-Benard problem with non-uniform wall temperatures of the form, $T_L=T_1+{\delta}{\Delta}T{\sin}kx$ and $T_U=T_2-{\delta}{\Delta}{\sin (kx)$, is numerically investigated. In the conduction-dominated regime with small a Rayleigh number, a two-tier structure appears with two counter-rotating rolls stacked on the top of each other. The flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximetely square-shape cells. Four multiple flows and dual flows classified by the number of cells are found at k=0.5 and k=1, respectively.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.9
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• pp.2981-2990
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• 1996

Dual solutions for steady natural convection of air between two horizontal concentric cylinders are numerically investigated in the range of $D_i$/TEX>/L(=diameter of inner cylinder/gap width)$\leq$10. It is found that, when the Rayleigh number based on the gap width exceeds a certain critical value, a new flow pattern forming two counter-rotating eddies in the half of the annulus can be realized, which is different from the crescent-shaped flow commonly observed. In the new flow pattern, the fluid near the top of the hot inner cylinder moves downward. This solution is found for D$_{i}$/L.geq.0.3, but not for$D_i$/TEX>/L$\leq$0.2. As $D_i$/TEX>/L increase, the critical Rayleigh number is decreased, and tends to a finite limit.t.

• 대한공업교육학회지
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• v.33 no.2
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• pp.300-311
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• 2008

This study investigates the natural convection of air(Pr=0.7) between two walls having a small- wave- number sinusoidal temperature distributions with a phase difference. The wave number and the phase difference of wall temperatures are k=0.5 and ㄱ/2, respectively. In the conduction-dominated regime at small Rayleigh number, two slightly inclined cells are formed over one wave length. At higher Rayleigh number, however, multicellular convection occurs in thermally unstable region. A spatial symmetry is intermittently broken in the transient period at the Rayleigh number near the critical value. The steady-state flows always satisfy the spatial symmetry. A steep increase of Nusselt number occurs near the Rayleigh number at which transition of flow pattern occurs.

• Korean Chemical Engineering Research
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• v.52 no.2
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• pp.199-204
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• 2014

In binary solidification compositional convection in a porous mushy layer influences the quality of the final products. We consider the mushy layer solidifying from below with a constant solidification velocity. The disturbance equations for the mushy layer are derived using linear stability theory. The basic-state temperature fields and the distribution of the porosity in the mushy layer are investigated numerically. When the superheat is large, the thickness of the mushy layer is relatively small compared to the thickness of the thermal boundary layer. With decreasing the superheat the critical Rayleigh number based on the thickness of the mushy layer increases and the mushy layer becomes stable to the compositional convection. The critical Rayleigh number obtained from the continuity conditions of temperature and heat flux at the mush-liquid interface is smaller than that from the isothermal condition at the upper boundary of the mushy layer.

• Korean Chemical Engineering Research
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• v.57 no.1
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

• Journal of computational fluids engineering
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• v.21 no.3
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1440-1448
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• 2004

Multiple solutions in natural convection of air (Pr=0.7) between two horizontal walls with mean temperature difference and the same periodic nob-uniformities are investigated. An analytical solution is found for small Rayleigh number, and the general solution is investigated by using a numerical method. In the conduction-dominated regime, two upright cells are formed between two walls over one wave length. When the wave number is small, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximately square-shape cells. And several kinds of multiple flows classified by the number of cells are found.

• Korean Chemical Engineering Research
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• v.50 no.1
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• pp.61-65
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• 2012

The onset of convection in a mushy layer is analyzed by using linear stability theory in time-dependent solidification of a binary melt. A simplified model of a near-eutectic mush, in which the mush is assumed to be a porous block, is used and the propagation theory is applied to determine the critical conditions for the onset of convection. The present critical Rayleigh number is higher than the existing experimental result and also theoretical results obtained by considering the mushy layer with an overlying liquid layer. The constant pressure (permeable) condition applied on the mush-liquid interface produces a lower critical Rayleigh number, which is closer to the experimental results of aqueous ammonium chloride solution, compared with the impermeable condition.

• Journal of computational fluids engineering
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• v.22 no.1
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• pp.110-115
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• 2017

Natural convection of a fluid with the Prandtl number of 7(water) in a horizontal annulus with constant temperature walls is numerically investigated. The inner cylinder is hotter than the outer cylinder. The flows are classified by the number of eddies in a half annulus. It is found that dual or triple solutions exists above a critical Rayleigh number for an annulus with a aspect ratio $D_i/L=4$. Transitions of $3{\rightarrow}1$ and $2{\rightarrow}1$ eddy flow occur with decrease of Rayleigh number. However, reverse transitions of $1{\rightarrow}3$ and $1{\rightarrow}2$ eddy flow do not occur with increase of Rayleigh number, and no hysteresis phenomenon is observed. In the regime of triple solutions, the 3 eddy flow has the largest mean Nusselt number value and the 1 eddy flow has the smallest value.