• 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.

• 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.

• 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.