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Thermal Convection Between Two Horizontal Plates with Small Amplitude Non-Uniform Temperatures  

Yoo Joo-Sik (Department of Mechanical Engineering Education, Andong National University)
Kim Yong-Jin (Korea Institute of Machinery & Materials)
Publication Information
Korean Journal of Air-Conditioning and Refrigeration Engineering / v.16, no.11, 2004 , pp. 999-1005 More about this Journal
Abstract
Thermal convection between two horizontal walls kept at small amplitude nonuniform temperatures of the form, $T_L=T_1+a{\Delta}T$ sin kx and $T_U=T_2+b{\Delta}T\;sin(kx-{\beta})$ with a, $b{\ll}1$, is numerically investigated. When the Rayleigh number is small, an upright cell is formed between two walls at ${\beta}=0$; the cell is tilted at ${\beta}={\pi}/2$, and a flow with two-tier-structure cells occurs at ${\beta}={\pi}$. As the Rayleigh number is increased, Nusselt number increases smoothly for ${\beta}=0\;and\;{\pi}/2$, but increases rather steeply for ${\beta}={\pi}$ near the critical Rayleigh number ($Ra_c=1708$). When the wave number is small (k=0.5), multicellular convection occurs over one wave length, for all phase differences, and multiple solutions are found.
Keywords
Thermal convection; Non-uniform temperatures; Wave number; Phase difference; Multiple solutions;
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