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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 30, 1996 - Issue 5
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Original Articles

NUMERICAL SIMULATION OF FLOW PATTERN FORMATION IN A BOTTOM HEATED CYLINDRICAL FLUID LAYER

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Pages 459-476 | Published online: 23 Mar 2007
 

Abstract

The temporal formation of the buoyancy-driven flow structures in a bottom heated, shallow, cylindrical fluid layer was numerically studied. The unsteady three-dimensional Navier-Stokes and energy equations were discretized by the power law scheme and solved by the fully implicit Marker-and-Cell method. Computations were carried out for the pressurized argon (Pr=0·69) and water (Pr=6·1) layers for various Rayleigh numbers and heating rates of the layer. In the pressurized argon layer at a slightly supercritical Rayleigh number with Raf;=1·05Rac a steady straight roll pattern was formed when the heating rate was very slow (a=0·001) after a long transient stage. When the heating rate was raised to a=0·01, a very different structure tike U-rolls was formed at steady state. In the water layer with Raf=l·05Rac, a straight roll pattern was again formed, but at a equals;0·07. At Raf;=1·13Rac, curved rolls with the three foci at the sidewall were formed for a=0·01. A pattern in the form of U-rolls appears at a=0·01. Regular concentric circular rolls prevail at a=1·0. When the Rayleigh number is further raised to 1·23Rac, the resulting steady flow is dominated by incomplete circular rolls with open ends near θ=0°

Notes

Address correspondence to Professor Tsing-Fa Lin, Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan, Republic of China. E-mail: [email protected]. tw

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