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RESEARCH PAPER

Three-Dimensional Instabilities of Natural Convection Flow in a Vertical Cylinder With Partially Heated Sidewall

[+] Author and Article Information
A. Rubinov, P. Z. Bar-Yoseph, A. Solan

Computational Mechanics Laboratory, Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel

V. Erenburg, A. Yu. Gelfgat, E. Kit

School of Mechanical Engineering, Tel-Aviv University, Ramat Aviv 69978, Israel

J. Heat Transfer 126(4), 586-599 (Apr 12, 2004) (14 pages) doi:10.1115/1.1773588 History: Received July 01, 2003; Revised April 12, 2004
Copyright © 2004 by ASME
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References

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Figures

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Geometry of the problem
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Streamlines (left frames) and isotherms (right frames) of base axisymmetric flow. All isolines are equally spaced. The temperature varies between 0 and 1: (a) A=2.5,Grcr=1.12×105max=23.59; (b) A=4,Grcr=3.18×105max=6.20; (c) A=8,Grcr=1.82×104max=2.01.
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Stability diagram: (a) Marginal Grashof number versus the aspect ratio for 1≤k≤4; and (b) Two most critical marginal stability curves for k=1 and 2 and comparison with experimental points 6.
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Marginal frequency of the azimuthal traveling wave for the modes k=1 and 2 (only non-zero ωm are shown)
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Amplitudes of the perturbations of (a) radial, (b) vertical, (c) azimuthal velocities, and (d) temperature. A=2.5,Grcr=1.12×105,k=2.
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Amplitudes of the perturbations of (a) radial, (b) vertical, (c) azimuthal velocities, and (d) temperature. A=2.9,Grcr=1.10×105,k=1.
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Amplitudes of the perturbations of (a) radial, (b) vertical, (c) azimuthal velocities, and (d) temperature. A=4,Grcr=3.18×105,k=1.
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Amplitudes of the perturbations of (a) radial, (b) vertical, (c) azimuthal velocities, and (d) temperature. A=6,Grcr=1.88×104,k=1.
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Amplitudes of the perturbations of (a) radial, (b) vertical, (c) azimuthal velocities, and (d) temperature. A=8,Grcr=1.82×104,k=1.
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Pattern of the temperature perturbation at A=2.5,Grcr=1.12×105,k=2: (a) four equally spaced isosurfaces; and (b) 21 equally spaced isolines in four different axial cross-sections.
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Pattern of the temperature perturbation at A=2.9,Grcr=1.10×105,k=1: (a) four equally spaced isosurfaces; and (b) 21 equally spaced isolines in four different axial cross-sections.
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Pattern of the temperature perturbation at A=4,Grcr=3.18×104,k=1: (a) four equally spaced isosurfaces; and (b) 21 equally spaced isolines in four different axial cross-sections.
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Pattern of the temperature perturbation at A=8,Grcr=1.82×104,k=1: (a) four equally spaced isosurfaces; and (b) 21 equally spaced isolines in four different axial cross-sections.
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Pattern of perturbation of the vertical velocity at A=8,Grcr=1.82×104,k=1: (a) six equally spaced isosurfaces; and (b) 21 equally spaced isolines in four different axial cross-sections.
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Marginal Grashof number versus the Prandtl number for A=4 and 1≤k≤3
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Isotherms (left frame) and streamlines for Pr=0 and growing Grashof number
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Streamlines and isotherms of the flow for Gr=2.3×105 and the Prandtl numbers slightly different from zero

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