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TECHNICAL PAPERS

Thermocapillary Instabilities of Low Prandtl Number Fluid in a Laterally Heated Vertical Cylinder

[+] Author and Article Information
B. Xu1

School of Mechanical and Materials Engineering,  Washington State University, Pullman, WA 99164bxu@wsu.edu

X. Ai, B. Q. Li

School of Mechanical and Materials Engineering,  Washington State University, Pullman, WA 99164

1

Author to whom correspondence should be addressed.

J. Fluids Eng 128(6), 1228-1235 (Mar 10, 2006) (8 pages) doi:10.1115/1.2353278 History: Received August 07, 2005; Revised March 10, 2006

Stabilities of surface-tension-driven convection in an open cylinder are investigated numerically. The cylinder is heated laterally through its sidewall and is cooled at free surface by radiation. A seeding crystal at constant temperature is in contact with the free surface. Axisymmetric base flow is solved using the high-order finite difference method. Three-dimensional perturbation is applied to the obtained base flow to determine the critical Marangoni numbers at which the axisymmetry is broken. The eigenvalue matrix equation is solved using linear fractional transformation with banded matrix structure taken into account. Critical Marangoni-Reynolds numbers are obtained at various boundary conditions.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of the cylinder being studied

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Figure 2

Critical Marangoni number of Marangoni convection in a vertical cylinder for m=1 and 2 at various aspect ratios

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Figure 3

Velocity field (a) and isotherms (b) of the base flow corresponding to R=H=1, Reγ=2×104, q=1.0, and Rd=0

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Figure 4

Velocity field (a) and isotherms (b) of the base flow corresponding to R=H=1, Reγ=2×104, q=2.0, and Rd=0.5

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Figure 5

Velocity field (a) and isotherms (b) of the base flow corresponding to R=H=1, Reγ=4×104, q=2.0, and Rd=0.5

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Figure 6

Critical Marangoni-Reynolds numbers with different seeding crystal sizes for R=H=1 and q=1.0

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Figure 7

Critical Marangoni-Reynolds numbers with different lateral heat fluxes for R=H=1 and Rd=0

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Figure 8

Eigenvalue spectrum of base flow with R=H=1, Reγ=27791, m=1, q=1.0, and Rd=0

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Figure 9

Patterns of temperature perturbation at the z=05 cross-sectional surface corresponding to R=H=1, m=1: (a)Reγ=27791 and Rd=0; (b)Reγ=35307 and Rd=0.5

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