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TECHNICAL PAPERS: Evaporation, Boiling, and Condensation

Surface Energy Variation Effect on the Onset of Thermocapillary Instability of a Thin Liquid Layer Heated from the Side

[+] Author and Article Information
Lin Wu

Department of Electrical Engineering, Princeton University, Princeton, NJ 08540

Kang Ping Chen

Department of Mechanical & Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

J. Heat Transfer 125(1), 63-69 (Jan 29, 2003) (7 pages) doi:10.1115/1.1527909 History: Received March 05, 2002; Revised September 17, 2002; Online January 29, 2003
Copyright © 2003 by ASME
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References

Figures

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Control volume with an interface. V1,V2 are two material volumes with surfaces ∂V1,∂V2 and an interface Σ in between. ∂Σ is the boundary of Σ. n1,n2 are outward normal vectors on ∂V1 and ∂V2 respectively. n12 is the normal vector on Σ pointing from 1 to 2. τ⁁ is a tangential vector of Σ on ∂Σ.
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The configuration of the one layer system horizontally unbounded. A constant temperature gradient is imposed in the positive x direction. Surface tension gradient drives the fluid to move in the direction shown with a linear basic state velocity profile.
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The configuration of the one layer system horizontally bounded (d/L≪1). A constant temperature gradient is imposed in the positive x direction. Surface tension gradient drives the fluid to move in the direction shown. A parabolic basic state velocity profile approximates the core region away from the ends when the aspect ratio L/d is very large.
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The effect of the parameter Γ on the minimum Marangoni number at each direction ϕ for the linear flow solution with Pr=0.5, Bi=0. At ϕ=83 deg, 97 deg, Mac=20.04, for Γ=0, and Mac=20.27, for Γ=0.1.
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The effect of the parameter Γ on the minimum Marangoni number at each direction ϕ for the linear flow solution with Pr=∞, Bi=0. At ϕ=90 deg, Mac=15.48, for Γ=0, and Mac=15.68, for Γ=0.1.
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The effect of the parameter Γ on the minimum Marangoni number at each direction ϕ for the linear flow solution with Pr=1, Bi=0. At ϕ=0 deg, 180 deg, Mac=20.67, for Γ=0, and Mac=21.09, for Γ=0.1, Mac=21.50, for Γ=0.2.
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The effect of the parameter Γ on the minimum Marangoni number at each direction ϕ for the return flow solution with Pr=1, Bi=0. At ϕ=55 deg, 125 deg, Mac=116.01, for Γ=0, and Mac=116.85, for Γ=0.1.
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The effect of the parameter Γ on the minimum Marangoni number at each direction ϕ for the return flow solution with Pr=10, Bi=0. At ϕ=20 deg, 160 deg, Mac=273.76, for Γ=0, and Mac=275.16 for Γ=0.1.
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Sketch of disturbance flow streamlines. Arrows indicate disturbance flow directions.
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The neutral stability curves for the linear flow solution with Pr=1, Bi=0, at the most dangerous directions ϕ=0 deg, 180 deg. The stabilizing effect of Γ increases with the wave number.
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The neutral stability curves for the return flow solution with Pr=10, Bi=0, at the most dangerous directions ϕ=20 deg, 160 deg. The stabilizing effect of Γ increases with the wave number.
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The stabilizing effect of Γ on the critical Marangoni number corresponding to the most dangerous direction as a function of the Prandtl number for the linear flow with Bi=0
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The stabilizing effect of Γ on the critical Marangoni number corresponding to the most dangerous direction as a function of the Prandtl number for the return flow with Bi=0

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