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Dielectrophoretic force-driven thermal convection in annular geometry
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10.1063/1.4792833
/content/aip/journal/pof2/25/2/10.1063/1.4792833
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4792833
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of the geometrical configuration in a plane transversal to the annulus axis.

Image of FIG. 2.
FIG. 2.

Basic electric gravity . (a) Its direction as function of the dimensionless temperature γ and the radius ratio η. CP and CF mean centripetal and centrifugal, respectively. (b) Some profiles of calculated for the electric tension = 1.08 × 10 V. The cylinder radii and liquid properties are taken from the Chandra and Smylie's experiment ( = 1.711 × 10 m, = 1.903 × 10 m, ρ = 937.7 kg m, α = 1.08 × 10 K, and = 3.7 × 10 K).

Image of FIG. 3.
FIG. 3.

Dispersion relation for different azimuthal mode number . (Pr = 100, η = 0.5, γ = 0.01, = 1498).

Image of FIG. 4.
FIG. 4.

Definitions of the wavenumber and the inclination angle ψ of convection rolls.

Image of FIG. 5.
FIG. 5.

Marginal curves for different azimuthal mode number at small and large radius ratios η: (a) η = 0.5 and (b) η = 0.9. The dimensionless temperature γ is fixed at 0.01.

Image of FIG. 6.
FIG. 6.

Critical electric Rayleigh number as function of the radius ratio η for different dimensionless temperatures γ. The horizontal lines show the critical Rayleigh number of the Rayleigh-Bénard instability (1708) and of the DEP convection in plane geometry (2129).

Image of FIG. 7.
FIG. 7.

Critical wavenumber and inclination angle ψ for an outward heating (γ = 0.01).

Image of FIG. 8.
FIG. 8.

Critical wavenumber for inward and outward heatings.

Image of FIG. 9.
FIG. 9.

Critical eigenmodes for small and large radius ratios η. For η = 0.3, = 2, = 1.91, and = 1177. For η = 0.9, = 25, = 1.68, and = 1732. The heating is outward with the dimensionless temperature γ = 0.01 for both cases.

Image of FIG. 10.
FIG. 10.

Normalized different contributions to the rate of change of the convection flow kinetic energy (Eq. (29) ) at critical conditions.

Image of FIG. 11.
FIG. 11.

Normalized different contributions to the rate of change of the convection flow kinetic energy (Eq. (29) ) at critical Rayleigh numbers: (a) at a small radius ratio η for different azimuthal mode number in an outward heating (η = 0.2, γ = 0.01, and = 888.4) and (b) at a large η for different heating directions (η = 0.98, = 2005, and 2355 for γ = 0.1 and −0.1, respectively). The Prandtl number is fixed at 10 for all.

Image of FIG. 12.
FIG. 12.

Stability boundaries in the voltage–temperature plane for different radius ratio η. Theoretical predictions of the existing theoretical works are also shown (· · · · · · · · · · · ·: Takashima and Hamabata for plane geometry; - - - -: Chandra and Smylie for η = 0.89; ▲ and □: Takashima for η = 0.91 and η = 0.99, respectively).

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/content/aip/journal/pof2/25/2/10.1063/1.4792833
2013-02-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dielectrophoretic force-driven thermal convection in annular geometry
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/2/10.1063/1.4792833
10.1063/1.4792833
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