Schematic illustration of the geometrical configuration in a plane transversal to the annulus axis.
Basic electric gravity . (a) Its direction as function of the dimensionless temperature γ e and the radius ratio η. CP and CF mean centripetal and centrifugal, respectively. (b) Some profiles of calculated for the electric tension V 0 = 1.08 × 104 V. The cylinder radii and liquid properties are taken from the Chandra and Smylie's experiment 7 (R 1 = 1.711 × 10−2 m, R 2 = 1.903 × 10−2 m, ρ = 937.7 kg m−3, α = 1.08 × 10−3 K−1, and e = 3.7 × 10−3 K−1).
Dispersion relation for different azimuthal mode number n. (Pr = 100, η = 0.5, γ e = 0.01, L = 1498).
Definitions of the wavenumber q and the inclination angle ψ of convection rolls.
Marginal curves for different azimuthal mode number n at small and large radius ratios η: (a) η = 0.5 and (b) η = 0.9. The dimensionless temperature γ e is fixed at 0.01.
Critical electric Rayleigh number L c as function of the radius ratio η for different dimensionless temperatures γ e . The horizontal lines show the critical Rayleigh number of the Rayleigh-Bénard instability (1708) and L c of the DEP convection in plane geometry (2129). 9
Critical wavenumber q c and inclination angle ψ for an outward heating (γ e = 0.01).
Critical wavenumber q c for inward and outward heatings.
Critical eigenmodes for small and large radius ratios η. For η = 0.3, n = 2, k = 1.91, and L = 1177. For η = 0.9, n = 25, k = 1.68, and L = 1732. The heating is outward with the dimensionless temperature γ e = 0.01 for both cases.
Normalized different contributions to the rate of change of the convection flow kinetic energy (Eq. (29) ) at critical conditions.
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 n in an outward heating (η = 0.2, γ e = 0.01, and L = 888.4) and (b) at a large η for different heating directions (η = 0.98, L = 2005, and 2355 for γ e = 0.1 and −0.1, respectively). The Prandtl number is fixed at 10 for all.
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 9 for plane geometry; - - - -: Chandra and Smylie 7 for η = 0.89; ▲ and □: Takashima 8 for η = 0.91 and η = 0.99, respectively).
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