Thermo-electrohydrodynamic convection in a rotating shell with central force field

Abstract

Thermally driven convection in a rotating shell of dielectric fluid is investigated. An imposed central electric force field induces thermo-electrohydrodynamic convection by the dielectrophoretic force in the presence of a radial temperature gradient. Depending on the strength of the dielectrophoretic force regular to irregular convective modes are observed that are reminiscent of the classical Rayleigh-Bénad convection. While the rotation has an influence on the nature of the convective modes, a force ratio is developed to characterise the evolving pattern formation. A time evolution of the convection showed mode merging, quasi-stationary states and irregular to axis-symmetric patterns. These patterns are further analysed by a spatial Fourier decomposition to calculate the mode number and drift rates related to the rotational and di-electrophoretic forcing. The heat transfer is evaluated by the Nusselt number, Nu, and showed a significant influence by the intensity of the respective forcing. With the use of the force ratio, ϒ, and the potential mode energy, Em, the convective modes could be classified into four distinct regimes that suggests two power laws for Nu∼RaE0.17±0.01 and Nu∼0.7−0.204/Em for values of ϒ≤0.7.