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

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, $E_m$, the convective modes could be classified into four distinct regimes that suggests two power laws for $Nu\sim R{a}_E^{0.17\pm 0.01}$ and $Nu\sim {0.7}^{-0.204/E_m}$ for values of $\Upsilon \le 0.7$.