Influence of dielectrical heating on convective flow in a radial force field

We present results of numerical and experimental investigations of thermal convection induced by internal heating in both a nonrotating and a rotating spherical gap filled with dielectric fluid. The inner and outer surfaces are maintained at constant temperatures T_{in} and T_{out}, respectively. A radial force field is produced due to the dielectrophoretic effect. The buoyancy force in the Navier-Stokes equation and the source term in the energy equation depend on the imposed oscillating electric field according to V_{rms}^{2}r^{-5} and V_{rms}^{2}r^{-4}, respectively, where V_{rms} is the root mean squared value of the voltage between spherical surfaces and r is the radial distance. Beginning with the nonrotating case, we perform linear instability analysis in the case of purely internal heating, i.e., both surfaces are maintained at the same temperature ΔT=T_{in}-T_{out}=0. Next, we consider a situation in which there is not only internal heating but also a temperature difference ΔT>0. While the spherical gap rotated, the occurring two-dimensional steady basic flow was calculated numerically. The stability of the basic flow was investigated by means of linear instability theory. The critical Rayleigh numbers and the critical azimuthal wave numbers are presented in dependence on the Taylor number. We calculate supercritical three-dimensional flows for comparison with experimentally obtained patterns in frames of the GeoFlow experiment on the International Space Station.