Exact solution for electrically-driven convection between vertical electrodes
A first-order model of electrically driven flows is described and applied to flows driven by Joule heating of a dielectric fluid. An exact solution for the reduced, first-order equations of electrohydrodynamics is developed for the case of a steady, fully developed flow between vertical, parallel, planar electrodes. The solution is shown to depend on four dimensionless groups: the Grashof and Reynolds numbers and two new quantities that represent the magnitude of charge-induced electric field perturbations over the magnitude of the field at an electrode surface and the ratio of the Joule heating rate to the thermal conduction rate, respectively. It is demonstrated that for small field perturbations the solution yields a parabolic velocity profile. The thermal and velocity profiles are only slightly asymmetrical for cases in which the electric field is strongly nonuniform due to space-charge perturbation of the field.
