The heat transfer enhancement by unipolar charge injection in a rectangular Rayleigh–Bénard convection

The heat transfer enhancement achieved by the additional electric field in Rayleigh–Bénard convection (RBC) of a dielectric fluid is numerically studied beyond the Rayleigh number Ra = 105. We carried out direct numerical simulations of RBC in a rectangular enclosure under the strong injection condition with a fixed non-dimensional injection parameter C = 10, a fixed mobility number M = 10, two Rayleigh numbers Ra = 105 and Ra = 106, and two Prandtl numbers Pr = 1 and Pr = 10 to investigate the characteristics of flow structure and heat transfer and evaluate the dependence on these parameters. It is observed that the flow structure exhibits multiple states with various steady or unsteady flow patterns such as four cells, three cells, and two cells (up/down). It is found that the introduction of an electric field is an effective way to achieve heat transfer enhancement. The heat flux is augmented more efficiently for a large Prandtl number and a low Rayleigh number, where the electric field has a strong effect relative to buoyancy. It is also found that heat transfer is most efficient when the flow pattern is in a three cells flow state.