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Mesoscopic simulation of electrohydrodynamic effects on laminar natural convection of a dielectric liquid in a cubic cavity

Electro-thermo-hydrodynamic (ETHD) flows induced by simultaneous Coulomb and buoyancy forces in a dielectric medium are studied. Previous results limited to two dimensions are extended to three dimensions. The fully coupled governing equations, including the Navier–Stokes equations, the electrohydrodynamic equations, and the energy equation, are solved using a unified lattice Boltzmann model. Various flow patterns, determined by the balance between the buoyancy-driven mechanism and the Coulomb-driven mechanism, can be observed for different combinations of the governing parameters (the electric Rayleigh number T and the Rayleigh number Ra). It is found that the electrical effect on enhancement of heat transfer becomes significant at a relatively low value of Ra. Besides, an approximately linear relationship is found between the Nusselt number Nu and T. Finally, ETHD flows for different directions of charge injection are investigated, and the results reveal that the heat transfer performance of the system is improved when the injection direction is the same as the direction of the temperature gradient.