Coupled thermovibrational and electroconvection dynamics in a square cavity

This study explores the combined effects of coulomb force and high-frequency, low-amplitude horizontal vibrations on thermal convection within a square enclosure filled with dielectric fluid. The governing equations are formulated using an averaged approach, incorporating vorticity of the mean velocity and stream functions for both mean and fluctuating flows. These equations are solved using the finite difference method with alternate direction implicit (ADI) scheme and an iterative successive under-relaxation (SUR) technique. The analysis focuses mainly on the impact of the electrical Rayleigh number ($100\le R{a}_e\le 700$) and the vibrational Rayleigh number ($10^3\le R{a}_v\le 10^6$) for liquid gas oil. The results show that at low $R{a}_e=100$, charge transport is controlled by drift and diffusion, forming thicker thermal layers. As $R{a}_v\ge 10^5$, charge mobility and thermal gradients are suppressed, while $R{a}_e=700$ enhances charge transport and heat redistribution. At low vibration ($R{a}_v=10^3$), increasing $R{a}_e$ leads to a 112% increase in the mean Nusselt number. At moderate vibration ($R{a}_v=10^5$), the enhancement drops to 55%, and at high vibration ($R{a}_v=10^6$), heat transfer decreases by 26%, indicating the suppression of electroconvection by vibrational forces. Flow transitions from vertical to horizontal eddies with increasing $R{a}_v$, and thermal buoyancy at $R{a}_t>0$ alters charge transport, with $R{a}_t=10^6$ inducing a dual-vortex regime that improves charge homogeneity. These findings reveal the importance of interplay between vibrational effects and electroconvection, highlighting the potential of advanced cooling techniques for thermal management in space systems.