Lattice Boltzmann Modeling of Electro‐Thermo‐Convection in Dielectric Liquids With Electric Conduction

ABSTRACT This paper develops a two‐relaxation‐time lattice Boltzmann method (TRT‐LBM) framework for simulating electro‐thermo‐convection (ETC) driven by conduction‐based charge transport in a two‐dimensional sidewall‐heated square cavity. The coupled flow, temperature, and charge density fields are resolved using the TRT‐LBM, while the electric potential is computed via a fast Fourier transform (FFT) based Poisson solver with domain extension. Numerical validations under hydrostatic and convective conditions demonstrate strong agreement with analytical and literature results. Parametric studies on the conduction number (), Rayleigh number (), and ion mobility ratio () reveal that the electric field suppresses natural convection by modifying the structure and thickness of heterogeneous charge layers. In the ohmic regime, a lower leads to stronger suppression of flow and heat transfer. At low Rayleigh numbers, the coupling between the electric body force and buoyancy within the charge layer can even induce symmetric secondary vortices. Furthermore, heat transfer suppression initially becomes more pronounced but gradually stabilizes as increases, as indicated by the decreasing relative Nusselt number . Within the investigated parameter range, the strongest suppression occurs at and , where . When the ion mobility ratio deviates from unity, the asymmetry introduced by unequal ion mobilities significantly alters the flow structure and heat transfer performance. As increases from 0.5 to 2.0, the average Nusselt number decreases from 2.49 to 2.21, corresponding to a reduction of approximately .