This study examines penetrative electrothermal convection driven by uniform internal heat generation in a horizontal layer of dielectric fluid-saturated anisotropic Brinkman porous medium subjected to a uniform AC electric field. Anisotropy in permeability and thermal diffusivity is incorporated, with the vertical permeability fixed at twice the horizontal value, while the thermal anisotropy parameter is varied. The boundaries are taken to be either rigid or stress-free, with an adiabatic lower surface and an upper surface subject to a Robin thermal condition. A linear stability analysis yields a generalized eigenvalue problem, which is solved numerically using a Galerkin method. The principle of exchange of stabilities is shown to hold for rigid–rigid, rigid–free and free–free boundary combinations. Increasing the AC electric Rayleigh number and the Darcy number advances the onset of convection, whereas larger thermal anisotropy and Biot numbers delay instability. Velocity boundary conditions exert a significant quantitative influence, with rigid boundaries being the most stabilizing. As a limiting case, pure electroconvection in the absence of buoyancy is also considered. Although the qualitative trends remain similar to those in the coupled electrothermal regime, substantially higher critical AC electric Rayleigh numbers and wavenumbers are required to trigger instability, reflecting the need for electric forcing alone to overcome viscous and porous dissipation.
Raju et al. (Sun,) studied this question.