Role of boundary conditions and volumetric heating in electrothermal anisotropic porous convection

This study presents a theoretical investigation into the linear instability of electrothermal convection in an internally heated, anisotropic dielectric fluid-saturated porous layer, modeled by the Darcy-Brinkman equation and subjected to an AC electric field. The porous medium exhibits anisotropy in both permeability and thermal diffusivity, with isotropy assumed in the horizontal plane. The vertical permeability is fixed at twice the horizontal value, while thermal diffusivity anisotropy is treated as a free parameter. The layer is bounded above and below by isothermal surfaces, which may be rigid or stress-free, with appropriate electric potential boundary conditions imposed. The principle of exchange of stabilities is shown to hold, and the resulting linear eigenvalue problem is solved using Galerkin’s method of weighted residuals for free-free (F–F), rigid-rigid (R–R), and mixed (R-F) boundary conditions. The analysis reveals that increasing the AC electric Rayleigh number, Darcy number, and internal heat generation promotes the onset of convection, whereas enhanced thermal anisotropy suppresses it. Importantly, the qualitative nature of the stability characteristics is preserved across all velocity boundary combinations. Besides, electroconvection without gravity is analyzed to isolate the role of electric forces, and the behavior is found to mirror that seen with gravitational forces.