Role of Boundary Conditions and Volumetric Heating in Electrothermal Anisotropic Porous Convection

Abstract

The study investigates the combined influence of uniform volumetric heating and an alternating current (AC) electric field on the onset of convection in an anisotropic, dielectric fluid-saturated Brinkman porous layer heated from below. The porous medium is anisotropic in both permeability and thermal diffusivity, with the vertical permeability fixed at twice the horizontal value, while the thermal anisotropy parameter is allowed to vary freely. The layer is bounded by isothermal surfaces subject to rigid-rigid, free-free, or rigid-free velocity conditions, with appropriate electric potentials applied. The generalized eigenvalue problem is solved numerically using Galerkin’s method, establishing the validity of the exchange of stabilities. The results show that increasing the AC electric Rayleigh number, Darcy number, and internal heat generation parameter hastens the onset of convection, whereas greater thermal anisotropy delays it. These trends persist across all boundary conditions, with rigid-rigid boundaries being the most stabilizing and free-free the least. However, at higher heat source strengths, the threshold values exhibit a reversal in trend between the rigid-free and free-free boundaries. The electric field alone can trigger instability at sufficiently high AC electric Rayleigh numbers, accompanied by a higher critical wavenumber. The findings elucidate the interplay among anisotropy, volumetric heating, and electric forcing, offering insights relevant to electrohydrodynamic cooling, microscale thermal management, porous insulation design, and energy conversion systems where coupled electric–thermal effects govern heat transport.