Volumetric heating and AC electric field effects on porous convection with general boundary conditions

Abstract

The onset of convective instability in an internally heated dielectric fluid-saturated porous layer under the influence of a uniform AC electric field for different types of boundary conditions is investigated. The flow in the porous medium is described by the Brinkman model with fluid viscosity different from effective viscosity. The lower adiabatic and the top with finite heat transfer coefficient to the external environment boundaries are considered to be either rigid or stress-free. The presence of a uniform volumetric heat source alters the conduction profile of the temperature field from linear to quadratic in the vertical coordinate. A modal linear stability analysis of the basic motionless state is carried out and the general regime of linear instability is investigated by solving the stability eigenvalue problem numerically using the Galerkin method of weighted residual technique. The neutral stability condition as well as the critical value of the thermal Rayleigh number is computed for rigid–rigid, free–free, and rigid–free boundaries for various values of governing parameters. It is seen that the nature of boundaries affect the stability of the system only quantitatively, though not qualitatively. The rigid–rigid boundaries offer a more stabilizing effect against convection in comparison with rigid–free and free–free boundaries. The study found that the effect of increasing thermal electric Rayleigh number and the Darcy number is to hasten the onset of instability, while the opposite trend is perceived with an increase in the ratio of viscosities and Biot number. The outcomes of this investigation are found to be in good agreement with past studies under the limiting cases.