Effects of alternating current electric field and thermal non-equilibrium on the Brinkman-Bénard instability

The onset of thermal convection in a layer of dielectric fluid-saturated Brinkman porous medium is investigated under the influence of a uniform vertical alternating current (AC) electric field using a local thermal non-equilibrium (LTNE) model considering the boundaries to be either free-free or rigid-rigid or lower rigid and upper free. It has been shown that the principle of exchange of stability is valid irrespective of the nature of boundaries. The eigenvalue problem is solved exactly for free-free boundaries and numerically using shooting method for rigid-rigid and lower rigid-upper free boundaries. The results for different velocity boundary conditions are found to be qualitatively similar but differ only quantitatively. It is observed that an increase in the AC electric Rayleigh number Rea is to augment heat transfer and to hasten the onset of convection, while an increase in the inter-phase heat transfer coefficient H, inverse Darcy number Da-1, and the ratio of viscosities Λ as well as a decrease in the porosity modified conductivity ratio γ is to delay the onset of electrothermal convection. Besides, increase in Rea and Da-1 as well as decrease in γ, H, and Λ is to reduce the size of convection cells. Asymptotic solutions for both small and large values of H for free-free boundaries compare well with those obtained from the exact formula. © 2017 by Begell House, Inc.