Numerical investigation of electrohydrodynamic instability in a vertical porous layer

The electrohydrodynamic instability of a vertical dielectric fluid saturated Brinkman porous layer whose vertical walls are maintained at different temperatures is considered. An external AC electric field is applied across the vertical porous layer to induce an unstably stratified electrical body force. The stability eigenvalue equation is solved numerically using the Chebyshev collocation method. The presence of inertia is found to instill instability on the system and the value of modified Darcy–Prandtl number PrD at which the transition from stationary to travelling-wave mode takes place is independent of the AC electric field but increases considerably with an increase in the value of Darcy number Da. The presence of AC electric field promotes instability but its effect is found to be only marginal. Although the flow is stabilizing against stationary disturbances with increasing Da, its effect is noted to be dual in nature if the instability is via travelling-wave mode. The streamlines and isotherms for various values of physical parameters at their critical state are presented and analyzed. Besides, energy norm at the critical state is also computed and found that the disturbance kinetic energy due to surface drag, viscous force and dielectrophoretic force have no significant effect on the stability of fluid flow.