Electrothermal convection in a rotating dielectric fluid layer: Effect of velocity and temperature boundary conditions

The simultaneous effect of a vertical AC electric field and rotation on the onset of thermal convective instability in a horizontal rotating dielectric fluid layer is studied by performing linear stability analysis. The lower and upper boundaries of the fluid layer are considered to be either rigid or free and either isothermal or insulated to temperature perturbations. The resulting eigenvalue problem is solved exactly for free-free isothermal boundaries. It is observed that the oscillatory convection is not a preferred mode of instability for dielectric fluids and the necessary conditions for its occurrence are independent of applied vertical AC electric field. For the other combinations of velocity and temperature boundary conditions, the problem is solved numerically using the Galerkin method. The similarities and differences between the results of isothermal and insulated boundaries are highlighted. It is noted that the effect of increasing AC electric Rayleigh number is to increase the transfer of heat more effectively and hence to hasten the onset of convection. To the contrary, the effect of rotation is to delay the electrothermal convection for a fixed type of boundary conditions. Although the rigid-rigid boundaries enhance the stability when compared to rigid-free and free-free boundaries up to moderate values of Taylor number, the situation is reversed at high Taylor number domain. This trend depends on the temperature boundary conditions as well.