Department of Mathematics, PES University, Bangalore 560 085, India.
ISRO Satellite Centre, Bangalore 560 017, India
Department of Mathematics, Bangalore University, Bangalore 560 001, India
The stability of buoyancy-driven parallel shear flow of a dielectric fluid confined between differentially heated vertical plates is investigated under the influence of a uniform horizontal AC electric field. The resulting generalized eigenvalue problem is solved numerically using Chebyshev collocation method with wave speed as the eigenvalue. The critical Grashof number Gc, the critical wave number αc and the critical wave speed cc are computed for wide ranges of AC electric Rayleigh number Rea and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. It is found that the AC electric Rayleigh number is to instill instability on convective flow against both stationary and travelling-wave mode disturbances. Nonetheless, the value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.