Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.