[en] The magnetohydrodynamic stability of an annular liquid jet, concentric with a solid cylinder as a mantle, and acting upon it through capillarity, electromagnetic (with varying magnetic field) and inertia forces, is discussed. An eigenvalue relation, valid to all nonaxisymmetric and axisymmetric disturbances, is derived and studied analytically and the results are confirmed numerically. The model is capillary unstable only to small axisymmetric disturbances whose wavelengths are longer than the annular jet circumference and stable to all other disturbances. The magnetic field inside the jet is stabilizing in all disturbances for all wavelengths and easily suppressing the capillary instability. The vacuum tangential varying magnetic field is destabilizing to the axisymmetric mode for all wavelengths, while to nonaxisymmetric modes it is stabilizing or destabilizing according to restrictions. The required restrictions for suppressing the capillary instability by the electromagnetic force are identified. The analytical stability results are confirmed numerically utilizing the stability criteria in the computer simulation for different values of the problem parameters

[en] The capillary instability of an annular liquid jet surrounding a solid cylinder is presented. A general dispersion equation is derived based on the linear-perturbation technique. The instability as well as stability characteristics of that model are identified analytically and confirmed numerically. The model is unstable only to the axisymmetric perturbation whose wavelengths are longer than the circumference of the liquid jet, while it is stable to all other perturbations. The maximum temporal amplification values prevailing on such a model are fairly lower than those of the full liquid jet. The thicker the solid cylinder, whether it is regular or irregular, the larger is its stabilizing effect

[en] The stability of an annular jet having a solid axis as a mantle, pervaded by uniform field and ambient with a general vacuum varying magnetic field, is presented. A general dispersion relation is derived, based on the linear perturbation technique. The instability as well as stability characteristics of that model are identified analytically and confirmed numeralically for different forms of the vacuum magnetic field to different modes of perturbation. There were unstable domains to nonaxisymmetric modes due to the varying fields. The required restrictions of the stability are determined and numerous special cases are studied. The thicker the solid cylinder, the larger its stabilizing effect and the motions (instabilities and oscillations) are slowed down, so easier observations are allowed than in the case of the full jet and than in the case of the annular jet having a gas-core jet

[en] The characteristics of Alfven surface waves along a cylindrical annular streaming column with a solid core and surrounded by a tenuous medium, and pervaded by a longitudinal magnetic field are studied analytically and numerically. Both axisymmetric (m = O) and non-axisymmetric (m ≠ O) modes are found to be dispersive. The Alfven-wave velocity decreases with increasing magnetic field. Under an infinitesimal perturbation, the motion of the system is laminar and stable for all values of m for all short and long wavelengths if the unperturbed state is non-streaming. If the system is streaming, there will be unstable domains not only for m = O but also for m ≠ O owing to the strong destabilizing influence of the streaming. However, this instability can be suppressed completely if the magnetic field is sufficiently high that the Alfven-wave velocity is greater than the streaming velocity. The thicker the solid core the greater is its stabilizing influence for m = ± 1, and vice versa for m O. A longitudinal field imparts a degree of rigidity to the conducting fluid, so it always has a strong stabilizing influence. (Author)

[en] The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by an oblique varying magnetic field, under the influence of capillary, inertia and Lorentz forces, has been developed. The problem is modelized. The basic equations are formulated, solved and upon applying appropriate boundary conditions the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the non-axisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform fields and varying transverse one. The axial fields are stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here the high compressibility increases rapidly the magneto dynamic stable domains and leads to shrinking those of instability.

[en] Mass transfer over stretching surface with variable concentration in a transverse magnetic field is examined. The boundary layer equations are transformed to ordinary differential equations, containing the magnetic parameter Mn and the concentration parameter λ. Numerical results for different values of the Schmidt number are presented. It is observed that the local mass transfer and concentration profile are very sensitive to the change in the values of the magnetic parameter Mn and the concentration parameter λ

[en] Unsteady mass transfer from a vertical plate in a transverse magnetic field is investigated assuming that all the fluid properties are constant. The solution is dependent on two parameters, namely the Prandtl number, Pr, and the Schmidt number, Sc. An analytical solution is presented which is valid at small values of time and this solution is extended to large values of time by using a modified Crank-Nicolson scheme

[en] The MHD stability of an ideal annular liquid around a solid cylinder surrounded by a streaming fluid with uniform velocity U has been developed. The MHD basic equations are linearized and solved. A general dispersion relation is derived and discussed numerically. It is found that the densities ratio has small stabilizing effect, the radii ratio has a stabilizing effect and the electromagnetic force due to the magnetic fields pervaded in the liquid and the fluid regions has strong stabilizing effect for all short and long wavelengths in all modes of perturbation. Such study may have astrophysical applications.

[en] The capillary instability of self-gravitating superposed streaming fluids of different densities with plane interface has been developed. Some reported works are recovered as limiting cases. The streaming has a strong stabilizing influence. The influence of the surface tension is found here as was obtained by (Hydrodynamic and Hydromagnetic Stability, (Oxford University Press) 1961) in the absence of the self-gravitating force. The latter is stabilizing or destabilizing according to some restrictions on the ratio of the densities ρ and ρ' of the superposed fluids. As ρ'=ρ, it was found that there is no dispersion and the resulting homogeneous self-gravitating system is marginally stable. The analytical (in)stability results are confirmed numerically for different values of ρ'/ρ

[en] The magnetohydrodynamic MHD instability of a dissipative compressible rotating self-gravitating fluid medium with general rotation and propagation has been investigated. The required basic equations for describing the present problem are formulated, linearized and solved, with excluding the singular solutions, based on the linear perturbation technique. Appropriate boundary conditions are applied with the aim of determining the unknowns of integrations and finally the desired dispersion relation has been derived in its general form. A lot of dispersion relations associated with physical problems are obtained from the present general one under appropriate and suitable choices