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1Author    Mohamed Fahmy, El-SayedRequires cookie*
 Title    Electrohydrodynamic Interfacial Stability Conditions in the Presence of Heat and Mass Transfer and Oblique Electric Fields  
 Abstract    A novel mathematical formulation to deal with interfacial stability problems of the Kelvin-Helmholtz type with heat and mass transfer in the presence of oblique electric fields is presented. The perturbed system is composed of two homogeneous, inviscid, incompressible, dielectric, and streaming fluids sep-arated by a horizontal interface, and bounded by two rigid planes. The effect of a phase transition on the instability is considered, and the linear dispersion relations are obtained and discussed. It is found that the electric field has a major effect and can be chosen to stabilize or destabilize the flow. For Ray-leigh-Taylor instability problems of a liquid-vapor system it is found that the effect of mass and heat transfer enhances the stability of the system when the vapor is hotter than the liquid, although the clas-sical stability criterion is still valid. For Kelvin-Helmholtz instability problems, however, the classical stability criterion is found to be substantially modified due to the effects of the electric field, mass and heat transfer. A new stability condition relating the magnitude and orientation of the electric field and the dielectric constants is obtained. Oblique electric fields are found to have stabilizing effects which are reduced by the normal components of the electric fields. The effects of orientation of the electric fields and fluid depths on the stability configuration are also discussed. 
  Reference    Z. Naturforsch. 54a, 470—47665 (1999); received June 9 1999 
  Published    1999 
  Keywords    Hydrodynamic Stability, Convection and Heat Transfer, Electrohydrodynamics 
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 TEI-XML for    default:Reihe_A/54/ZNA-1999-54a-0470.pdf 
 Identifier    ZNA-1999-54a-0470 
 Volume    54 
2Author    Mohamed Fahmy, El-SayedRequires cookie*
 Title    Hydromagnetic Instability Conditions for Viscoelastic Non-Newtonian Fluids  
 Abstract    The effect of a horizontal magnetic field and a non-Newtonian stress tensor, as described by the Wal-ters B' model, on the instability of two second order fluids of high kinematic viscosities and viscoelas-ticities is investigated. For the potentially stable configuration, it is found that the system is stable or unstable for a wavenumber range depending on the kinematic viscoelasticity. For the potentially un-stable configuration, it is found that the stability criterion is dependent on orientation and magnitude of the magnetic field which is found to stabilize a certain range of the unstable configuration related to the viscoelasticity values. The behaviour of growth rates with respect to Alfven velocities are examined analytically, and it is found that the magnetic field has a dual role on the instability problem. For the exponentially varying stratifications, the system is found to be stable or unstable for the stable and un-stable stratifications under certain physical conditions, and the growth rates are found to increase or de-crease with increasing the stratification parameter values, according to some restrictions satisfied by the chosen wavenumbers range. 
  Reference    Z. Naturforsch. 55a, 460—466 (2000); received August 31 1999 
  Published    2000 
  Keywords    Hydrodynamic Stability, Non-Newtonian Fluid Flows, Magnetohydrodynamics 
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 TEI-XML for    default:Reihe_A/55/ZNA-2000-55a-0460.pdf 
 Identifier    ZNA-2000-55a-0460 
 Volume    55 
3Author    Mohamed Fahmy, El-SayedRequires cookie*
 Title    Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids  
 Abstract    The stability o f the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids o f equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent o f the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range o f the unstable configuration even in the presence o f the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a. 
  Reference    Z. Naturforsch. 56a, 416 (2001); received December 13 2000 
  Published    2001 
  Keywords    Hydrodynamic Stability, Non-Newtonian Fluid Flows, Magnetohydrodynamics 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0416.pdf 
 Identifier    ZNA-2001-56a-0416 
 Volume    56 
4Author    Mohamed Fahmy, El-SayedRequires cookie*
 Title    Electrohydrodynamic Kelvin-Helmholtz Instability of Two Rotating Dielectric Fluids  
 Abstract    A linear stability analysis of a novel electrohydrodynamic Kelvin-Helmholtz system consisting of the superposition of two uniformly rotating dielectric media is presented. The characteristic equation for such an arrangement is derived, which in turn yields a stability criterion for velocity differences of disturbances at a given rotation frequency. The conditions of stability for long and short wave perturbations are obtained, and their dependence on rotation, surface tension and applied electric field is discussed. Limiting cases for vanishing fluid velocities, rotation frequency, and applied electric field are also discussed. Under suitable limits, results of previous works are recovered. A detailed analysis for tangential and normal applied electric fields, in the presence and absence of surface charges, is carried out. 
  Reference    Z. Naturforsch. 53a, 17—26 (1998); received February 27 1997 
  Published    1998 
  Keywords    Hydrodynamic Stability, Electrohydrodynamics, Interfacial Instability, Rotational Flows, Dielectric Fluids 
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 TEI-XML for    default:Reihe_A/53/ZNA-1998-53a-0017.pdf 
 Identifier    ZNA-1998-53a-0017 
 Volume    53 
5Author    M. F. El-Sayed, D. K. CallebautRequires cookie*
 Title    Nonlinear Electrohydrodynamic Stability of Two Superposed Bounded Fluids in the Presence of Interfacial Surface Charges  
 Abstract    The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between two superposed dielectric fluids with uniform depths in the presence of a normal electric field, taking into account the interfacial surface charges. The evolution of the amplitude for travelling waves is governed by a nonlinear Schrödinger equation which gives the criterion for modulational instability. Numerical results are given in graphical form, and some limiting cases are recovered. Three cases, in the pure hydrodynamical case, depending on whether the depth of the lower fluid is equal to or greater than or smaller than the one of the upper fluid are considered, and the effect of the electric field on the stability regions is determined. It is found that the effect of the electric field is the same in all the cases for small values of the field, and there is a value of the electric field after which the effect differs from case to case. It is also found that the effect of the electric field is stronger in the case where the depth of the lower fluid is larger than the one of the upper fluid. On the other hand, the evolution of the am-plitude for standing waves near the cut-off wavenumber is governed by another type of nonlinear Schrödinger equation with the roles of time and space are interchanged. This equation makes it possible to determine the nonlinear dispersion relation, and the nonlinear effect on the cut-off wavenumber. 
  Reference    Z. Naturforsch. 53a, 217—232 (1998); received January 23 1998 
  Published    1998 
  Keywords    Hydrodynamic Stability, Electrohydrodynamics, Nonlinearity, Interfacial Instability, Dielectric Fluids, Surface Charges 
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 TEI-XML for    default:Reihe_A/53/ZNA-1998-53a-0217.pdf 
 Identifier    ZNA-1998-53a-0217 
 Volume    53 
6Author    Mohamed Fahmy, El-SayedRequires cookie*
 Title    The Effects of Collisions with Neutral Particles on the Instability of Two Superposed Composite Plasmas Streaming Through Porous Medium  
 Abstract    The effects of collisions with neutral atoms on the hydromagnetic stability of the plane interface separating two streaming superposed composite plasmas of uniform densities in a porous medium are investigated. In the absence of fluid velocities, it is found, for a potentially stable configuration, that the system remains stable, while for a potentially unstable configuraion, the unstable system becomes stable under a certain condition of the wavenumber depending on the values of the fluid densities, Alfven velocities, and the orientation of the magnetic field. The porosity of the porous medium does not have any significant effect on the stability criterion. In the presence of fluid velocities, it is found that, the instability criterion is independent of the permeability of the medium and the collision effects with neutral particles. The criterion determing the stability does not depend on the permeability of the medium but depends on the density of neutral particles. The porosity of the medium is found to have a significant effect on both the stability and instability criteria in this case. The role of the permeability of the medium, the collisional frequency, and the porosity of the porous medium on the growth rate of the unstable mode is examined analitically. Routh's test of stability is applied to confirm the above results. 
  Reference    Z. Naturforsch. 54a, 411—416 (1999); received April 19 1999 
  Published    1999 
  Keywords    Hydrodynamic Stability, Flows through Porous Media, Magnetohydrodynamics, Plasma flow, Instabilities in Plasma 
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 TEI-XML for    default:Reihe_A/54/ZNA-1999-54a-0411.pdf 
 Identifier    ZNA-1999-54a-0411 
 Volume    54