Ahmed Y. Ghaly

Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity

Abstract The effect of variable viscosity, chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate has been analyzed. The fluid viscosity is assumed to vary as an inverse linear function of temperature. By means of the similarity solutions, deviation of the velocity, concentration and temperature fields as well as the skin friction and heal transfer results from their constant values are determined numerically by using Chebyshev finite difference method. The effects of variable viscosity, chemical reaction and Schmidt number parameters on the velocity, concentration and temperature profiles have been studied.

Radiation effects on a certain MHD free-convection flow

Abstract Free-convection heat and mass transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity, temperature and concentration. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, Prandtl number, Grashof number and Schmidt number on the profiles of the velocity components, temperature and concentration. Numerical results show that the radiation have significant influences on the velocity and temperature profiles, Nusselt number and local shear stress. The results indicate that the velocity, fluids temperature and local shear stress decrease as the radiation parameter increases. The Nusslet number increases as the radiation parameter increases.

Nonlinear interfacial stability for magnetic fluids in porous media

Abstract The weakly nonlinear stability is employed to analyze the interfacial phenomenon of two magnetic fluids in porous media. The effect of an oblique magnetic field to the separation face of two fluids is taken into account. The solutions of equations of motion under nonlinear boundary conditions lead to deriving a nonlinear equation in terms of the interfacial displacement. This equation is accomplished by utilizing the cubic nonlinearity. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and nonlinear Ginzburg–Landau equation, for the higher-order problem, describing the behaviour of the system in a nonlinear approach. Regions of stability and instability are identified for the magnetic field intensity versus the wave number. It is found that the oblique magnetic filed has a stabilizing influence under some certain conditions for the directions of the magnetic fields. The resistance coefficient has a destabilizing influence in the linear description. Further, in the nonlinear scope, the increase of the resistance parameters plays both stabilizing and destabilizing role in the stability criteria.

Destabilizing effect of time-dependent oblique magnetic field on magnetic fluids streaming in porous media

The present work studies Kelvin-Helmholtz waves propagating between two magnetic fluids. The system is composed of two semi-infinite magnetic fluids streaming throughout porous media. The system is influenced by an oblique magnetic field. The solution of the linearized equations of motion under the boundary conditions leads to deriving the Mathieu equation governing the interfacial displacement and having complex coefficients. The stability criteria are discussed theoretically and numerically, from which stability diagrams are obtained. Regions of stability and instability are identified for the magnetic fields versus the wavenumber. It is found that the increase of the fluid density ratio, the fluid velocity ratio, the upper viscosity, and the lower porous permeability play a stabilizing role in the stability behavior in the presence of an oscillating vertical magnetic field or in the presence of an oscillating tangential magnetic field. The increase of the fluid viscosity plays a stabilizing role and can be used to retard the destabilizing influence for the vertical magnetic field. Dual roles are observed for the fluid velocity in the stability criteria. It is found that the field frequency plays against the constant part for the magnetic field.