Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

Abstract

The current study concerns, the effect of a horizontal magnetic field on the stability of three horizontal finite layers of immiscible fluids in porous media. The problem examines few representatives of porous media, in which the porous media are assumed to be uniform, homogeneous and isotropic. The dispersion relations are derived using suitable boundary and surface conditions in the form of two simultaneous Mathieu equations of damping terms having complex coefficients. The stability conditions of the perturbed system of linear evolution equations are investigated both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in detail in terms of various parameters governing the flow on the stability behavior of the system such as the streaming velocity, permeability of the porous medium and the magnetic properties. In the special case of uniform velocity, the fluid motion has been displayed in terms of streamlines concept, in which the streamlines contours are plotted. In the uniform velocity motion, a fourth order polynomial equation with complex coefficients is obtained. According to the complexity of the mathematical treatments, when the periodicity of the velocity is taken into account, the method of multiple scales is applied to obtain stability solution for the considered system. It is found that a stability effect is found for increasing, the magnetic permeability ratio, the magnetic field, and the permeability parameter while the opposite influence is observed for increasing the upper layer velocity.

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

“…It should be noted that, in the absence of the periodicity of the magnetic field (), the above equations are similar to those obtained by AlHamdan and Alkharashi …”

“…They demonstrated that the irrotational shearing stresses have a stabilizing effect in the presence of heat and mass transfer throughout the interface. In addition, AlHamdan and Alkharashi discussed the problem of the stability characterization of three permeable layer models under a magnetic field. In this study, they ignored the stability analysis of a uniform streaming.…”

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

“…This means that the viscosity proportion has a stabilizing influence, particularly for larger wave numbers. The same results correspond to the linear stability studies earlier obtained by Moatimid et al [5], El-Dib and Ghaly [27], and AlHamdan, and Alkharashi [29]. Physically, this stabilizing influence is popular in the casting process, as the aim is to keep the free surface of the liquid quiescent, thus avoiding the entrainment of surface debris.…”

“…In other words, it indicates how straightforwardly a fluid is affected by an induced magnetic field. The findings of the examination of the linear stability of three horizontal finite layers of immiscible fluids in porous media are in good agreement with AlHamdan, and Alkharashi [29].…”

“…( 35)-( 37) agree with the results earlier obtained by Moatimid [28] for a single interface between two ferro-fluids. Additionally, in the same situation, AlHamdan, and Alkharashi [29] derived analogous arguments.…”