THE STABILITY OF SOME PHYSICALLY REALISTIC MODELS USING CHANDRASEKHER'S TECHNIQUES (original) (raw)
2016, isara solutions
https://doi.org/10.32804/CASIRJ
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Abstract
The paper examines the stability of an in compressible, non-viscous fluid with horizontal magnetic field and vertical rotation confined between two parallel plates. Here an attempt has been made to investigate the stability of some physically realistic models using Chandrashekhar's technique. A number of results have been obtained which help is a better understanding of a physical situation.
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Heat Transfer-Asian Research, 2019
The current article aims at investigating the effect of a periodic tangential magnetic field on the stability of a horizontal flat sheet. The media were considered porous, the three viscous-fluid layers were initially streaming with uniform velocities, and the magnetic field admitted the presence of free-surface currents. Furthermore, the transfer of mass and heat phenomenon was taken into account. The analysis, in this paper, was followed by the viscous potential theory. Moreover, the stability of the boundary-value problem resulted in coupled secondorder linear differential equations with damping and complex coefficients. In regard to the uniform and periodic magnetic field, the standard normal mode approach was applied to deduce a general dispersion relation and judge the stability criteria. In addition, several unfamiliar cases were reported, according to appropriate data choices. The stability conditions were theoretically analyzed, and the influences of the various parameters in the stability profile were identified through a set of diagrams. In accordance wth the oscillating field, the coupled dispersion equations were combined to give the established Mathieu equation. Therefore, the governed transition curves were, theoretically, obtained. Finally, the results were numerically confirmed.
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MATEC Web of Conferences, 2012
The linear stability of plan Poiseuille flow of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field is investigated numerically. The fourth-order Sommerfeld equation governing the stability analysis is solved by spectral method with expansions in lagrange's polynomials, based on collocation points of Gauss-Lobatto. The critical values of Reynolds number, wave number and wave speed are computed. The results are shown through the neutral curve. The main purpose of this work is to check the combined effect of magnetic field and fluid's elasticity on the stability of the plane Poiseuille flow. Based on the results obtained in this work, the magnetic field is predicted to have a stabilizing effect on the Poiseuille flow of viscoelastic fluids. Hence, it will be shown that for second-order fluids (K < 0), the critical Reynolds numbers Re c increase when the Hartman number M increases for different values of elasticity number K, which is a known result. The more important result we have found, concerning second-grade fluids (K > 0) is that the critical Reynolds numbers Re c increase when the Hartman number M increases for certain value of elasticity number K and decrease for others. The latter result is in contrast to previous studies.
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The linear stability of a plane Poiseuille flow of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field is investigated numerically. The fourth-order modified Orr-Sommerfeld equation governing the stability analysis is solved by a spectral method with expansions in Lagrange polynomials, based on collocation points of Gauss-Lobatto. The combined effects of a magnetic field and fluid's elasticity on the stability picture of the plane Poiseuille flow are investigated in two regards. Firstly, the critical values of a Reynolds number and a wavenumber, indicating the onset of instabilities, are computed for several values of a magnetic Hartman number, M, and at different values of an elasticity number, K. Secondly, the structure of the eigenspectrum of the second-order and second-grade models in the Poiseuille flow is studied. In accordance to previous studies, the magnetic field is predicted to have a stabilizing effect on the Poiseuille flow of viscoelastic fluids. Hence, for second-order (SO) fluids for which the elasticity number K is negative, the critical Reynolds number Re c increases with increasing the Hartman number M, for various values of the elasticity number K. However, for second-grade (SG) fluids (K > 0), the critical Reynolds number Re c increases with increasing the Hartman number only for certain values of the elasticity number K, while decreases for the others.
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Article history: Received: 10 October 2018 Accepted: 18 November 2018 In the present work, the Rayleigh-Taylor instability of two rotating superposed magnetized fluids within the presence of a vertical or a horizontal magnetic flux has been investigated. The nonlinear theory is applied, by solving the equation of motion and uses the acceptable nonlinear boundary conditions. However, the nonlinear characteristic equation within the elevation parameter is obtained. This equation features a transcendental integro-Duffing kind. The homotopy perturbation technique has been applied by exploitation the parameter growth technique that results in constructing the nonlinear frequency. Stability conditions are derived from the frequency equation. It's illustrated that the rotation parameter plays a helpful result. It's shown that the stability behavior within the extremely uniform rotating fluids equivalents to the system while not rotation. A periodic solution for the elevation functi...
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This paper elucidates a trend in solving nonlinear oscillators of the rotating Kelvin-Helmholtz instability. The system is constituted by the vertical flux or the horizontal flux. He’s multiple-scales perturbation methodology has been applied and therefore the system is represented by a generalized homotopy equation. This approach ends up in a periodic answer to a nonlinear oscillator with high nonlinearity. The cubic-quintic nonlinear Duffing equation is obligatory as a condition to uniformly answer. This equation is employed to derive the stability criteria. The transition curves are plotted to investigate the stability image. It's shown that the angular velocity suppresses the instability. The tangential flux plays a helpful role, whereas the vertical field encompasses a destabilizing influence. Within the existence of the rotation, the velocity ratio reduces stability configuration.
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