NONLINEAR INSTABILITY OF FERROFLUIDS IN POROUS MEDIA UNDER A HORIZONTAL MAGNETIC FIELD | ||
| Delta Journal of Science | ||
| Article 1, Volume 28, Issue 1, July 2004, Pages 1-32 PDF (2.11 M) | ||
| Document Type: Research and Reference | ||
| DOI: 10.21608/djs.2004.158523 | ||
| Authors | ||
| ABDEL RAOUF F. ELHEFNAWY1; MAHMOUD A. MAHMOUD2; MOSTAFA A. A. MAHMOUD2; GAMAL M. KHEDR2 | ||
| 1DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, BANHA UNI VERSITY, BANHA 13518, EGYPT | ||
| 2DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, BANHA UNIVERSITY, BANHA 13518, EGYPT | ||
| Abstract | ||
| The nonlinear instability analysis of the free surface of two weak VIscous magnetic fluids, subjected to vertical vibrations and a horizontal magnetic Tield, has been examined in porous media. Ihe two fluids are immiscible in all properties. Both have Tinite- thickneSs, homogeneous, and incompressible fluids. Although the motionS are assumed to be irrotational, weak VIscous erects are include d in the boundary conditions of the normal stress tensor balance. The influence of both surface tension and gravity torce is also considered. The method of multiple scale perturbations is used to obtain a dispersion relation for the lin ear theory and a Gin zburg- Landau equation for the nonlinear theory, describing the behaviour of the System. nere 1S also the obtaining of a nonlinear diffusion equation, describing the evolution of the wave packets, near the marginal state. Further, the online ar Schrodin ger equation Is obtained when the effect of both the viscosity and Darcy's coefficients are neglected. The stability conditions are discussed and the interplay between the applied magnetic field and several other factors in determining the interface behavior is analyzed Stability analysis and numerical calculations are used to describe linear and nonlinear stages of the interface evolution. The numerical calculations indicate the existence or more than a new region of stability and instability due to the noniinear effects. In the linear theory, it is found that the horizpntal magnetic field decreases as the wave number increases. his'means that the magnetic field has a stabilizing influence on the wave motion. While the vis co sity and Darcy's coefficients have a destabilizing effect. In the nonlinear theory, it is found that these parameters have an important role in the stability criterion of the problem. | ||
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