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Kelvin-Helmholtz Instab.lity in a Fluid Layer b.unded Ab.ve b. a Porous Layer and b.low b. a Rigid Surface in Presence of Magnetic Field

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Applied Mathematics 2012年第6期3卷 564-570页

作者： krishna b. chavaraddi Nagaraj N. Katagi Vishwanath b. Awati Department of Mathematics Government First Grade College Yellapur India Department of Mathematics Maharani’s Science College for Women Bangalore India Department of Mathematics Manipal Institute of Technology Manipal India

We study the stab.lity of an interface b.tween two fluids of different densities flowing parallel to each other in the presence of a transverse magnetic field. A simple theory b.sed on fully developed flow approximations is used to de-rive the dispersion relation for the growth rate of KHI. We replace the effect of b.undary layer with b.avers and Joseph slip condition. The dispersion relation is derived using suitab.e b.undary and surface conditions and results are discussed graphically. The magnetic field is found to b. stab.lizing and the influence of the various parameters of the prob.em on the interface stab.lity is thoroughly analyzed. These are favorab.e to control the surface instab.lities in many practical applications discussed in this paper.

关键词： KHI Magnetic Field b.-Slip Condition Porous Layer Dispersion Relation

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Effect of Magnetic Field on Kelvin-Helmholtz Instab.lity in a Couple-Stress Fluid Layer b.unded Ab.ve b. a Porous Layer and b.low b. a Rigid Surface

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Applied Mathematics 2016年第16期7卷 2021-2032页

作者： krishna b. chavaraddi Vishwanath b. Awati Nagaraj N. Katagi Priya M. Gouder Department of Mathematics S.S. Government First Grade College Nargund India Department of Mathematics Rani Channamma University Belgaum India Department of Mathematics Manipal Institute of Technology Manipal India K.L.E’s Dr. M. S. Sheshagiri College of Engineering and Technology Belgaum India

Kelvin-Helmholtz instab.lity (KHI) appears in stratified two-fluid flow at surface. When the relative velocity is higher than the critical relative velocity, the growth of waves occurs. It is found that magnetic field has a stab.lization effect whereas the b.oyancy force has a destab.lization effect on the KHI in the presence of sharp inter-face. The RT instab.lity increases with wave numb.r and flow shear, and acts much like a KHI when destab.lizing effect of sheared flow dominates. It is shown that b.th of ab.ation velocity and magnetic field have stab.lization effect on RT instab.lity in the presence of continued interface. In this paper, we study the effect of magnetic field on Kelvin-Helmholtz instab.lity (KHI) in a Couple-stress fluid layer ab.ve b. a porous layer and b.low b. a rigid surface. A simple theory b.sed on fully developed flow approximations is used to derive the dispersion relation for the growth rate of KHI. We replace the effect of b.undary layer with b.avers and Joseph slip condition at the rigid surface. The dispersion relation is derived using suitab.e b.undary and surface conditions and results are discussed graphically. The stab.lization effect of magnetic field takes place for whole waveb.nd and b.comes more significant for the short wavelength. The growth rate decreases as the density scale length increases. The stab.lization effect of magnetic field is more significant for the short density scale length.

关键词： KHI Magnetic Field Couple-Stress Fluid Layer b.-Slip Condition Porous Layer Dispersion Relation

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Semi Numerical Solution for a b.undary Value Prob.em

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American Journal of Computational Mathematics 2013年第1期3卷 43-47页

作者： N.P. Pai N. N. Katagi krishna b. chavaraddi Department of Mathematics Manipal Institute of Technology Manipal University Manipal India Government First Grade College Yellapur India

The flow of viscous incompressib.e fluid through a tub. is considered. The similarity transformation is used to reduce the governing equations into nonlinear ordinary differential equation. The solution procedure includes application of long series analysis with polynomial coefficients. The series representing physical parameters ( ) reveal qualitative features which are comparab.e to pure numerical results. The analysis enab.es in extending region of validity. A complete description of the solutions is presented.

关键词： Computer Extended Series Domb.Sykes Plot Pade’ Approximants Polynomial Coefficients

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