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EFFECT OF MAGNETIC FIELDS ON THE MOTION OF POROUS PARTICLES FOR HAPPEL AND KUWABARA MODELS

卷 21, 册 7, 2018, pp. 637-664
DOI: 10.1615/JPorMedia.v21.i7.50
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摘要

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous spheres subject to a uniform transverse magnetic field is analytically studied through the use of unit cell models. Both flows are also considered parallel and perpendicular to assemblages of porous circular cylinders-in-cell models under the effect of uniform magnetic fields. At the porous-medium/clear-fluid interface, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. The flow inside the porous particleis governed by the Brinkman model and the flow in the fictitious envelope medium is governed by Stokes equations with different Hartman numbers in the flow regions. The analytical solutions for the hydrodynamic drag force exerted on the porous particle-in-cell models, the volume flow rate of fluid through the cylindrical regions, and the expressions of Kozeny constant are obtained for parallel and perpendicular flow. For various cases, the Kozeny constant is analyzed against the fractional void volume, the Hartmann numbers,the viscosity ratio, the stress jump coefficient, and a coefficient that is proportional to the permeability of the porous region. Streamlines in and around the porous particle are constructed for the Happel and Kuwabara unit cell models at different values of relevant physical parameters. In the limits of the motions of impermeable spheres and cylinders in the cell surface and near the cell surface with a small curvature, the numerical values of the Kozeny constant are in good agreement with the available values in the literature.

对本文的引用
  1. Krishna Prasad Madasu, Bucha Tina, Effect of Magnetic Field on the Steady Viscous Fluid Flow Around a Semipermeable Spherical Particle, International Journal of Applied and Computational Mathematics, 5, 3, 2019. Crossref

  2. Madasu Krishna Prasad, Bucha Tina, Impact of magnetic field on flow past cylindrical shell using cell model, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 8, 2019. Crossref

  3. Madasu Krishna Prasad, Bucha Tina, Creeping flow of fluid sphere contained in a spherical envelope: magnetic effect, SN Applied Sciences, 1, 12, 2019. Crossref

  4. Saad E.I., Time-varying Brinkman electrophoresis of a charged cylinder-in-cell model, European Journal of Mechanics - B/Fluids, 79, 2020. Crossref

  5. Madasu Krishna Prasad, Bucha Tina, MHD Viscous Flow Past a Weakly Permeable Cylinder Using Happel and Kuwabara Cell Models, Iranian Journal of Science and Technology, Transactions A: Science, 44, 4, 2020. Crossref

  6. Prasad M Krishna, Bucha Tina, Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models, Pramana, 94, 1, 2020. Crossref

  7. Madasu Krishna Prasad, Bucha Tina, Influence of MHD on micropolar fluid flow past a sphere implanted in porous media, Indian Journal of Physics, 95, 6, 2021. Crossref

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  11. Namdeo Ravendra Prasad, Gupta Bali Ram, Impact of Magnetic Field on the Flow of a Conducting Fluid Past an Impervious Spheroid Embedded in Porous Medium, International Journal of Applied and Computational Mathematics, 8, 3, 2022. Crossref

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