Flow past composite cylindrical shell of porous layer with a liquid core: magnetic effect
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(2020) 42:452
TECHNICAL PAPER
Flow past composite cylindrical shell of porous layer with a liquid core: magnetic effect Krishna Prasad Madasu1 · Tina Bucha1 Received: 18 December 2019 / Accepted: 28 July 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract The creeping flow of a magnetic fluid perpendicular to a porous cylindrical shell is investigated, employing the unit cell model. The viscous fluid is assumed to be flowing in three zones divided as fluid, annular porous, and cavity regions, respectively. We apply a uniform magnetic field in a transverse direction of flow and then emphasize the influence of the Hartmann layers which are developed in their vicinity. Modified Stokes and modified Brinkman’s equations are employed in the liquid and porous regions, respectively. Happel and Kuwabara cell models are used as the interface conditions at the cell surface, and at the fluid–porous interface, continuity of velocity components, continuity of normal stresses, and stress jump condition for tangential stresses are applied. An expression for Kozeny constant for the cylindrical shell is presented. Representation of Kozeny constant under the influences of the pertinent parameters such as Hartmann numbers, stress jump coefficient, fractional void volume, viscosity ratios, permeability, and separation is displayed through graphs and a table. The results are compared with the cases which do not involve magnetic effect. They reveal the strong impact of Hartmann’s numbers on the resisting force experienced on the cylindrical shell. The results agree well with previous available works. Keywords Cylindrical particle · Stokes flow · Hartmann number · Brinkman’s model · Kozeny constant
1 Introduction In various natural and artificial flows, magnetic fields seem to influence the characteristics of the fluid flow. Magnetohydrodynamics is a branch of science which deals with the flow of conducting fluid under magnetic influences. A combination of fluid mechanics and electromagnetic field theory results in magnetohydrodynamics (MHD). The presence of the magnetic fields generates an electromagnetic force known as the Lorentz force, which acts on the fluid and alters the behavior of the flow [1]. MHD flow has attracted many researchers owing to its boundless applications in various fields such as biological science, astrophysics, geophysics, metallurgy, etc. One of its practical applications includes its Technical Editor: Daniel Onofre de Almeida Cruz. * Krishna Prasad Madasu [email protected]; [email protected] Tina Bucha [email protected] 1
Department of Mathematics, National Institute of Technology, Raipur 492010, India
scope to suppress the flow rate. Due to its enormous physical importance, its applications are found in several domains of engineering including microelectronic devices, pumps, mixers, nuclear reactors, purification of molten metals, microfluidics, coolers of nuclear reactors, accelerators, etc. Magnetic fields are also used to monitor the convective heat tran
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