Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

Abstract

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no-slip condition, continuity of velocity and stresses at interfaces along with Happle's no-couple stress condition as the boundary conditions. The expressions for the linear velocity, micro-rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro-rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work. boundary, problem could not have simple analytical solution. To overcome the disadvantages of Uchida's model, Happel 4 and Kuwabara 5 developed a model in which the particle and the outer hypothetical cell are of same geometry. According to Happel 4 and Kuwabara, 5 there is no-stress and nil vorticity at the boundary of cell surface respectively. Later on, Kvashnin 6 and Mehta-Morse 7 followed the same geometry concept with different boundary conditions at the cell's surface. The four models i.e. Happel's, Kuwabara's, Kvashnin's and Mehta-Morse's model respectively gave path to many authors to formulate and solve the problem of flow through assemblage of porous particles with numerous applications in real-life. Vasin et al. 8 investigated the flow around spherical particles covered with porous shell and calculated the hydrodynamic permeability of a membrane. They used different boundary conditions at outer hypothetical cell and compared the obtained results. Deo et al. 9 studied the flow through a concentric cluster of porous cylindrical particles with solid core using Happel's cell model technique. Yadav et al. 10 studied the Stokes flow of fluid through a porous membrane composed of porous spherical particles enclosing a solid core and they solved the problem using cell model technique. They calculated the hydrodynamic permeability of a membrane for each four aforementioned cell models and compared them. Deo et al. 11 investigated the hydrodynamic permeability of a membranes built up by porous cylindrical/spherical particles with impermeable core using cell models technique. They made use of jump condition at fluid-porous interface which was suggested by Ochoa-Tapia-Whitaker 12,13 and observed the variation in the membrane's permeability with respect to the other parameters. Tiwari et al. 14 analyzed the Stokes flow of Newtonian fluid through aggregates of non-homogeneous porous cylindri...

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