Eur. Phys. J. Plus (2021) 136: 27
https://doi.org/10.1140/epjp/s13360-020-00990-9

Regular Article

Flow through membrane built up by impermeable spheroid coated with porous layer under the influence of uniform magnetic field: effect of stress jump condition

¹ Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, U.P., India
² Department of Mathematics, Noida Institute of Engineering and Technology, 201306, Greater Noida, India

^a pramodky@mnnit.ac.in

Received: 25 October 2020
Accepted: 7 December 2020
Published online: 3 January 2021

Abstract

The present problem is concerned with the axi-symmetrical flow of viscous Newtonian fluid over the membrane composed of spheroidal particles with impermeable core. Here, we analyzed the hydrodynamic permeability of the membrane when the steady, axi-symmetric, Newtonian fluid with uniform velocity $\tilde{\mathbf{U}}$ is passing through the membrane along z-axis. The Stokes flow takes place in the presence of transversely applied magnetic field $\tilde{\mathbf{B}}$ of uniform strength. A method named as cell model technique is used to reduce the problem of aggregates of particles into the problem of single particle. On the solid surface, no-slip condition and on the fluid–porous interface, continuity of velocity components & normal stress, discontinuity of shearing stress is employed. On the boundary of enveloping cell, we have employed Happel’s model, Kuwabara’s model, Kvashnin’s model, and Mehta–Morse’s model. The comparison of the hydrodynamic permeability and normalized mobility of the particles obtained by all above four well-known boundary conditions at hypothetical cell is shown graphically. In this work, we discussed about the various controlling parameters (fluid parameters) which can be used to control the hydrodynamic permeability of the membrane. Some previous results are also reviewed using the results of present problem and also shown the important comparisons with the former problems.