Effect of Magnetic Field on Hydrodynamic Permeability of Biporous Membrane Relative to Micropolar Liquid Flow
Satya Deo, Deepak Kumar Maurya, А. Н. Филиппов
Abstract
This work concerns the effect of magnetic field on hydrodynamic permeability of biporous membrane relative to the flow of micropolar liquid using four known cell models. The governing equations of micropolar liquid are expressed in modified form using Nowacki’s approach. Fluid velocity, microrotation vectors, shear stresses and couple stresses, which are combinations of modified Bessel functions of first and second kinds, are investigated. Arbitrary integration constants are determined by applying analyticity condition at origin, continuity of velocities (both linear and microrotational), continuity of stresses (both shear and couple) at the porous interfaces along with an equivalent condition to Happel, Kuwabara, Kvashnin and Mehta–Morse models at the cell surface. Expressions of volumetric flow rate, superficial/filtration velocity and hydrodynamic permeability are reported. The graphs of hydrodynamic permeability, fluid velocity and microrotation are plotted under the effect of micropolar parameter, Hartmann number, permeability parameters and conductivity ratio parameters, and discussed for different values of these parameters.