Role of transverse magnetic field on flow of immiscible micropolar fluids through coaxial horizontal cylindrical membrane using cell models

The current work examines the hydromagnetic flow of two immiscible micropolar fluids through horizontal coaxial cylindrical cells, which are made up of a hypothetical cylindrical cell enclosing a solid impermeable cylindrical core covered in a porous layer. Fluid motion is occurring along the common axis of cylindrical shells, and a uniform magnetic field is employed perpendicular to the direction of fluid flow. The appropriate boundary conditions involving the equivalent form of four well-known cell models are employed to analyze the problem. For regions I and II, analytical expressions for the microrotations, stresses, and velocities of micropolar fluids have been established. Additionally, the general (analytical) expression for microrotation and velocity is emphasized. The volume of fluid particles moving through a swarm of porous particles in unit time is calculated using the mathematical expression for hydrodynamic permeability. For a range of flow parameters such as micropolar parameter, conductivity ratio, Hartmann number, and permeability parameter, the graphical exhibition of hydrodynamic permeability, fluid velocity, and microrotation is drawn. At the porous interface, the numerical values of hydrodynamic permeability, tangential stresses, couple stresses, microrotations, and velocities are evaluated. Tables representing different values of the micropolar parameter, conductivity ratio, Hartmann number, and permeability parameter are used to display the numerical data and to validate the graphs. The numerical estimates obtained by the experiments in laboratory are matching with the graphical data. The obtained results are an extension of results reported by Yadav et al. [Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field, Math. Methods Appl. Sci. 43, 1925–1937 (2020)] and Deo et al. [Influence of magnetic field on micropolar fluid flow in a cylindrical tube enclosing an impermeable core coated with porous layer, Colloid J. 82, 649–660 (2020)].