Multiphase flow of three immiscible non-Newtonian fluids through porous cylindrical annulus under magnetic field

Abstract

The present work concerns the flow of three immiscible non-Newtonian fluids: a couple stress fluid, a micropolar fluid and a Jeffery fluid through a cylindrical pipe under applied uniform magnetic field in the direction perpendicular to the flow. The Jeffery fluid flows through the deepest cavity, while the couple stress fluid and the micropolar fluid flow through the outer and middle cylindrical shells, respectively. Jeffery’s equations of motion govern the flow of Jeffery fluid, while the well-known Brinkman equation and Eringen’s field equations govern the movement of couple stress fluid and micropolar fluid, respectively. Analytical expressions for microrotational velocity, flow rate, shear and couple stresses, and velocity are obtained using appropriate boundary conditions. Graphical and detailed studies have been made on the effects of several parameters on fluid velocity, microrotational velocity, couple stress, and flow rate. These parameters include porosity, permeability, couple stress, micropolar, viscosity ratios, and electrical conductivity ratios.