Magnetohydrodynamic analysis of a couple stress fluid porous cylinder enclosed by a Newtonian shell using Happel, Kvashnin, and Mehta–Morse models

This study presents a comprehensive analytical investigation of axisymmetric, steady, and incompressible flow within a porous cylindrical core saturated with a couple stress fluid, concentrically enclosed by a Newtonian fluid layer under the influence of a uniform magnetic field. The Brinkman-extended Darcy formulation is employed to describe the hydrodynamic behavior in the porous region, assuming isotropic permeability. The governing equations are expressed using a stream function approach and are solved analytically through the method of separation of variables, incorporating modified Bessel functions of the first and second kinds. To reflect various physical boundary scenarios, three classical cell models, Happel, Kvashnin, and Mehta–Morse, are imposed at the outer interface of the Newtonian fluid layer. Closed-form solutions are derived for the dimensionless velocity components, pressure distribution, tangential stresses, and couple stress tensors. The integration constants are evaluated by enforcing the continuity of velocity and stress at the fluid-porous interface, along with the appropriate outer boundary conditions, using symbolic computation via Mathematica. An explicit expression for the drag force exerted on the porous core and its associated drag coefficient is established. A parametric analysis is conducted to explore the effects of the viscosity ratio, permeability, couple stress parameter, and volume fraction on the velocity profiles, pressure field, and drag characteristics. The results indicate that the Mehta–Morse condition produces a more pronounced impact on the streamline topology and flow resistance when compared to the Happel and Kvashnin models. These findings have potential applications in biomedical transport, enhanced oil recovery, and magnetic drug targeting systems. They contribute valuable insights into magnetically influenced couple stress fluid flow in porous media and are inspired by emulsion hydrodynamics encountered in chemical engineering, wherein complex rheological behavior frequently coexists with the influence of porous media characteristics.