Modeling of magnetized immiscible micropolar-Newtonian fluid flow through co-rotating cylinders: Homotopy analysis method

In this work, the authors have analyzed the magneto-hydrodynamic (MHD) flow of non-miscible micropolar-Newtonian fluids through annular regions of three co-rotating concentric cylinders under the impact of stress jump condition. Here, it is considered that the inner and outer cylinders are impermeable while the middle cylinder is anisotropic permeable, and a non-isotropic porous material is filled between inner and middle cylinders. The Newtonian fluid is flowing between inner and middle cylinders, however, the non-miscible micropolar fluid takes place through a region composed of middle and outer cylinders. The motion of non-miscible micropolar-Newtonian fluids in rotating cylinders takes place due to the rotation of inner, middle, and outer cylinders along with the pressure gradient in the presence of a uniform magnetic field. Here, Brinkman model is used for the flow of Newtonian fluid through the non-isotropic porous material. In this work, the Navier slip condition and stress jump boundary condition are employed along with the continuity of the velocities. Here, the authors have also used hyperstick boundary conditions at the boundary of the outer cylinder and at the interfaces of two immiscible fluid flows. The governing equations are solved by the semi-analytic Homotopy Analysis Method (HAM). Here, the authors examined the variation in the pressure, head loss, radial velocity, tangential velocity, micro-rotational velocity, interfacial velocity, and stream function with respect to Hartmann number, stress jump conditions, material parameter, slip parameter, permeability parameter, couple stress parameter, and porosity. From the present model, it has been demonstrated that the interfacial velocity of immiscible Newtonian-micropolar fluid is increased with increasing the permeability and decreasing the porosity of porous medium, while the radial and tangential velocities of immiscible fluid increased by increasing the porosity and permeability of porous medium. It is also noticed that the material parameter enhanced the pressure, but the couple stress parameter decreased the head loss of micropolar fluid. The present model can be used in thermal enhancement and journal bearing to understand the nature of micropolar fluid as a lubricant in blood/plasma flow in arteries.