In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

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The present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro-rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar–Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc.

The present problem is concerned with the flow of micropolar/Eringen fluid sandwiched between two Newtonian fluid layers through the horizontal porous channel. The flow in both the regions is steady, incompressible and the fluids are immiscible. The flow is driven by a constant pressure gradient and a magnetic field of uniform strength is being applied in the direction perpendicular to the flow. The flow of electrically conducting fluids, in the three regions, is governed by the Brinkman equation with the assumption that the effective viscosity of each fluid is the same as the viscosity of the fluid. No-slip conditions at the end of the plates, continuity of velocity, continuity of shearing stress and constant rotational velocity at the interface have been used as the boundary conditions to get the solution of the problem considered. The numerical values of the solution obtained are used to analyse the effect of various transport parameters, such as permeability of porous region, magnetic number, viscosity ratio etc. on the velocity profile and micro rotational velocity profile graphically. Also, the variations in the flow rate and the wall shear stress, with respect to the governing parameters, are presented in tabular form.

This paper concerns with the flow of viscous, steady, incompressible and immiscible fluids of different viscosities in the channel formed by two infinite parallel plates. The flow is driven by the constant pressure gradient in the presence of the transverse magnetic field of uniform strength. Both the regions of the channel are filled with the highly porous media and having different permeabilities. The flow through the channel is governed by the Brinkman equation with the inclusion of inertia term. No-slip conditions at the end of plates, continuity of velocity and continuity of shearing stress at the interface have been used as boundary conditions to get the solution of the considered problem. The effect of various fluid parameters like permeability and porosity of porous regions, magnetic number, etc., on the flow velocity profile, the flow rate has been discussed graphically. Also, comparative study of the problem has been done.