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The present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique. Traditional boundary conditions on hypothetical cell surface were added with an additional condition: the no spin condition / no couple stress condition. Expressions for velocity and microrotation vector components have been obtained analytically. Effect of various parameters such as particle volume fraction, permeability parameter, micropolarity number etc.on hydrodynamic permeability of membrane has been discussed.

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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.