In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.

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The paper deals with the pulsating flow of an incompressible micropolar fluid through a channel bounded by permeable beds. The fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by micropolar fluid flow equations and that in the permeable regions by Darcy law. The Beavers–Joseph (BJ) slip boundary conditions are used at the interfaces of the permeable beds. The governing equations are solved analytically and the expressions for velocity, microrotation, mass flux and shear stress are obtained. The effects of diverse parameters on the velocity and microrotation are studied numerically and the results are presented through graphs.

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