M. Devakar

This paper deals with an unsteady flow of a micropolar fluid sandwiched between Newtonian fluids through a horizontal channel. The governing time-dependent partial differential equations are solved...

The aim of this article is to study the unsteady flow of immiscible couple stress fluid sandwiched between Newtonian fluids through a horizontal channel. The fluids and plates are initially at rest. At an instant of time, a constant pressure gradient is applied along the horizontal direction to generate the flow. The time-dependent partial differential equations are solved numerically using the finite difference method. The continuity of velocities and shear stresses at the fluid-fluid interfaces has been considered. The obtained results are displayed through graphs and are discussed for various fluid parameters pertaining the flow. The volume flow rate is also obtained numerically for diverse fluid parameters and is presented through a table. It is noticed that fluid velocities increased with time and reached a steady state after a certain time level. Also, the presence of couple stresses reduced the fluid velocities. Volume flow rate increased with Reynolds number and is reduced by increase of ratio of viscosities.

The present paper is concerned with the study of fully developed flow of two immiscible micropolar and Newtonian fluids through a horizontal circular cylinder. Two immiscible fluids are assumed to occupy the horizontal circular cylinder; the micropolar fluid is in the inner cylindrical region while the Newtonian fluid is in the rest of the cylinder. The flow is generated due to a constant pressure gradient in the direction of the axis of the cylinder. Two steady flow situations have been studied: In the first situation, both micropolar and Newtonian fluid flow regions are nonporous, while in the second problem the Newtonian fluid region is assumed to be porous. In both problems, the relevant coupled differential equations governing the two-fluid flows are modeled. In addition to the classical no-slip condition on the boundary, the continuity of velocity and shear stress at the fluid-fluid interface is presumed for solving the governing equations analytically. The influence of various flow parameters on the fluid velocity and microrotation is studied, and the results are illustrated through graphs. It is found that, in both problems, the micropolarity parameter has a decreasing effect on the fluid velocity and microrotation. The results also indicate that the porosity parameter decreases the velocity of the fluid.