The paper deals with the flow of two immiscible couple stress fluids between two homogeneous permeable beds. The flow is considered in two zones: zone I and II contain free flow of two immiscible couple stress fluids between two permeable porous beds at the bottom and top. The flow in the free channel bounded by two permeable beds is assumed to be governed by Stokes's couple stress fluid flow equations and that in the permeable beds by Darcy's law. The continuity of velocity, vorticity, shear stress and couple stress are imposed at the fluid-fluid interface and Beavers-Joseph (BJ) slip boundary conditions are employed at the fluid-porous interface. The equations are solved analytically and the expressions for velocity, skin friction and volumetric flow rate are obtained. The effects of the physical governing parameters on velocity are investigated.

In this paper, we study laminar viscous fluid flow about a circular cylinder placed in a square cavity of uniform crosssection generated by applying injection/suction at the opposite-side walls. Constant temperature is maintained on the walls without suction and on the boundary of the cylinder and constant heat flux is maintained on the walls with suction. In the literature, the problems dealing with flow past a cylinder in a cavity are very a few. The fluid flow pattern in the form of stream lines and temperature distribution in the form of isothermal lines are studied. The flow is assumed to be Stokesian and hence the resulting coupled equations for stream function and vorticity, and the energy equation for temperature are solved numerically by using the standard 5-point formula. Fictitious nodes are introduced for derivative boundary conditions for stream function by using central-difference scheme and 3-point backward difference formula is used for derivative boundary conditions on temperature. It is observed that the temperature increases drastically when a cylinder is kept in the cavity, i.e. it makes the quick heat transfer. Similarly, when a cylinder is placed near to a corner, the heat transfer is more rapid. Suction enhances the heat transfer.

The flow generated by performing longitudinal and torsional oscillations of a porous circular cylinder which is subjected to constant suction/injection at the surface of the porous cylinder is studied. A finite difference method is proposed to analyse the velocity components and micro-rotation components, in an infinite expanse of an incompressible micropolar fluid. The effects of cross viscosity parameter, couple stress parameter, Reynolds number and Gyration parameter on the axial and torsional velocity components and on the micro-rotation components are shown graphically. Drag force acting on the wall of the cylinder is derived and the effects of micropolar parameters and suction parameter on the drag are shown graphically.

The laminar viscous fluid flow past a circular cylinder placed in a square cavity of a uniform cross‐section is generated by applying injection/suction at the adjacent sidewalls. The temperature on the side walls without suction and on the boundary of the cylinder is kept constant, and constant heat flux is maintained on the walls with suction. The streamline flow pattern and isothermal lines are drawn. The flow is assumed to be Stokesian. Hence, the resulting biharmonic equation is solved for stream function by expressing it in two coupled equations, and a 5‐point formula is used to solve these equations. Fictitious nodes are introduced for derivative boundary conditions for stream function by using a central difference scheme, and a 3‐point backward difference formula is used for derivative boundary conditions on temperature.

The flow generated by performing longitudinal and torsional oscillations of a porous circular cylinder which is subjected to constant suction/injection at the surface of the porous cylinder is studied. A finite difference method is proposed to analyse the velocity components and micro-rotation components, in an infinite expanse of an incompressible micropolar fluid. The effects of cross viscosity parameter, couple stress parameter, Reynolds number and Gyration parameter on the axial and torsional velocity components and on the micro-rotation components are shown graphically. Drag force acting on the wall of the cylinder is derived and the effects of micropolar parameters and suction parameter on the drag are shown graphically.