Flow a couple-stress fluid through an annular curvilinear channel with one semi-porous wall

The flow of a couple -stress fluid in an annular curvilinear channel with a porous insert is considered. The porous insert is connected with a inner impermeable rotating surface which approaches the outer fixed surface of an annular curvilinear channel. The equations of motion governing of the flow reduce to the coupled Reynolds and Poisson equations which can be uncoupled by using the Morgan-Cameron approximation and closed-form solution can be obtained. Expressions for the pressure distribution in a channel clearance are given. As an example the flow through the channel modelled by two concentric spherical surfaces is discussed.