BRINKMAN FLOW IN A COMPOSITE CHANNEL PARTIALLY FILLED WITH POROUS MEDIUM OF VARYING PERMEABILITY

In this paper our study is concerned with the fully developed laminar flow of a viscous, incompressible fluid in a composite parallel plate channel. The channel is divided into two equal regions. The lower region is filled with a porous layer of variable permeability and the upper region is clear. We assume that permeability of the porous region is a quadratically increasing function of thickness of porous layer. We investigate two important and most useful flows namely; (i) Poiseulle flow and (ii) Couette-Poiseulle flow through the composite channel. The Brinkman equation is used to analyze the flow in porous region and the Stokes equation is used for the fluid flow in clear region. Analytical solutions are obtained for the fluid velocity, volumetric flow rate, and skin friction. In the limiting case, when permeability of the porous region is infinite, the obtained results reduce to the classical results for Poiseulle and Couette-Poiseuille flow of viscous fluid in clear region. The effects of various parameters on the flow are discussed and presented graphically. Obtained results are useful in petroleum industry and hydraulic engineering.