Effect of Constant Wall Permeability and Porous Media on the Creeping Flow through Round Vessel

The present study reports the influence of constant wall permeability and porous media on the creeping flow passing through round vessel. The inverse method is used to obtain the exact solution. To understand the behaviour of flow, the mathematical expression for stream function, velocity components, wall shear stress, pressure distribution, flow rate and leakage flux are provided. Our main purpose here is to demonstrate the constant permeability of the wall and of porous media on the existence of flow properties because of its applicability "flow through permeable renal disease tubule" in biological sciences. Flow properties at an entrance, mid place and at exit are discussed graphically for involved parameters and it is observed that low permeability of porous medium slow down the velocity of fluid along axial coordinate while minor change is observed along radial coordinate. While constant wall permeability shows the opposite behaviour on the same properties. Fractional permeation rate from the diseased vessel, wall permeation velocity, pressure drop and leakage flow rate are tabulated for physiological data of rat kidney. It is observed that for increasing wall permeability and high osmotic pressure drop provided maximum fractional permeation rate 84%. It is also noted that leakage flow and the amount of permeate fluid are independent of porosity of porous media, they only depend on the constant wall permeability. Comparison of the present study with the previous work in view of fractional permeation rate is also provided in the results section.