Flow of a Newtonian fluid in a non-uniform wavy and permeable tube

Abstract

In this paper, a viscous incompressible fluid flow in a wavy non-uniform rigid tube with permeable wall by taking in to account the influence of slip velocity at the wall is studied. It is assumed that the exchange of fluid across the wall obeys Starling’s hypothesis, that is, the rate of flow per unit area through the wall surface is proportional to the difference between the pressure of the fluid within and outside the wall. The nonlinear governing equations of motion are linearized by perturbation method by assuming δ (ratio of inlet width to wavelength) as a small parameter and the resulting equations are solved by numerical methods. The effects of permeability parameter (α), slope parameter (k), slip coefficient (ξ) and Reynolds number (R_e) on the velocity profiles, pressure and flow rate are presented graphically. Results concerning the velocity, pressure and flow rate, indicate that the slip and permeability parameters influence the flow field significantly. Discussions are made from physiological point of view.

Keywords

• Fluid flow

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