Analysis of slip effects on slow viscoelastic flow of second order fluid through a small diameter permeable tube

There are various models which describe the hydro-dynamical aspects of the fluid flow and solute transport in small diameter permeable tubes without incorporating the slip effects, which play an important role to predict the flow behavior with higher accuracy. This study aims to investigate the slip effects on the slow, steady-state and axisymmetric flow of an incompressible second order Rivlin–Ericksen fluid in a small diameter cylindrical tube with constant wall permeability. The momentum equations have been derived in cylindrical coordinates and are converted in the form of a single compatibility equation which governs the stream function of the flow. Navier slip condition has been used to take slip phenomenon into account near the wall of the tube. Compatibility equation has been solved analytically subject to the associated boundary conditions by using Langlois recursive approach method. The detailed expressions have been obtained for velocity components, pressure, volume flow rate, pressure drop along longitudinal axis, wall shear stress, fractional reabsorption and leakage flux. Behavior of all the flow variables against the slip parameter has been examined graphically in detail. Overall, the solutions obtained her e show a great agreement with the work in literature. One of the key findings in this study is that the volume flow rate Q is found to be independent of the slip parameter ϕ.