An Analytical Study of Creeping Flow of a Second‐Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption

Abstract

This study is focused on investigating the effects of linear absorption parameter on creeping flow of a second-order fluid through a narrow leaky tube. These flows are experienced in several biological and industrial procedures, for instance, in proximal convoluted tubule of a human kidney, in hemodialysis devices, in filtration processes of food industry, journal bearing, and slide bearing. Inertial effects are neglected due to creeping motion assumption and low Reynolds number. Langlois recursive approach method is used to linearize the governing compatibility equation and to obtain an approximate analytical solution by reverse solution method. Analytical expressions for various physically important quantities like velocity profile, bulk flow, mean pressure drop in longitudinal direction, wall shear stress, leakage flux, fractional absorption, and stream function are obtained in dimensionless form. The obtained solution shows great similarity with the already available work in the literature. Variation in flow variables with linear absorption parameter is analysed in detail. The special case of uniform absorption in creeping motion of second-order fluid is presented in a separate section. It is noticed that velocity field, in case of uniform absorption, is independent of non-Newtonian parameters. Therefore, it is asserted that any two dimensional axisymmetric Newtonian velocity fields is also a solution for second-order fluids with identical boundary conditions.