Abstract
Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary conditions. The aim of this article is to investigate the hydrodynamical aspects of steady, axisymmetric and slow flow of a general second-order Rivlin-Ericksen fluid in a porous-walled circular tube with constant wall permeability. The governing compatibility equation have been derived and solved analytically for the stream function by applying Langlois recursive approach for slow viscoelastic flows. Analytical expressions for velocity components, pressure, volume flow rate, fractional reabsorption, wall shear stress and stream function have been obtained correct to third order. The effects of wall Reynolds number and certain non-Newtonian parameters have been studied and presented graphically. The obtained analytical expressions are in agreement with the existing solutions in literature if non-Newtonian parameters approach to zero. The solutions obtained in this article may be considered as a generalization to the existing work. The results indicate that there is a significant dependence of the flow variables on the wall Reynolds number and non-Newtonian parameters.
Highlights
IntroductionThe problem of finding the dynamics of fluid flow through a small diameter cylindrical tube with porous walls is being of much interest among the researchers and scientists for last few decades because of its application in many physical and physiological processes
The problem of finding the dynamics of fluid flow through a small diameter cylindrical tube with porous walls is being of much interest among the researchers and scientists for last few decades because of its application in many physical and physiological processes. Such flows occur in hollow fiber dialyzer, flat plate dialyzer, renal tubule and in desalination processes with reverse osmosis
A considerable contribution in the study of hydrodynamics of flow of Glomerular Filtrate in renal tubule was made by Macey [1]
Summary
The problem of finding the dynamics of fluid flow through a small diameter cylindrical tube with porous walls is being of much interest among the researchers and scientists for last few decades because of its application in many physical and physiological processes. Such flows occur in hollow fiber dialyzer, flat plate dialyzer, renal tubule and in desalination processes with reverse osmosis. A considerable contribution in the study of hydrodynamics of flow of Glomerular Filtrate in renal tubule was made by Macey [1] He solved Stokes equations by assuming reabsorption as a linear function of longitudinal length of the tubule. Kelman [2] showed that the bulk flow passing through a cross section of the tubule at any point is decreasing exponentially in major flow direction
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