Hydrodynamical Study of Micropolar Fluid in a Porous-Walled Channel: Application to Flat Plate Dialyzer

Dianchen Lu,Muhammad Kahshan,A M Siddiqui

doi:10.3390/sym11040541

Dianchen Lu, Muhammad Kahshan + Show 1 more

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https://doi.org/10.3390/sym11040541

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Abstract

This article investigates the two-dimensional creeping flow of a non-Newtonian micropolar fluid in a small width permeable channel. Fluid is absorbed through permeable walls at a variable rate. This situation arises in filtration and mass transfer phenomena in industrial and engineering processes. The exact solution of the equations of motion is obtained. Graphs of the velocity profiles and pressure drop reveal the significant impact of the non-Newtonian nature of the micropolar fluid on the flow. The obtained solutions are used to discuss the hydrodynamical aspects of the physiological phenomenon of blood filtration in an artificial kidney, the flat plate dialyzer (FPD). Expressions for finding the ultrafiltration rate and mean pressure drop in an FPD are derived. Ultrafiltration rate and the mean pressure difference in an FPD are computed using derived expressions. A comparison of these with the existing empirical and experimental results shows a good agreement. For certain values of parameters, the derived form of the flow rate reveals that the axial flow rate in an FPD decays exponentially along the membrane length. This is a well-established and admitted result used by several researchers for studying the hydrodynamics of blood flow in renal tubules of kidneys. It is concluded that the presented model can be used to study the hydrodynamical aspects of blood flow in an FPD.

Highlights

IntroductionGlomerular tubular ultrafiltration, transpiration cooling, proximal tubular reabsorption, and the process of blood filtration in an artificial kidney are some examples of these processes [1,2,3,4,5,6,7]
Ultrafiltration and reverse osmosis are encountered in many industrial and biological processes.Reverse osmotic desalination, glomerular tubular ultrafiltration, transpiration cooling, proximal tubular reabsorption, and the process of blood filtration in an artificial kidney are some examples of these processes [1,2,3,4,5,6,7]
Having the importance of physical aspects described in the previous paragraph, this article is aimed at studying the hydrodynamical aspects of a non-Newtonian fluid, the micropolar fluid, in a porous-walled channel whose walls absorb the fluid at a variable rate in accordance with Darcy’s law [20] and considering the wall slip effects

Summary

Introduction

Glomerular tubular ultrafiltration, transpiration cooling, proximal tubular reabsorption, and the process of blood filtration in an artificial kidney are some examples of these processes [1,2,3,4,5,6,7]. In these processes, the filtering fluid is normally pumped at an elevated pressure through porous-walled channels and tubes.

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