A mathematical model of blood flow in a permeable channel: application to flat plate dialyzer

Abstract

This article presents the theoretical study of the physiological phenomenon brought up by filtration of a non-Newtonian Casson fluid between two parallel permeable membranes. This situation corresponds to blood filtration process in a flat plate hemodialyzer (FPH). Seepage of fluid across the membrane is considered in accordance with the Darcy’s law and the equations of motion governing the flow are modeled. Using the low Reynolds number and long membrane length assumption, equations of motion are solved exactly. Equations describing velocity and pressure filed and various flow variables are derived and effects of wall slip parameter, wall filtration coefficient and the yield stress are presented graphically. A strong influence of these parameters is observed on the flow in an FPH. Theoretical values of the membrane filtration coefficient and mean pressure drop in an FPH are calculated and they are found to be in close agreement with the corresponding available empirical and experimental values in the literature. For certain limiting range of physical parameters, derived solutions reveal that the axial flow rate of Casson fluid in an FPH decays at an exponential rate. This is a physically valid and widely admitted result, used by several researchers in studying the blood filtration process in renal tubules of mammalian kidneys. Since the presented solutions in this article are reduced to their corresponding Newtonian fluid flow solutions between permeable membrane, therefore, it is concluded that a wide range of applications in physiology and engineering can be covered up by the present investigation.

Analytical study of creeping flow of Maxwell fluid in a permeable slit with linear re-absorption

“…Using equation (34) into equations (25)(26)(27)(28)(29)(30)(31)(32)(33) and eliminating pressure from equations ( 26) and ( 27) simultaneously, we get = 4 ψ ð1Þ ¼ 0: (35) Now to attain the solution of equation ( 35) together with the boundary conditions given in equations (31)(32)(33) we will use the inverse method, [19][20][21] so for that we assume ψ ð1Þ of the form ψ ð1Þ ðx,yÞ ¼ KðxÞR ð1Þ ðyÞ þ T ð1Þ ðyÞ (36) where…”

“…ðyÞ and T ð1Þ ðyÞ are unspecified functions to be determined. Now invoking equation (36) in equations (31)(32)(33)(34)(35) one writes the following boundary value problems R ð1Þiv ðyÞ ¼ 0, (37) with boundary conditions…”

“…Bhatti et al 35 studied the second-order fluid flow in a porous tube with uniform reabsorption. Kashan et al 36 studied the Casson fluid flow through a slit with a permeable wall and found the exact solution for the velocity, pressure, and shear stress. But no study is found to the best of our knowledge which relates the effects of linear reabsorption with Maxwell fluid flow through a permeable tube.…”

Design and Development of a Computational Tool for a Dialyzer by Using Computational Fluid Dynamic (CFD) Model

“…Donato et al non-dimensionalized the hollow fiber dialyzer's mathematical model to find factors that play a vital role in improving the dialyzer's clearance rate [17,18]. A study was brought up by filtration of a non-Newtonian Casson fluid between two parallel permeable membranes [19]. The effect of the interplay among parameters on internal filtration is also investigated [20].…”

Visualization of stratification based Eyring–Powell material flow capturing nonlinear convection effects

“…It is corroborated that radiation consideration for heat transportation is an effectual mode to capsize thermal layers where temperature difference between body and liquid free-stream is higher [9]. Few endeavors under radiative effect are divulged in investigations [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Besides, the mass transportation analysis under chemical reaction attribute has effectiveness in hydrometallurgical industries.…”