Hydrodynamics of viscous fluid through porous slit with linear absorption

Abdul M. Siddiqui, T. Haroon, A. Shahzad

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.

Original languageEnglish (US)
Pages (from-to)361-378
Number of pages18
JournalApplied Mathematics and Mechanics (English Edition)
Volume37
Issue number3
DOIs
StatePublished - Mar 1 2016

Fingerprint

Viscous Fluid
Hydrodynamics
Absorption
Fluids
Flow rate
Fluxes
Flow Rate
Kidney
Leakage
Pressure distribution
Pressure drop
Purification
Sorption
Rats
Shear stress
Flow of fluids
Blood
Fractional
Boundary conditions
Nonhomogeneous Boundary Conditions

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

@article{a0bdd97beeaa419185f0697c7721e224,
title = "Hydrodynamics of viscous fluid through porous slit with linear absorption",
abstract = "The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.",
author = "Siddiqui, {Abdul M.} and T. Haroon and A. Shahzad",
year = "2016",
month = "3",
day = "1",
doi = "10.1007/s10483-016-2032-6",
language = "English (US)",
volume = "37",
pages = "361--378",
journal = "Applied Mathematics and Mechanics",
issn = "0253-4827",
publisher = "Springer China",
number = "3",

}

Hydrodynamics of viscous fluid through porous slit with linear absorption. / Siddiqui, Abdul M.; Haroon, T.; Shahzad, A.

In: Applied Mathematics and Mechanics (English Edition), Vol. 37, No. 3, 01.03.2016, p. 361-378.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Hydrodynamics of viscous fluid through porous slit with linear absorption

AU - Siddiqui, Abdul M.

AU - Haroon, T.

AU - Shahzad, A.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.

AB - The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.

UR - http://www.scopus.com/inward/record.url?scp=84958739389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958739389&partnerID=8YFLogxK

U2 - 10.1007/s10483-016-2032-6

DO - 10.1007/s10483-016-2032-6

M3 - Article

VL - 37

SP - 361

EP - 378

JO - Applied Mathematics and Mechanics

JF - Applied Mathematics and Mechanics

SN - 0253-4827

IS - 3

ER -