Hydrodynamics of viscous fluid through porous slit with linear absorption

doi:10.1007/s10483-016-2032-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (3): 361-378.doi: https://doi.org/10.1007/s10483-016-2032-6

Hydrodynamics of viscous fluid through porous slit with linear absorption

A. M. SIDDIQUI¹, T. HAROON², A. SHAHZAD²

1. Department of Mathematics, Pennsylvania State University, York Campus, Pennsylvania 17403, U. S. A.;
2. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 45550, Pakistan

收稿日期:2015-01-14 修回日期:2015-09-14 出版日期:2016-03-01 发布日期:2016-03-01
通讯作者: T. HAROON E-mail:tahiraharoon@comsats.edu.pk

Hydrodynamics of viscous fluid through porous slit with linear absorption

A. M. SIDDIQUI¹, T. HAROON², A. SHAHZAD²

1. Department of Mathematics, Pennsylvania State University, York Campus, Pennsylvania 17403, U. S. A.;
2. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 45550, Pakistan

Received:2015-01-14 Revised:2015-09-14 Online:2016-03-01 Published:2016-03-01
Contact: T. HAROON E-mail:tahiraharoon@comsats.edu.pk

摘要/Abstract

摘要：

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.

关键词: exact solution, renal tubule, linear absorption, porous slit

Abstract:

Key words: porous slit, renal tubule, linear absorption, exact solution

中图分类号:

A. M. SIDDIQUI, T. HAROON, A. SHAHZAD. Hydrodynamics of viscous fluid through porous slit with linear absorption[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(3): 361-378.

参考文献

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Hydrodynamics of viscous fluid through porous slit with linear absorption

Hydrodynamics of viscous fluid through porous slit with linear absorption

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