Application of creeping flow through a linearly absorbing slit filled with porous medium to diseased renal tubules

Siddiqui, A. M.; Azim, Q. A.; Sunny, Danish Ali

doi:10.1007/s10237-020-01401-9

Cited by 5 publications

(6 citation statements)

References 28 publications

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“…We attained the results of Maxwell fluid with constant reabsorption 43 by inserting a1=0 in the above solution. Results for viscous fluid with linear reabsorption 20 can be obtained by substituting λ=0 in the solution of the present study.…”

Section: Graphical Explanationmentioning

confidence: 99%

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

Mehboob

Maqbool

Ramzan

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This research presents the analytical study of the creeping flow of a Maxwell fluid in a permeable slit under the effect of linear reabsorption. Analysis of fluid leakage on the slit wall is carried out with the help of the law of conservation of momentum in the rectangular coordinates. The mathematical model in the form of the system of nonlinear partial differential equations is solved by the recursive approach explaining the hydrodynamic aspects of creeping Maxwell fluid flow. The expressions for the velocity field, hydrostatic pressure, stream function, leakage flux, and fractional reabsorption on the boundary of the slit are obtained from the mathematical model. Graphical analysis is also established to demonstrate the effects of emerging parameters due to linear reabsorption on slit boundary and relaxation time. It is analyzed that the horizontal and vertical velocity decelerates by the growing values of the relaxation parameter, but the reabsorption rate gives an increasing effect on the shear stress, volume flow rate, and vertical velocity. This analytical study will help the bioengineers in designing the medical tools with the required pressure and flow rate, therefore the application of this model for the hemodialyzer is also important.

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Section: Graphical Explanationmentioning

confidence: 99%

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

Mehboob

Maqbool

Ramzan

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…and seek for a reverse solution of the (10) subject to the conditions ( 11)- (15). As E 2 � (z 2 /zr 2 ) − (1/r)(z/zr)+ (z 2 / zz 2 ) so E 4 � ((z 2 /zr 2 ) − (1/r)(z/zr)) 2 + 2((z 2 /zr 2 )− (1/r)(z/ zr))(z 2 /zz 2 ) + (z 4 /zz 4 ).…”

Section: First-order Solutionunclassified

“…As E 2 � (z 2 /zr 2 ) − (1/r)(z/zr)+ (z 2 / zz 2 ) so E 4 � ((z 2 /zr 2 ) − (1/r)(z/zr)) 2 + 2((z 2 /zr 2 )− (1/r)(z/ zr))(z 2 /zz 2 ) + (z 4 /zz 4 ). us, equation (10) reduces to…”

Section: First-order Solutionunclassified

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An Analytical Study of Creeping Flow of a Second-Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption

Bano

Siddiqui

Bhatti

2022

Journal of Mathematics

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This study is focused on investigating the effects of linear absorption parameter on creeping flow of a second-order fluid through a narrow leaky tube. These flows are experienced in several biological and industrial procedures, for instance, in proximal convoluted tubule of a human kidney, in hemodialysis devices, in filtration processes of food industry, journal bearing, and slide bearing. Inertial effects are neglected due to creeping motion assumption and low Reynolds number. Langlois recursive approach method is used to linearize the governing compatibility equation and to obtain an approximate analytical solution by reverse solution method. Analytical expressions for various physically important quantities like velocity profile, bulk flow, mean pressure drop in longitudinal direction, wall shear stress, leakage flux, fractional absorption, and stream function are obtained in dimensionless form. The obtained solution shows great similarity with the already available work in the literature. Variation in flow variables with linear absorption parameter is analysed in detail. The special case of uniform absorption in creeping motion of second-order fluid is presented in a separate section. It is noticed that velocity field, in case of uniform absorption, is independent of non-Newtonian parameters. Therefore, it is asserted that any two dimensional axisymmetric Newtonian velocity fields is also a solution for second-order fluids with identical boundary conditions.

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“…They computed the analytic solution of the problem and obtained very interesting quantities for the flow problem. Siddiqui et al [33] modeled the creeping flow of linearly absorbing channels and their study was motivated by the fluid through renal tubules in a kidney that are diseased. Deng et al [34] evaluated the flow problem beyond the critical Reynolds number, Darcy law, and the development of channel flow.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Ishaq,

Fatima,

Afzal

et al. 2023

Preprint

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The current study examines the features of a two-dimensional steady incompressible flow of creeping couple stress fluid across a permeable channel with uniform reabsorption. The mathematical model that governs this flow is composed of linear partial differential equations and homogeneous boundary constraints. The Inverse method approach, an analytical technique, is used to find solutions to the problem. By converting the momentum equations to stream functions, the inverse approach helps derive all the relevant physical quantities, including the longitudinal and transverse velocities, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. Using MATLAB software, the dependent functions such as stream function, pressure, and volume flow are evaluated for different parameter values. The findings indicate that the longitudinal velocity is affected by the initial flow rate, while the transverse velocity shows no change in its profile. The streamlines become more straight and identical as the flow rate increases. Backward flow occurs at the end of the slit due to the porosity parameter. However, the initial flow rate does not impact the transverse velocity of the fluid in the permeable channel. This study fully describes a mathematical foundation for understanding fluid movement across permeable boundaries, which have practical applications in areas such as gaseous diffusion, filtration, and biological mechanisms.

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Application of creeping flow through a linearly absorbing slit filled with porous medium to diseased renal tubules

Cited by 5 publications

References 28 publications

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

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

An Analytical Study of Creeping Flow of a Second-Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

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