Abstract
The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms.
Highlights
Flow-through permeable boundaries have enormous importance from many decades due to their tremendous applications in bio-sciences and engineering, such as processes like membrane filtration, desalination processes using reverse osmosis, transpiration cooling, blood flow, renal proximal tubule flow within a kidney and filtration of blood in hemodialysis of an artificial kidney are the key examples related to flows in permeable boundaries [1,2,3,4,5,6]
We have considered the Maxwell fluid to investigate the slow flow through permeable slit having wall slip with uniform reabsorption and present the solutions using the recursive approach proposed by Langlois [23,24]
We have presented the slow flow of a Maxwell fluid through the permeable slit under the influence of a slip condition and the recursive approach is consider to get an analytical solution
Summary
Flow-through permeable boundaries have enormous importance from many decades due to their tremendous applications in bio-sciences and engineering, such as processes like membrane filtration, desalination processes using reverse osmosis, transpiration cooling, blood flow, renal proximal tubule flow within a kidney and filtration of blood in hemodialysis of an artificial kidney are the key examples related to flows in permeable boundaries [1,2,3,4,5,6]. We consider the creeping flow of Maxwell fluid through the permeable slit in accordance with slip condition at porous walls and uniform reabsorption. Bhatti et al [45] used this approach to investigate the slow flow of a second order fluid through a uniformly permeable circular tube and we implement this approach to get solutions of creeping flow of a Maxwell fluid and discuss combined effects of absorption parameter, viscoelasticity and slip parameter on flow variables involved at different positions of the channel and obtain the explicit expressions for axial and radial velocity components, total pressure difference, mean pressure drop, normal stresses difference, wall shear stress, leakage flux and fractional reabsorption
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