Hydrodynamical Study of Micropolar Fluid in a Porous-Walled Channel: Application to Flat Plate Dialyzer
Abstract
:1. Introduction
- the fluid flowing in the channel was assumed to be Newtonian in nature,
- the no-slip condition was assumed to be held at the permeable wall,
- a seepage velocity of a constant, linear, or exponential type at the porous wall was assumed in advance.
- The constitutive equation of the micropolar fluid model can be reduced to the Newtonian fluid model as a special case when certain parameters in this model are set to zero. Thus, a variety of industrial and biological non-Newtonian fluids along with the previously-studied Newtonian fluid can be investigated by the current results.
- Results for the no-slip flow can be recovered from our obtained solutions when the slip parameter approaches zero.
- The obtained solution also reveals that for particular values of parameters, a uniform, linear, and exponentially-decaying flow rate can be deduced from the results of the current article, which were assumed in advance in the previous studies.
2. Basic Equations
3. Problem Statement
4. Dimensionless Formulation and Solution
5. Numerical Results and Discussion
6. Application to a Flat Plate Dialyzer
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
FPD | Flat plate dialyzer |
Fluid density | |
Coefficient of viscosity | |
Coefficient of the micro-rotation viscosity | |
Viscosity coefficients of the angular velocity | |
Micro-inertia coefficient | |
u | Dimensionless tangential velocity component |
v | Dimensionless transverse velocity component |
Dimensionless microrotation velocity | |
Inlet flow rate | |
Inlet pressure | |
Ratio of the channel width to its length | |
Coupling number | |
Micropolar fluid parameter | |
K | Dimensionless wall filtration coefficient |
W | Channel width to height ratio |
Dimensionless wall slip parameter | |
Dimensionless ultrafiltration rate | |
Dimensionless mean pressure drop |
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Parameter | Abbreviation | Numerical Value |
---|---|---|
Number of blood | 8 | |
compartments | ||
Membrane length | L | 42 cm |
Membrane width | w | cm |
Membrane thickness | t | cm |
Blood half channel | a | cm |
height | ||
Fluid viscosity | dynes-s/cm | |
Transmembrane | ||
pressure difference | 150 mm Hg | |
at the entrance | ||
Total ultrafiltration | 200 mL/h | |
rate | ||
Total entrance | 160 mL/min | |
volume flow rate |
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Lu, D.; Kahshan, M.; Siddiqui, A.M. Hydrodynamical Study of Micropolar Fluid in a Porous-Walled Channel: Application to Flat Plate Dialyzer. Symmetry 2019, 11, 541. https://doi.org/10.3390/sym11040541
Lu D, Kahshan M, Siddiqui AM. Hydrodynamical Study of Micropolar Fluid in a Porous-Walled Channel: Application to Flat Plate Dialyzer. Symmetry. 2019; 11(4):541. https://doi.org/10.3390/sym11040541
Chicago/Turabian StyleLu, Dianchen, Muhammad Kahshan, and A. M. Siddiqui. 2019. "Hydrodynamical Study of Micropolar Fluid in a Porous-Walled Channel: Application to Flat Plate Dialyzer" Symmetry 11, no. 4: 541. https://doi.org/10.3390/sym11040541