| Citation: |
Hameed Ullah, Huafei Sun, Abdul Majeed Siddiqui, Tahira Haroon. CREEPING FLOW ANALYSIS OF SLIGHTLY NON-NEWTONIAN FLUID IN A UNIFORMLY POROUS SLIT[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 140-158. doi: 10.11948/2019.140
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CREEPING FLOW ANALYSIS OF SLIGHTLY NON-NEWTONIAN FLUID IN A UNIFORMLY POROUS SLIT
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Abstract
This paper provides the analysis of the steady, creeping flow of a special class of slightly viscoelastic, incompressible fluid through a slit having porous walls with uniform porosity. The governing two dimensional flow equations along with non-homogeneous boundary conditions are non-dimensionalized. Recursive approach is used to solve the resulting equations. Expressions for stream function, velocity components, volumetric flow rate, pressure distribution, shear and normal stresses in general and on the walls of the slit, fractional absorption and leakage flux are derived. Points of maximum velocity components are also identified. A graphical study is carried out to show the effect of porosity and non-Newtonian parameter on above mentioned resulting expressions. It is observed that axial velocity of the fluid decreases with the increase in porosity and non-Newtonian parameter. The outcome of this theoretical study has significant importance both in industry and biosciences.-
Keywords:
- Creeping flow /
- non-Newtonian fluid /
- porous slit /
- recursive approach
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References
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Hameed Ullah, Huafei Sun, Abdul Majeed Siddiqui, Tahira Haroon. CREEPING FLOW ANALYSIS OF SLIGHTLY NON-NEWTONIAN FLUID IN A UNIFORMLY POROUS SLIT[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 140-158. doi: 10.11948/2019.140
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- Figure 1. Geometry of the Problem.
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Figure 2. Effect of porosity parameter
$ S $ on axial velocity$ u(y) $ for$ \beta = 0, $ (a)$ x = 0.1, $ (b)$ x = 10, $ (c)$ x = 20 $ . -
Figure 3. Effect of porosity parameter
$ S $ on axial velocity$ u(y) $ for$ \beta = 0.2, $ (a)$ x = 0.1, $ (b)$ x = 10, $ (c)$ x = 20 $ . -
Figure 4. Effect of non-Newtonian parameter
$ \beta $ on axial velocity$ u(y) $ for$ S = 0.2, $ (a)$ x = 0.1, $ (b)$ x = 10, $ (c)$ x = 20 $ . -
Figure 5. Effect of porosity parameter
$ S $ on radial velocity$ v(y) $ for (a)$ \beta = 0, $ (b)$ \beta = 0.4, $ (c)$ \beta = 0.8 $ . -
Figure 6. Effect of (a) porosity parameter
$ S $ when$ \beta = 0 $ and (b)$ \beta $ when$ S = 0 $ , on pressure difference$ p(x, 0)-p(0, 0) $ . -
Figure 7. Effect of
$ S $ on (a) axial flow rate and (b) wall shear stress keeping$ \beta = 0.2 $ . Effect of$ \beta $ on (c) wall shear stress keeping$ S = 0.2 $ . -
Figure 8. Stream lines for
$ \beta = 0, $ (a)$ S = 0.2, $ (b)$ S = 0.4, $ (c)$ S = 0.8 $ . -
Figure 9. Stream lines for
$ S = 0.2 $ (a)$ \beta = 0.4, $ (b)$ \beta = 0.6, $ (c)$ \beta = 0.8 $ .