Creeping flow of viscous fluid through a proximal tubule with uniform reabsorption: a mathematical study

2016 ◽  
Vol 10 ◽  
pp. 795-807 ◽  
Author(s):  
T. Haroon ◽  
A. M. Siddiqui ◽  
A. Shahzad
Keyword(s):  
Viscous Fluid ◽  
Proximal Tubule ◽  
Creeping Flow ◽  
Mathematical Study

Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow

1987 ◽  
Vol 179 ◽  
pp. 283-305 ◽  
Author(s):  
George I. Zahalak ◽  
Peddada R. Rao ◽  
Salvatore P. Sutera
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Series Solution ◽  
Large Deformations ◽  
Boundary Value ◽  
Creeping Flow ◽  
Symbol Manipulation ◽  
Viscous Shear ◽  
Fifth Order

This paper treats the steady flow fields generated inside and outside an initially circular, inextensible, cylindrical membrane filled with an incompressible viscous fluid when the membrane is placed in a two-dimensional shear flow of another viscous fluid. The Reynolds numbers of both the interior and exterior flows were assumed to be zero (‘creeping flow’), but no further approximations were made in the formulation. A series solution of the resulting free boundary-value problem in powers of a dimensionless shear rate parameter was constructed through fifth order. When combined with a conformal coordinate transformation this series gave accurate results for large deformations of the membrane (up to an aspect ratio of 2.5). The rather tedious algebraic manipulations required to obtain the series solution were done by computer with a symbol-manipulation program (reduce), which both formulated the boundary-value problems for each successive order and solved them. Results are presented which show how the shear rate and fluid viscosities influence the internal and external velocity and pressure fields, the membrane deformation and its ‘tank-treading’ frequency, and the membrane tension.This work demonstrates that classical perturbation techniques combined with computer algebra offer a useful alternative to purely numerical methods for problems of this type.

scholarly journals Heat Transfer Analysis of MHD Viscous Fluid in A Ciliated Tube with Entropy Generation

2021 ◽  
Author(s):  
Noreen Akbar ◽  
Salman Akhtar ◽  
E. Maraj ◽  
Ali Anqi
Keyword(s):  
Heat Transfer ◽  
Viscous Fluid ◽  
Entropy Generation ◽  
Creeping Flow ◽  
Heat Transfer Analysis ◽  
Inertial Forces ◽  
Metachronal Wave ◽  
Viscous Forces ◽  
Transfer Study ◽  
Large Wavelength

This investigation aims to explain the study of heat transfer and entropy generation of magnetohydrodynamic (MHD) viscous fluid flowing through a ciliated tube. Heat transfer study has massive importance in various biomedical and biological industry problems. The metachronal wave propagation is the leading cause behind this viscous creeping flow. A low Reynolds number is used as the inertial forces are weaker than viscous forces, and also creeping flow limitations are fulfilled. For the cilia movement, a very large wavelength of a metachronal wave is taken into account. Entropy generation is used to examine the heat transfer through the flow. Exact mathematical solutions are calculated and analyzed with the help of graphs. Streamlines are also plotted.

Creeping flow around a deforming sphere

1972 ◽  
Vol 56 (1) ◽  
pp. 61-71 ◽  
Author(s):  
S. P. Lin ◽  
A. K. Gautesen
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Strouhal Number ◽  
Creeping Flow ◽  
Incompressible Viscous Fluid

The flow of an incompressible viscous fluid past a deforming sphere is studied for small values of the Reynolds number. The deformation is assumed to be radial but is otherwise quite general. The case of S = O(l), where S is the Strouhal number, is investigated in detail. In particular, the drag is obtained up to O(R2 In R), where R is the Reynolds number.

Flow induced by the presence of a non-conducting ellipsoid of revolution in fluid carrying a uniform current

1970 ◽  
Vol 42 (1) ◽  
pp. 129-138 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Flow Field ◽  
Viscous Fluid ◽  
Circular Disk ◽  
Creeping Flow ◽  
Whole Space ◽  
Ellipsoid Of Revolution ◽  
Uniform Current ◽  
Induced Flow ◽  
The Magnetic Field

The Stokes creeping flow, induced by the passage of a uniform current parallel to the axis of a stationary non-conducting ellipsoid of revolution in an incompressible viscous fluid occupying, apart from the ellipsoidal region, the whole space, is investigated. The magnetic field, which is due to the distortion of the uniform current by the ellipsoid, is zero all over the surface of the ellipsoid. The induced flow field is symmetric with respect to the axis, and also with respect to a plane through the centre perpendicular to the axis of the ellipsoid. The case of a non-conducting circular disk, with its plane perpendicular to the direction of the undisturbed current, is deduced from that of a planetary ellipsoid.

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