Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

2012 ◽  
Vol 67 (10-11) ◽  
pp. 628-632
Author(s):  
Karem Boubaker ◽  
Yasir Khan
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Unsteady State ◽  
Newtonian Flow ◽  
Shooting Technique ◽  
Radial Profiles ◽  
Boubaker Polynomials ◽  
Newtonian Method ◽  
Expansion Scheme

In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

Numerical Modeling of Non-Newtonian Fluid Flow in a Porous Medium Using a Three-Dimensional Periodic Array

1998 ◽  
Vol 120 (1) ◽  
pp. 131-135 ◽  
Author(s):  
Masahiko Inoue ◽  
Akira Nakayama
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Pressure Gradient ◽  
Newtonian Fluid ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Inertia Effects ◽  
Flow Through

Three-dimensional numerical experiments have been conducted to investigate the viscous and porous inertia effects on the pressure drop in a non-Newtonian fluid flow through a porous medium. A collection of cubes placed in a region of infinite extent has been proposed as a three-dimensional model of microscopic porous structure. A full set of three-dimensional momentum equations is treated along with the continuity equation at a pore scale, so as to simulate a flow through an infinite number of obstacles arranged in a regular pattern. The microscopic numerical results, thus obtained, are processed to extract the macroscopic relationship between the pressure gradient-mass flow rate. The modified permeability determined by reading the intercept value in the plot showing the dimensionless pressure gradient versus Reynolds number closely follows Christopher and Middleman’s formula based on a hydraulic radius concept. Upon comparing the results based on the two- and three-dimensional models, it has been found that only the three-dimensional model can capture the porous inertia effects on the pressure drop, correctly. The resulting expression for the porous inertia possesses the same functional form as Ergun’s, but its level is found to be only one third of Ergun’s.

scholarly journals The flow of a viscous fluid with a predetermined pressure gradient through periodic structures

2019 ◽  
Vol 21 (2) ◽  
pp. 222-243
Author(s):  
Mariya S. Deryabina ◽  
Sergey I. Martynov
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Thin Plates ◽  
Dimensional Structure ◽  
Finite Width ◽  
Two Dimensional ◽  
Smooth Functions

In the Stokes approximation, the problem of viscous fluid flow through two-dimensional and three-dimensional periodic structures is solved. A system of thin plates of a finite width is considered as a two-dimensional structure, and a system of thin rods of finite length is considered as a three-dimensional structure. Plates and rods are periodically located in space with certain translation steps along mutually perpendicular axes. On the basis of the procedure developed earlier, the authors constructed an approximate solution of the equations for fluid flow with an arbitrary orientation of structures relative to a given vector of pressure gradient. The solution is sought in a finite region (cells) around inclusions in the class of piecewise smooth functions that are infinitely differentiable in the cell, and at the cell boundaries they satisfy the continuity conditions for velocity, normal and tangential stresses. Since the boundary value problem for the Laplace equation is solved, it is assumed that the solution found is unique. The type of functions allows us to separate the variables and to reduce the problem's solution to the solution of ordinary differential equations. It is found that the change in the flow rate of a fluid through a characteristic cross section is determined mainly by the geometric dimensions of the cells of the free liquid in such structures and is practically independent of the size of the plates or rods.

scholarly journals Fast multipole solvers for three-dimensional radiation and fluid flow problems

1999 ◽  
Vol 7 ◽  
pp. 408-417 ◽  
Author(s):  
J. H. Strickland ◽  
L. A. Gritzo ◽  
R. S. Baty ◽  
G. F. Homicz ◽  
S. P. Burns
Keyword(s):  
Fluid Flow ◽  
Three Dimensional ◽  
Fast Multipole ◽  
Flow Problems

Laminar Fluid Flow Around Two Wall-Mounted Blocks of Different Size

2009 ◽  
Author(s):  
Mohammad Mehdi Tavakol ◽  
Mohammad Eslami
Keyword(s):  
Fluid Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Bluff Bodies ◽  
Wake Region ◽  
Science And Engineering ◽  
Vortical Structures ◽  
Laminar Fluid Flow ◽  
Pressure Distributions

Fluid flow around single or multiple bluff bodies mounted on a surface has great significance in science and engineering. Understanding the characteristics of different vortices formed around wall-mounted bodies is quite necessary for different applications. Although the case of a single surface mounted cube has been studied extensively, only little attention has been paid to the flow around two or more rectangular blocks in array. Therefore, a CFD code is developed to calculate three dimensional steady state laminar fluid flow around two cuboids of arbitrary size and configuration mounted on a surface in free stream conditions. The employed numerical scheme is finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Results are presented for two rectangular blocks of the different size mounted on a surface in various inline arrangements. Streamlines are plotted for blocks of different size ratio. Velocity and pressure distributions are also plotted in the wake region behind the obstacles. It is shown that how the behavior of flow field and vortical structures depend on the respective size and location of the larger block in comparison with the case of two inline wall mounted cubes of the same size.

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