scholarly journals Herschel-Bulkley Model of Blood Flow through a Stenosed Artery with the Effect of Chemical Reaction on Solute Dispersion

2021 ◽  
Vol 17 (4) ◽  
pp. 457-474
Author(s):  
Siti Nurul Aifa Mohd Zainul Abidin ◽  
Nurul Aini Jaafar ◽  
Zuhaila Ismail
Keyword(s):  
Blood Flow ◽  
Chemical Reaction ◽  
Fluid Model ◽  
Plug Flow ◽  
Circulatory System ◽  
Mean Velocity ◽  
Axial Diffusivity ◽  
Length Increase ◽  
Stenosed Artery ◽  
Flow Through

A non-Newtonian mathematical model of blood described as a Hershel-Bulkley fluid model flowing in a stenosed artery with the effect of a chemical reaction is mathematically studied. The expressions of the shear stress, mean velocity and absolute velocity in the plug and non-plug flow field are evaluated analytically. The convective-diffusion equation is solved using the Taylor-Aris technique subject to the relevant boundary constraint in determining the concentration, relative and effective axial diffusivity. The efficiency of the dispersion process is affected by the presence of chemical reaction and stenosis in blood flow. The normalized velocity decreases as stenosis height and stenosis length increase. The relative axial diffusivity is significantly lower while the effective axial diffusivity decreases considerably as the chemical reaction rate, the height of the stenosis and the length of the stenosis increase. Besides, it is observed that as the solute disperses in the presence of stenosis, the flow quantities are lesser than in the absence of stenosis. Further, this study helps in understanding many physiological processes for instance dispersion of drugs or nutrients in the circulatory system. Also, to enhance the dispersion of a solute in blood flow through narrow arteries in the presence of chemical reaction and stenosis.

scholarly journals UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL

2016 ◽  
Vol 58 (1) ◽  
pp. 96-118 ◽  
Author(s):  
AKBAR ZAMAN ◽  
NASIR ALI ◽  
O. ANWAR BEG ◽  
M. SAJID
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Initial Boundary ◽  
Momentum Conservation ◽  
Rheological Parameters ◽  
Stenosed Artery ◽  
Flow Through

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

Modeling electro-magneto-hydrodynamic of blood flow in multi-stenosed artery using fractional deivatives without singular kernel

2020 ◽  
Author(s):  
F. J. Dzuliana ◽  
Uddin Salah ◽  
Roslan Rozaini ◽  
Md Akhir Mohd Kamalrulzaman
Keyword(s):  
Blood Flow ◽  
Pressure Gradient ◽  
Fractional Derivatives ◽  
Magnetic Particles ◽  
Circulatory System ◽  
Singular Kernel ◽  
Electric And Magnetic Fields ◽  
Stenosed Artery ◽  
Flow Through ◽  
Common Problems

Stenosis is one of the most common problems in blood flow through arteries. Stenosis means narrowing arteries. Among the various cardiovascular diseases, stenosis is a major one that affects blood flow in the arteries and becomes the leading cause of death worldwide. Therefore, several studies were conducted either experimentally or mathematically to understand stenosis effects on blood flow through arteries. This study investigates the Newtonian fluid’s electro-magneto-hydrodynamic flow mixed with uniformly distributed magnetic particles through a multi-stenosed artery. The fluid is acted by an arbitrary timedependent pressure gradient, external electric and magnetic fields, and the porous medium. The governing equations are considered as fractional partial differential equations based on the Caputo–Fabrizio time-fractional derivatives without singular kernel. The fractional model of blood flow in the multi-stenosed artery will be presented subject to several external factors. These include the severity of the stenosis and the magnetic particles with the presence of an electromagnetic field. The steady and unsteady parts of the pressure gradient that give rise to the systolic and diastolic pressures are considered as the pumping action of the heart, which in turn produces a pressure gradient throughout the human circulatory system. The fractionaloperator’s effect and pertinent system parameters on blood flow axial velocities are presented and discussed for future works.

scholarly journals On Two-Fluid Blood Flow through Stenosed Artery with Permeable Wall

2014 ◽  
Vol 11 (1-2) ◽  
pp. 39-45
Author(s):  
Rupesh K. Srivastav ◽  
V. P. Srivastava
Keyword(s):  
Blood Flow ◽  
Present Model ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Mechanical Study ◽  
Stenosed Artery ◽  
Flow Through ◽  
Flowing Blood ◽  
Two Fluid Model ◽  
Two Fluid

The present investigation concerns the fluid mechanical study on the effects of the permeability of the wall through an axisymmetric stenosis in an artery assuming that the flowing blood is represented by a two-fluid model. The expressions for the blood flow characteristics, the impedance, the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of the peripheral layer on these blood flow characteristics are quantified through numerical computations and presented graphically and discussed comparatively to validate the applicability of the present model.

scholarly journals Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery

2021 ◽  
Vol 87 (3) ◽  
pp. 134-147
Author(s):  
Siti Nurulaifa Mohd ZainulAbidin ◽  
Zuhaila Ismail ◽  
Nurul Aini Jaafar
Keyword(s):  
Blood Flow ◽  
Dispersion Model ◽  
Fluid Model ◽  
Momentum Equation ◽  
Bingham Fluid ◽  
Dispersion Function ◽  
Solute Dispersion ◽  
Stenosed Artery ◽  
Flow Through ◽  
Height Increase

An artery narrowing referred to as atherosclerosis or stenosis causes a reduction in the diameter of the artery. When blood flow through an artery consists of stenosis, the issue of solute dispersion is more challenging to solve. A mathematical model is developed to examine the unsteady solute dispersion in an overlapping stenosed artery portraying blood as Bingham fluid model. The governing of the momentum equation and the constitutive equation is solved analytically. The generalized dispersion model is imposed to solve the convective-diffusion equation and to describe the entire dispersion process. The dispersion function at steady-state decreases at the center of an artery as the stenosis height increase. A reverse behavior is shown at an unsteady-state. As the plug core radius, time and stenosis height increase, the dispersion function decreases at the center of an artery. There is a high amount of red blood cells at the center of the artery but no influences near the wall. Hence, this model is useful in transporting the drug or nutrients to the targeted stenosed region in the treatment of diseases and in understanding many physiological processes.

Sign in / Sign up

Export Citation Format

Share Document