scholarly journals Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery

2021 ◽  
Vol 86 (2) ◽  
pp. 56-73
Author(s):  
Nurul Aini Jaafar ◽  
Siti NurulAifa Mohd ZainulAbidin ◽  
Zuhaila Ismail ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Blood Flow ◽  
Chemical Reaction ◽  
Power Law ◽  
Plug Flow ◽  
Arterial Disease ◽  
Arterial Stenosis ◽  
Dispersion Function ◽  
Dispersion Process ◽  
Solute Dispersion ◽  
Power Law Index

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

Clinical Application of Transcranial Color Doppler Ultrasound in Carotid Endarterectomy

2021 ◽  
Vol 11 (2) ◽  
pp. 437-444
Author(s):  
Yicheng Huang ◽  
Junyan Peng ◽  
Rong Mi ◽  
Zhenxing Yang ◽  
Linquan Zhu ◽  
...  
Keyword(s):  
Blood Flow ◽  
Middle Cerebral Artery ◽  
Cerebral Artery ◽  
Color Doppler ◽  
Arterial Disease ◽  
Arterial Stenosis ◽  
Intracranial Arterial Stenosis ◽  
Ischemic Cerebrovascular Disease ◽  
Artery Disease ◽  
Transcranial Color Doppler

Ischemic cerebrovascular diseases are important duet to the high incidence, disability, mortality, and recurrence. Intracranial arterial stenosis caused by atherosclerosis is an important pathological basis of ischemic cerebrovascular disease. Therefore, convenient, non-invasive, cheap and accurate screening methods have become the goal of everyone's joint efforts. The purpose of this study was to investigate the value of transcranial Doppler in judging arterial stenosis, and to explore the best cut-off point for assessing the blood flow velocity of middle cerebral artery disease and the compensation of the posterior branch of middle cerebral artery disease. Using retrospective analysis, binomial logistic regression analysis was performed on risk factors related to ischemic cerebrovascular disease. The 60 patients with intracranial stenosis were selected for TCD (Transcranial Color Doppler) and CTA (Computed Tomography Angiography) examinations within one week of onset. CTA was used as the diagnostic criterion to analyze the accuracy of TCD in the diagnosis of intracranial arterial disease. ROC (Receiver Operating Characteristic) curve was used to determine the optimal cutoff point of blood flow velocity for MCA (Middle Cerebral Artery) lesions. TCD has high specificity and sensitivity in the diagnosis of intracranial arterial disease, and it can be widely used in clinic as a simple, convenient and cheap diagnostic method for screening intracranial arterial stenosis.

scholarly journals Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160294 ◽  
Author(s):  
Jyotirmoy Rana ◽  
P. V. S. N. Murthy
Keyword(s):  
Fluid Flow ◽  
Newtonian Fluid ◽  
Transport Coefficients ◽  
Blood Stream ◽  
Weissenberg Number ◽  
Dispersion Coefficients ◽  
Dispersion Process ◽  
Solute Dispersion ◽  
Link Type ◽  
Power Law Index

The theory of miscible dispersion in a straight circular pipe with interphase mass transfer that was investigated by Sankarasubramanian & Gill (1973Proc. R. Soc. Lond. A333, 115–132. (doi:10.1098/rspa.1973.0051); 1974Proc. R. Soc. Lond. A341, 407–408. (doi:10.1098/rspa.1974.0195)) in Newtonian fluid flow is extended by considering various non-Newtonian fluid models, such as the Casson (Rana & Murthy 2016J. Fluid Mech.793, 877–914. (doi:10.1017/jfm.2016.155)), Carreau and Carreau–Yasuda models. These models are useful to investigate the solute dispersion in blood flow. The three effective transport coefficients, i.e. exchange, convection and dispersion coefficients, are evaluated to analyse the dispersion process of solute. The convection and dispersion coefficients are determined asymptotically at large time which is sufficient to understand the nature of the solute dispersion process in a tube. The axial mean concentration is analysed, using the asymptotic expressions for these three coefficients. The effect of the wall absorption parameter, Weissenberg number, power-law index, Yasuda parameter and Peclet number on the dispersion process is discussed clearly in this study. A comparative study of the solute dispersion among the Newtonian and all other non-Newtonian models is presented. At low shear rate, it is observed that Carreau fluid behaves like Newtonian fluid, whereas the other fluids exhibit significant differences during the solute dispersion. This study may be applicable to understand the dispersion process of drugs in the blood stream.

scholarly journals Analysis of Blood Flow in Arterial Stenosis Using Casson and Power-Law Fluid Model

2013 ◽  
Vol 14 (2) ◽  
pp. 73
Author(s):  
Riri Jonuarti
Keyword(s):  
Blood Flow ◽  
Power Law ◽  
Fluid Model ◽  
Blood Flow Rate ◽  
Casson Fluid ◽  
Arterial Stenosis ◽  
Fluid Models ◽  
Power Law Fluid ◽  
Pass Through ◽  
Flow Power

Simulation of blood flow behaviour in the arteries and in arterial stenosis has been made and will be discussed in this paper. This simulation uses pulsatile flow and blood flow in artery without stenosis is considered as a dynamic fluid, compressed and condensed. Whereas, in the case of arterial stenosis has been used Casson and Power-law fluid models. In the arteries without stenosis, blood flow velocity profiles show the same pattern for each Womersley number, but with different speed value. In the case of arterial stenosis, blood flow rate decreases with increasing stenosis position away from axis of blood vessels. Resistances to flow are increases with increasing the size (height and length) of stenosis, both for the Casson and Power-law fluid models. If resistance to flow increases, it is more difficult for the blood to pass through an artery, result the flow decreases and heart has to work harder to maintain adequate circulation.Keywords : Artery, blood flow, power-law fluid, Casson fluid, stenosis  

scholarly journals Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

2018 ◽  
Vol 7 (4.10) ◽  
pp. 491
Author(s):  
S. Sreenadh ◽  
B. Sumalatha ◽  
A. N.S.Srinivas
Keyword(s):  
Power Law ◽  
Plug Flow ◽  
Elastic Parameters ◽  
External Pressures ◽  
Power Law Fluids ◽  
Special Cases ◽  
Flow Through ◽  
Two Parameters ◽  
Power Law Index ◽  
Elastic Walls

In order to model the blood flow through an artery in presence of catheter, we considered a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls. The power law index ( ) and yield stress ( ) are the two parameters of the Herschel - Bulkley fluid. By giving different values for the above mentioned parameters, we get the Newtonian, Bingham and Power-law fluids as special cases. The exact solutions for the flow quantities such as velocity, plug flow velocity and flux are derived. The flux is determined as a function of inlet, outlet, external pressures and the elastic property of the channel. The effect of elastic parameters on flux variation is analyzed. Further when and our results qualitatively agree with those of Rubinow and Keller [2]. In addition, velocity of the Herschel- Bulkley fluid flow is expressed in terms of elastic parameters.  

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 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.

scholarly journals A comparison of Newtonian and non-Newtonian models for pulsatile blood flow simulations

2013 ◽  
Vol 21 (5-6) ◽  
pp. 147-153 ◽  
Author(s):  
Iqbal Husain ◽  
Fotini Labropulu ◽  
Chris Langdon ◽  
Justin Schwark
Keyword(s):  
Blood Flow ◽  
Power Law ◽  
Three Dimensional ◽  
Arterial Stenosis ◽  
Pulsatile Blood Flow ◽  
Blood Flows ◽  
Newtonian Model ◽  
Wide Range ◽  
Flow Effects ◽  
Three Dimensional Models

AbstractMathematical modeling of blood flows in the arteries is an important and challenging problem. This study compares several non-Newtonian blood models with the Newtonian model in simulating pulsatile blood flow through two three-dimensional models of an arterial stenosis and an aneurysm. Four non-Newtonian blood models, namely the Power Law, the Casson, the Carreau, and the Generalized Power Law, as well as the Newtonian model of blood viscosity, are used to investigate the flow effects induced by these different blood constitutive equations. The aim of this study is three-fold: firstly, to investigate the variation in wall shear stress in an artery with a stenosis or aneurysm at different flow rates and degrees of severity; secondly, to compare the various blood models and hence quantify the differences between the models and judge their significance; and lastly, to determine whether the use of the Newtonian blood model is appropriate over a wide range of shear rates.

scholarly journals Study of Non-Newtonian biomagnetic blood flow in a stenosed bifurcated artery having elastic walls

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hasan Shahzad ◽  
Xinhua Wang ◽  
Ioannis Sarris ◽  
Kaleem Iqbal ◽  
Muhammad Bilal Hafeez ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Power Law ◽  
Hartmann Number ◽  
Fluid Structure Interaction ◽  
Shear Stresses ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Power Law Index ◽  
Elastic Walls

AbstractFluid structure interaction (FSI) gained attention of researchers and scientist due to its applications in science fields like biomedical engineering, mechanical engineering etc. One of the major application in FSI is to study elastic wall behavior of stenotic arteries. In this paper we discussed an incompressible Non-Newtonian blood flow analysis in an elastic bifurcated artery. A magnetic field is applied along $$x$$ x direction. For coupling of the problem an Arbitrary Lagrangian–Eulerian formulation is used by two-way fluid structure interaction. To discretize the problem, we employed $$P_{2} P_{1}$$ P 2 P 1 finite element technique to approximate the velocity, displacement and pressure and then linearized system of equations is solved using Newton iteration method. Analysis is carried out for power law index, Reynolds number and Hartmann number. Hemodynamic effects on elastic walls, stenotic artery and bifurcated region are evaluated by using velocity profile, pressure and loads on the walls. Study shows there is significant increase in wall shear stresses with an increase in Power law index and Hartmann number. While as expected increase in Reynolds number decreases the wall shear stresses. Also load on the upper wall is calculated against Hartmann number for different values of power law index. Results show load increases as the Hartmann number and power law index increases. From hemodynamic point of view, the load on the walls is minimum for shear thinning case but when power law index increased i.e. for shear thickening case load on the walls increased.

Sign in / Sign up

Export Citation Format

Share Document