scholarly journals Slip Effects on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
A. Sinha ◽  
G. C. Shit ◽  
P. K. Kundu
Keyword(s):  
Pulsatile Flow ◽  
Slip Velocity ◽  
Fluid Model ◽  
Nonlinear Differential Equations ◽  
Volumetric Flow Rate ◽  
Casson Fluid ◽  
Time Dependent ◽  
Arterial Segment ◽  
Body Acceleration ◽  
Casson Fluid Model

A theoretical investigation concerning the influence of externally imposed periodic body acceleration on the flow of blood through a time-dependent stenosed arterial segment by taking into account the slip velocity at the wall of the artery has been carried out. A mathematical model is developed by treating blood as a non-Newtonian fluid obeying the Casson fluid model. The pulsatile flow is analyzed by considering a periodic pressure gradient and the inertial effects as negligibly small. A suitable generalized geometry for time-dependent stenosis is taken into account. Perturbation method is used to solve the coupled implicit system of nonlinear differential equations that govern the flow of blood. Analytical expressions for the velocity profile, volumetric flow rate, and wall shear stress are obtained. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in this study. The computational results are presented graphically. The results for different values of the parameters involved in the problem under consideration presented here show that the flow is appreciably influenced by slip velocity in the presence of periodic body acceleration.

scholarly journals MATHEMATICAL ANALYSIS OF BLOOD FLOW THROUGH AN ARTERIAL SEGMENT WITH TIME‐DEPENDENT STENOSIS

2008 ◽  
Vol 13 (3) ◽  
pp. 401-412 ◽  
Author(s):  
Jagadis Chandra Misra ◽  
Sudi D. Adhikary ◽  
Gopal Chandra Shit
Keyword(s):  
Pulsatile Flow ◽  
Plasma Layer ◽  
Volumetric Flow Rate ◽  
Core Layer ◽  
Casson Fluid ◽  
Time Dependent ◽  
Arterial Segment ◽  
Small Vessels ◽  
Physiological Fluid ◽  
Peripheral Plasma Layer

A mathematical model is developed here with an aim to study the pulsatile flow of blood through an arterial segment having a time‐dependent stenosis. Blood is considered to consist of a core layer where erythrocytes are concentrated and a peripheral plasma layer that is free from erythrocytes. The plasma layer is taken to behave as a Newtonian fluid, while the core layer is represented by as a Casson fluid (non‐Newtonian) model. The pulsatile flow is analyzed by considering a periodic pressure gradient, which is a function of time. A perturbation analysis is employed to solve the governing differential equations by taking the Womersley frequency parameter to be small (α < 1). This is a realistic assumption for physiological fluid flows, particularly for flow of blood in small vessels. Using appropriate boundary conditions, analytical expressions for the velocity profile, the volumetric flow rate, the wall shear stress and the flow resistance have been derived. These expressions are computed numerically and the computational results are presented graphically, in order to illustrate the variation of different quantities that are of particular interest in the study.

scholarly journals Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
D. S. Sankar ◽  
Nurul Aini Binti Jaafar ◽  
Yazariah Yatim
Keyword(s):  
Blood Flow ◽  
Circular Tube ◽  
Fluid Model ◽  
Nonlinear Differential Equations ◽  
Outer Region ◽  
Casson Fluid ◽  
Flat Plates ◽  
Axial Diffusivity ◽  
Casson Fluid Model ◽  
Relative Diffusivity

The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption

2016 ◽  
Vol 793 ◽  
pp. 877-914 ◽  
Author(s):  
Jyotirmoy Rana ◽  
P. V. S. N. Murthy
Keyword(s):  
Pulsatile Flow ◽  
Dispersion Model ◽  
Fluid Model ◽  
Critical Time ◽  
Transient State ◽  
Casson Fluid ◽  
Small Time ◽  
Dispersion Process ◽  
Pulsatile Pressure ◽  
Casson Fluid Model

The analysis of axial dispersion of solute is presented in a pulsatile flow of Casson fluid through a tube in the presence of interfacial mass transport due to irreversible first-order reaction catalysed by the tube wall. The theory of dispersion is studied by employing the generalized dispersion model proposed by Sankarasubramanian & Gill (Proc. R. Soc. Lond. A, vol. 333 (1592), 1973, pp. 115–132). This dispersion model describes the whole dispersion process in terms of three effective transport coefficients, i.e. exchange, convection and dispersion coefficients. In the present study, the effects of yield stress of Casson fluid ${\it\tau}_{y}$, wall absorption parameter ${\it\beta}$, amplitude of fluctuating pressure component $e$ and Womersley frequency parameter ${\it\alpha}$ on the dispersion process are discussed under the influence of pulsatile pressure gradient. In a pulsatile flow, the plug flow radius changes during the period of oscillation and it has an effect on the dispersion process. Even with the Casson fluid model also, in an oscillatory flow, for small values of ${\it\alpha}$, the dispersion coefficient $K_{2}$ is positive, but when the value of ${\it\alpha}$ is as large as 3, $K_{2}$ takes both positive and negative values due to the fluctuations in the velocity profiles. This nature becomes more predominant for ${\it\tau}_{y}$, $e$ and ${\it\beta}$. It is observed that initially, for small time, the amplitude and magnitude of fluctuations of $K_{2}$ becomes more rapid and increases with time but it decreases after certain time and reaches a non-transient state for large time. Like in the case of Newtonian model, double frequency period for $K_{2}$ is observed at small time for large values of ${\it\alpha}$ with the Casson model for blood. It is seen that critical time for which $K_{2}$ reaches a non-transient state is independent of ${\it\tau}_{y}$ and $e$ but is dependent on ${\it\alpha}$. It is also observed that the axial distribution of mean concentration $C_{m}$ of solute depends on ${\it\tau}_{y}$ and ${\it\beta}$. But the effect of $e$ and ${\it\alpha}$ on $C_{m}$ is not very significant. This dispersion model in non-Newtonian pulsatile flow can be applied to study the dispersion process in the cardiovascular system and blood oxygenators.

scholarly journals PULSATILE FLOW AND HEAT TRANSFER OF A MAGNETO-MICROPOLAR FLUID THROUGH A STENOSED ARTERY UNDER THE INFLUENCE OF BODY ACCELERATION

2011 ◽  
Vol 11 (03) ◽  
pp. 643-661 ◽  
Author(s):  
G. C. SHIT ◽  
M. ROY
Keyword(s):  
Heat Transfer ◽  
Pulsatile Flow ◽  
Micropolar Fluid ◽  
Flow Resistance ◽  
Hartmann Number ◽  
Volumetric Flow Rate ◽  
Arterial Segment ◽  
Body Acceleration ◽  
Flow And Heat Transfer ◽  
Stenosed Artery

With an aim to investigate the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis is under consideration in this article. The flow of blood is presented by an unsteady micropolar fluid, and the heat-transfer characteristics have been taken into account. The nonlinear equations that govern the flow are solved numerically using finite difference technique by employing a suitable coordinate transformation. The numerical results have been observed for axial and microrotation component of velocity, fluid acceleration, wall shear stress (WSS), flow resistance, temperature, and the volumetric flow rate. It thus turns out that the rate of heat transfer increases with the increase of Hartmann number H, while the WSS has a reducing effect on the Hartmann number H and an enhancing effect on the ratio of viscosity K as well as on the constriction height δ.

scholarly journals Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110316
Author(s):  
Salman Akhtar ◽  
Luthais B McCash ◽  
Sohail Nadeem ◽  
Salman Saleem ◽  
Alibek Issakhov
Keyword(s):  
Blood Flow ◽  
Flow Problem ◽  
Fluid Model ◽  
Casson Fluid ◽  
Viscous Effects ◽  
Heating Effects ◽  
Casson Fluid Model ◽  
Flow Through ◽  
Mathematical Equations ◽  
Mathematica Software

The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as [Formula: see text]. The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter [Formula: see text] and flow rate [Formula: see text]. The trapping declines in size with incrementing [Formula: see text], for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

scholarly journals Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Khalid ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Fluid Model ◽  
Casson Fluid ◽  
Convection Flow ◽  
Constant Wall Temperature ◽  
Transform Method ◽  
Casson Fluid Model

The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

An approximate Casson fluid model for tube flow of blood1

Biorheology ◽  
1975 ◽  
Vol 12 (2) ◽  
pp. 111-119 ◽  
Author(s):  
Walter P. Walawender ◽  
Te Yu Chen ◽  
David F. Cala
Keyword(s):  
Fluid Model ◽  
Casson Fluid ◽  
Tube Flow ◽  
Casson Fluid Model
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