The effect of body acceleration on the dispersion of solute in a non-Newtonian blood flow through an artery

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Husnina Saadun ◽  
Nurul Aini Jaafar ◽  
Md Faisal Md Basir ◽  
Ali Anqi ◽  
Mohammad Reza Safaei
Keyword(s):  
Blood Flow ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Solute Concentration ◽  
Casson Fluid ◽  
Blood Velocity ◽  
Content Type ◽  
Body Acceleration ◽  
Lead Angle ◽  
Flow Through

Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

scholarly journals A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Dynamics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 9-17
Author(s):  
Andrea Natale Impiombato ◽  
Giorgio La Civita ◽  
Francesco Orlandi ◽  
Flavia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Blood Flow ◽  
Boundary Conditions ◽  
Quadratic Function ◽  
Pulsatile Blood Flow ◽  
Flow Through ◽  
Simplified Analysis ◽  
Function Models ◽  
Flow Reversals

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.

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 Mathematical Modeling of Treatment Effect on Tumor Growth and Blood Flow through a Channel with Magnetic Field

2021 ◽  
pp. 66-79
Author(s):  
K. W. Bunonyo ◽  
C. U. Amadi
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Tumor Growth ◽  
Blood Velocity ◽  
Frequency Parameter ◽  
Womersley Number ◽  
Permeability Parameter ◽  
Flow Through

In this research, we investigated the effect of tumor growth on blood flow through a micro channel by formulated the governing model with the assumption that blood is an incompressible, eclectrially conducting fluid which flow is caused by the pumping action of the heart and suction. The governing model was scaled using some dimensionless variables and the region of the tumor was obtained from Dominguez [1] which was incorporated in our model. The model is further reduced to an ordinary differential equation using a perturbation condition. However, the ordinary differential equation was solved using method of undermined coefficients, and the constants coefficients obtained via matrix method. Furthermore, the simulation to study the effect of the pertinent parameters was done suing computation software called Mathematica. It is seen in our investigation that the entering parameters such as magnetic field parameter, the Reynolds number, womersley number, oscillatory frequency parameter, and permeability parameter affect the blood velocity profile in decreasing and increasing fashion.

Effects of complex boundary conditions on natural convection of a viscoplastic fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2792-2808 ◽  
Author(s):  
Behnam Rafiei ◽  
Hamed Masoumi ◽  
Mohammad Saeid Aghighi ◽  
Amine Ammar
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Heated Wall ◽  
Uniform Heating ◽  
Content Type ◽  
Yield Stress Fluids ◽  
Complex Boundary

Purpose The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides. Design/methodology/approach The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid. Findings Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number. Originality/value Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

scholarly journals Unsteady solute dispersion in blood rheology with reversible phase exchange at the artery wall

2018 ◽  
Vol 7 (2) ◽  
pp. 750
Author(s):  
D S Sankar ◽  
Nurul Aini Jaafar ◽  
Yazariah Yatim
Keyword(s):  
Blood Flow ◽  
Diffusion Coefficient ◽  
Blood Rheology ◽  
Expansion Method ◽  
Casson Fluid ◽  
Longitudinal Diffusion ◽  
Flowing Fluid ◽  
Derivative Series ◽  
Flow Through ◽  
Reversible Phase

The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in the unsteady dispersion of solute in blood flow through a narrow artery is analysed mathematically, modelling the blood as Casson fluid. The resulting convective diffusion equation along with the initial and boundary conditions is solved analytically using the derivative series expansion method. The expressions for the negative asymptotic phase exchange, negative asymptotic convection, longitudinal diffusion coefficient and mean concentration are obtained. It is noted that when the solute disperses in blood flow through a narrow artery, the negative exchange coefficient, the negative convection coefficient increase and the longitudinal diffusion coefficient decreases with the increase of the Damköhler number and partition coefficient.

scholarly journals Natural convection of Casson fluid in a square enclosure

2020 ◽  
Vol 16 (5) ◽  
pp. 1245-1259
Author(s):  
Mohammad Saeid Aghighi ◽  
Christel Metivier ◽  
Hamed Masoumi
Keyword(s):  
Natural Convection ◽  
Yield Stress ◽  
Casson Fluid ◽  
Small Degree ◽  
Content Type ◽  
Square Enclosure ◽  
Casson Model ◽  
Side Walls ◽  
The Mean ◽  
Viscoplastic Models

PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

scholarly journals Numerical Simulation of Magnetohydrodynamic Influences on Casson Model for Blood Flow through an Overlapping Stenosed Artery

2021 ◽  
pp. 1016-1024
Author(s):  
Ahmed Bakheet ◽  
Esam A. Alnussairy
Keyword(s):  
Blood Flow ◽  
Flow Characteristics ◽  
Correction Method ◽  
Casson Fluid ◽  
Governing Equations ◽  
Finite Difference Technique ◽  
Stenosed Artery ◽  
Flow Phenomena ◽  
Flow Through ◽  
Unsteady Blood Flow

Magnetohydrodynamic (MHD) effects of unsteady blood flow on Casson fluid through an artery with overlapping stenosis were investigated. The nonlinear governing equations accompanied by the appropriate boundary conditions were discretized and solved based on a finite difference technique, using the pressure correction method with MAC algorithm. Moreover, blood flow characteristics, such as the velocity profile, pressure drop, wall shear stress, and patterns of streamlines, are presented graphically and inspected thoroughly for understanding the blood flow phenomena in the stenosed artery.

scholarly journals The Effect of Slip Velocity on Unsteady Peristalsis MHD Blood Flow through a Constricted Artery Experiencing Body Acceleration

2019 ◽  
Vol 24 (3) ◽  
pp. 645-659 ◽  
Author(s):  
J. Nandal ◽  
S. Kumari ◽  
R. Rathee
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Axial Velocity ◽  
Slip Velocity ◽  
Volumetric Flow Rate ◽  
Body Acceleration ◽  
Stenosed Artery ◽  
Flow Through

Abstract In this analysis, we present a theoretical study to examine the combined effect of both slip velocity and periodic body acceleration on an unsteady generalized non-Newtonian blood flow through a stenosed artery with permeable wall. A constant transverse magnetic field is applied on the peristaltic flow of blood, treating it as an elastico-viscous, electrically conducting and incompressible fluid. Appropriate transformation methods are adopted to solve the unsteady non-Newtonian axially symmetric momentum equation in the cylindrical polar coordinate system with suitably prescribed conditions. To validate the applicability of the proposed analysis, analytical expressions for the axial velocity, fluid acceleration, wall shear stress and volumetric flow rate are computed and for having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted with varying values of flow variables, to analyse the influence of the axial velocity, wall shear stress and volumetric flow rate of streaming blood.

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