Mathematical Analysis of Carreau Fluid model for Blood Flow in Tapered Constricted Arteries

The pulsatile flow of blood through a tapered constricted narrow artery is investigated in this study, treating the blood as Carreau fluid model. The constriction in the artery is due to the formation of asymmetric stenosis in the lumen of the artery. The expressions obtained by Sankar (2016) for the various flow quantities are used to analyze the flow with different arterial geometry. The influence of various flow parameters on the velocity distribution, wall shear stress and longitudinal impedance to flow is discussed. The velocity of blood increases with the increase of the power law index and stenosis shape parameter and it decreases considerably with the increase of the maximum depth of the stenosis. The wall shear stress and longitudinal impedance to flow decrease with the increase stenosis shape parameter, amplitude of the pulsatile pressure gradient, flow rate, power law index and Weissenberg number. The estimates of the percentage of increase in the wall shear stress and longitudinal impedance to flow increase with the increase of the angle tapering and these increase significantly with the increase of the maximum depth of the stenosis. The mean velocity of blood decreases considerably with the increase of the artery radius (except in arteriole), maximum depth of the stenosis and angle of tapering and it is considerably higher in pulsatile flow of blood than in the steady flow of blood

Two-Layered Pulsatile Blood Flow in a Stenosed Artery with Body Acceleration and Slip at Wall

Pulsatile flow of blood through an artery in presence of a mild stenosis has been investigated in this paper assuming the body fluid blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Bingham Plastic and the peripheral region of plasma as a Newtonian fluid. This model has been used to study the influence of body acceleration, non- Newtonian nature of blood and a velocity slip at wall, in blood flow through stenosed arteries. By employing a perturbation analysis, analytic expressions for the velocity profile, Plug-core radius, flow rate, wall shear stress and effective viscosity, are derived. The variations of flow variables with different parameters are shown diagrammatically and discussed. It is noticed that velocity and flow rate increase but effective viscosity decreases, due to a wall slip. Flow rates and speed are enhanced further due to the influence of body acceleration

Multicompartmental poroelastic modelling for CSF production and circulation

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.This study proposes the implementation of a Multiple-Network Poroelastic Theory (MPET) model for the purpose of investigating in detail the transport of water within the cerebral environment. The advantage of using the MPET representation is that it accounts for fluid transport between CSF, brain parenchyma and cerebral blood. They key novelty in the model discussed in the present study is the amalgamation of anatomically accurate Choroid Plexus regions, with their individual feeding arteries. This model is used to demonstrate the impact of aqueductal stenosis and atresia of the Foramina of Luschka and Magendie on the cerebral ventricles. The possible implications of treating such a condition with the aid of endoscopic third ventriculostomy are investigated and discussed.This study is supported by the Research Councils UK cross council initiative led by EPSRC and contributed to by AHRC, ESRC, and MRC

Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries

Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as �i� Herschel-Bulkley fluid and �ii� Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar �2010� for two-fluidHerschel-Bulkleymodel and Sankar and Lee �2011� for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model

Mathematical Analysis of Single and Two Phase Flow of Blood in Narrow Arteries with Multiple Contrictions

The pulsatile flow of blood in narrow arteries with multiple-stenoses under body acceleration is analyzed mathematically, treating blood as (i) single-phase Herschel-Bulkley fluid model and (ii) two-phase Herschel-Bulkley fluid model. The expressions for various flow quantities obtained by Sankar and Ismail (2010) for single-phase Herschel-Bulkley fluid model and Sankar (2010c) for two-phase Herschel-Bulkley fluid model are used to compute the data for comparing these fluid models in a new flow geometry. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow are marginally lower for two-phase H-B fluid model than those of the single-phase H-B fluid model. It is found that the velocity decreases significantly with the increase yield stress of the fluid and the reverse behavior is noticed for longitudinal impedance to flow. It is also noticed that the velocity distribution and flow rate are higher for two-phase Herschel-Bulkley fluid model than those of the single-phase Herschel-Bulkley fluid model. It is also recorded that the estimates of the mean velocity increase with the increase of the body acceleration and this behavior is reversed when the stenosis depth increases

Pulsatile Flow of Blood in a Constricted Artery with Body Acceleration

Pulsatile flow of blood through a uniform artery in the presence of a mild stenosis has been investigated in this paper. Blood has been represented by a Newtonian fluid. This model has been used to study the influence of body acceleration and a velocity slip at wall, in blood flow through stenosed arteries. By employing a perturbation analysis, analytic expressions for the velocity profile, flow rate, wall shear stress and effective viscosity, are derived. The variations of flow variables with different parameters are shown diagrammatically and discussed. It is noticed that velocity and flow rate increase but effective viscosity decreases, due to a wall slip. Flow rate and speed enhance further due to the influence of body acceleration. Biological implications of this modeling are briefly discussed

The gravitational effects of blood flow in irregular stenosed artery with various severity / Yan BinTan and Norzieha Mustapha

The mathematical study investigates the influences of gravitational force in an artery segment onthe various severity of the stenosis. Blood flow along the arterial segment is considered as incompressible Newtonian fluid. An unsteady two-dimensional nonlinear model is taken where the governing Navier-Stokes equations are added with significant gravity term. Marker and Cell (MAC) method based on finite difference approximations in a staggered grid is selected to solve the problem. Results obtained show that slight difference of areal occlusion percentage of severe stenosis in a vessel can lead to significant impacts on blood flow patterns. With the presence of the gravitational acceleration force, the pressure and axial velocity along the vessel is generally higher than without the gravitational force. Besides, the wall shear stress is lowerand therecirculation region is smallerin the presence of gravitational forc