D. S. Sankar | ITB - Institut Teknologi Brunei (original) (raw)

Papers by D. S. Sankar

International Journal of Non-Linear Mechanics, 2008

ABSTRACT

Communications in Nonlinear Science and Numerical Simulation, 2011

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating t... more This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.

Archive of Applied Mechanics, Oct 23, 2023

JP Journal of Heat and Mass Transfer, 2018

This non-linear mathematical model analyses the pulsatile blood flow in a tapered narrow artery w... more This non-linear mathematical model analyses the pulsatile blood flow in a tapered narrow artery with mild multiple stenoses in the presence of body acceleration, considering blood as non-Newtonian Carreau fluid. Double perturbation method is applied to solve the resulting non-linear boundary value problem and the asymptotic solutions to the flow rate, pressure gradient, velocity profile, wall shear stress and longitudinal impedance to flow are obtained. It is noted that the blood velocity rises when the angle of tapering of artery, body acceleration D. S. Sankar and Usik Lee 372 and power law index increase, whereas this rheological behavior is reversed for longitudinal impedance to flow and wall shear stress when each of the aforesaid parameters increases. It is also found that the wall shear stress in blood flow increases considerably when the maximum depth of the stenosis increases and it decreases considerably when the pulsatile Reynolds number increases. The estimates of the percentage of increase in the longitudinal impedance to flow increase significantly with the increase of the maximum depth of the stenosis and Weissenberg number. It is also observed that the mean velocity of blood increases noticeably with the increase of angle of tapering of the artery and body acceleration parameter.

Applied and Computational Mechanics, 1999

In this article, the influence of microstructure in the Casson fluid flow through a porous medium... more In this article, the influence of microstructure in the Casson fluid flow through a porous medium is investigated, by extending the Buckingham-Reiner’s one-dimensional model to plane-Poiseuille flow and Hagen-Poiseuille flow geometries. While analyzing the flow characteristics in single-channel/pipes or multiple channels/pipes of different width/radius, four different probability density functions are used to model the pores widths/radii distributions. It is found that when the pressure gradient increases, the Buckingham-Reiner function raises slowly in the plane-Poiseuille flow, whereas in Hagen-Poiseuille flow, it rises rapidly. In all kinds of distribution of pores, the fluid’s mean velocity and porosity of the flow medium are considerably higher in the Hagen-Poiseuille flow than in the plane-Poiseuille flow, and this behavior is reversed for the permeability of the flow medium. The fluid’s mean velocity, porosity, and permeability of the flow medium increases appreciably with th...

Computer Methods and Programs in Biomedicine, 2021

BACKGROUND AND OBJECTIVE This study aims to investigate the haemodynamical factors with the motiv... more BACKGROUND AND OBJECTIVE This study aims to investigate the haemodynamical factors with the motive to spell out some useful information for better interpretation and treatment of cardiovascular diseases. Numerous researchers theoretically investigated the movement of blood in the vascular system, treating blood as either single-layered or two-layered fluid representation. In this contemporary study, a four-layered fluid model is developed to analyse the rheological elements of blood when it flows via constricted arteries with slight constriction and the arterial wall is considered as porous medium. METHODS The momentum and constitutive equations are solved together with the suitable boundary conditions in an attempt to get the results on the distribution of velocity, volumetric flow rate, pressure gradient, shear stresses at the wall and resistive impedance to flow in which methods of integration and perturbation are utilized. The analytical/numerical solutions and graphical results are obtained by the extensive use of MATLAB software. RESULTS It is of importance to state that the magnitude of the shear stresses on the wall reduces with the rise of Darcy number, Weissenberg number and power law index. Velocity of blood however, rises with the upsurge in Darcy slip parameter, Weissenberg number and power law index. It is pertinent to record that when the stenosis depth rises from 0 to 0.15, the ratio of increase in the mean velocity of healthy, anemic and diabetic subjects are recorded as 4.58, 2.62 and 22.44 respectively. It is also found that the ratio of increase in the wall shear stress in the aforementioned states of blood are found to be 4.7, 4.27 and 3.62 respectively when the stenosis depth rises from 0 to 0.15. CONCLUSION The nature of increased flow resistance in all three different situations such as anemic, healthy, and diabetic shows that the larger the constriction in the artery, the less amount of blood is transported to crucial organs which results in the sudden death of subjects. It is hoped that the outcomes of this study would be useful to medical practitioners and bio-medical engineers in predicting the behavior of blood flow in narrowed blood vessels for a more probable treatment modalities.

International Journal of Applied Mechanics and Engineering, 2020

A computational model is presented to explore the properties of heat source, chemically reacting ... more A computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation Rd, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter M and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.

International Journal of Non-Linear Mechanics, 2011

ABSTRACT The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetr... more ABSTRACT The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel–Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel–Bulkley material are significantly lower than those of the single-phase Herschel–Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.

Abstract and Applied Analysis, 2012

Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence... more 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-fluid Herschel-Bulkley model 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. ...

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

The pulsatile flow of blood through stenosed narrow arteries with body acceleration is analyzed b... more The pulsatile flow of blood through stenosed narrow arteries with body acceleration is analyzed by treating blood as Herschel-Bulkley fluid. Perturbation method is used to solve the resulting system of nonlinear partial differential equations with appropriate boundary conditions. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius and longitudinal impedance are obtained. The effects of different parameters on these flow quantities are discussed. It is found that the velocity and flow rate increase with the increase of the pressure gradient, body acceleration and pulsatile Reynolds number, whereas they decrease with the increase of the yield stress and depth of the stenosis. It is noted that the plug core radius and wall shear stress increase with the increase of the yield stress and depth of the stenosis, but they decrease with the increase of the body acceleration and pulsatile Reynolds number. It is also observed that the estimates of the increase in the longitudinal impedance rise with an increase of the stenosis depth and yield stress and an opposite trend is noticed with an increase of the body acceleration.

INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2020)

The pulsatile flow of blood through a tapered constricted narrow artery is investigated in this s... more 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.

Journal of Mechanical Science and Technology

International Journal of Engineering & Technology

The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in... more 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.

Journal of Physics: Conference Series

The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the... more The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the presence of magnetic field is analysed, modelling the suspension of all the erythrocytes in the inner phase region as Herschel-Bulkley fluid and the cell depleted plasma in the outer-phase region as Newtonian fluid. Explicit finite difference method is employed to obtain the numerical solution to various flow measurements from the modelled initial boundary value problem. It is found that when the magnetic field parameter increases, the velocity increases and wall shear stress and longitudinal impedance to flow increase. The estimates of the increase in the longitudinal impedance to flow for the two-phase H-B fluid model is higher than that of the single-phase H-B fluid model.

International Journal of Advances in Engineering Sciences and Applied Mathematics

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric sten... more This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.

International Journal of Non-Linear Mechanics

ABSTRACT

International Journal of Non-Linear Mechanics, 2008

ABSTRACT

Communications in Nonlinear Science and Numerical Simulation, 2011

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating t... more This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.

Archive of Applied Mechanics, Oct 23, 2023

JP Journal of Heat and Mass Transfer, 2018

This non-linear mathematical model analyses the pulsatile blood flow in a tapered narrow artery w... more This non-linear mathematical model analyses the pulsatile blood flow in a tapered narrow artery with mild multiple stenoses in the presence of body acceleration, considering blood as non-Newtonian Carreau fluid. Double perturbation method is applied to solve the resulting non-linear boundary value problem and the asymptotic solutions to the flow rate, pressure gradient, velocity profile, wall shear stress and longitudinal impedance to flow are obtained. It is noted that the blood velocity rises when the angle of tapering of artery, body acceleration D. S. Sankar and Usik Lee 372 and power law index increase, whereas this rheological behavior is reversed for longitudinal impedance to flow and wall shear stress when each of the aforesaid parameters increases. It is also found that the wall shear stress in blood flow increases considerably when the maximum depth of the stenosis increases and it decreases considerably when the pulsatile Reynolds number increases. The estimates of the percentage of increase in the longitudinal impedance to flow increase significantly with the increase of the maximum depth of the stenosis and Weissenberg number. It is also observed that the mean velocity of blood increases noticeably with the increase of angle of tapering of the artery and body acceleration parameter.

Applied and Computational Mechanics, 1999

In this article, the influence of microstructure in the Casson fluid flow through a porous medium... more In this article, the influence of microstructure in the Casson fluid flow through a porous medium is investigated, by extending the Buckingham-Reiner’s one-dimensional model to plane-Poiseuille flow and Hagen-Poiseuille flow geometries. While analyzing the flow characteristics in single-channel/pipes or multiple channels/pipes of different width/radius, four different probability density functions are used to model the pores widths/radii distributions. It is found that when the pressure gradient increases, the Buckingham-Reiner function raises slowly in the plane-Poiseuille flow, whereas in Hagen-Poiseuille flow, it rises rapidly. In all kinds of distribution of pores, the fluid’s mean velocity and porosity of the flow medium are considerably higher in the Hagen-Poiseuille flow than in the plane-Poiseuille flow, and this behavior is reversed for the permeability of the flow medium. The fluid’s mean velocity, porosity, and permeability of the flow medium increases appreciably with th...

Computer Methods and Programs in Biomedicine, 2021

BACKGROUND AND OBJECTIVE This study aims to investigate the haemodynamical factors with the motiv... more BACKGROUND AND OBJECTIVE This study aims to investigate the haemodynamical factors with the motive to spell out some useful information for better interpretation and treatment of cardiovascular diseases. Numerous researchers theoretically investigated the movement of blood in the vascular system, treating blood as either single-layered or two-layered fluid representation. In this contemporary study, a four-layered fluid model is developed to analyse the rheological elements of blood when it flows via constricted arteries with slight constriction and the arterial wall is considered as porous medium. METHODS The momentum and constitutive equations are solved together with the suitable boundary conditions in an attempt to get the results on the distribution of velocity, volumetric flow rate, pressure gradient, shear stresses at the wall and resistive impedance to flow in which methods of integration and perturbation are utilized. The analytical/numerical solutions and graphical results are obtained by the extensive use of MATLAB software. RESULTS It is of importance to state that the magnitude of the shear stresses on the wall reduces with the rise of Darcy number, Weissenberg number and power law index. Velocity of blood however, rises with the upsurge in Darcy slip parameter, Weissenberg number and power law index. It is pertinent to record that when the stenosis depth rises from 0 to 0.15, the ratio of increase in the mean velocity of healthy, anemic and diabetic subjects are recorded as 4.58, 2.62 and 22.44 respectively. It is also found that the ratio of increase in the wall shear stress in the aforementioned states of blood are found to be 4.7, 4.27 and 3.62 respectively when the stenosis depth rises from 0 to 0.15. CONCLUSION The nature of increased flow resistance in all three different situations such as anemic, healthy, and diabetic shows that the larger the constriction in the artery, the less amount of blood is transported to crucial organs which results in the sudden death of subjects. It is hoped that the outcomes of this study would be useful to medical practitioners and bio-medical engineers in predicting the behavior of blood flow in narrowed blood vessels for a more probable treatment modalities.

International Journal of Applied Mechanics and Engineering, 2020

A computational model is presented to explore the properties of heat source, chemically reacting ... more A computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation Rd, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter M and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.

International Journal of Non-Linear Mechanics, 2011

ABSTRACT The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetr... more ABSTRACT The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel–Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel–Bulkley material are significantly lower than those of the single-phase Herschel–Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.

Abstract and Applied Analysis, 2012

Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence... more 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-fluid Herschel-Bulkley model 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. ...

International Journal of Nonlinear Sciences and Numerical Simulation, 2010

The pulsatile flow of blood through stenosed narrow arteries with body acceleration is analyzed b... more The pulsatile flow of blood through stenosed narrow arteries with body acceleration is analyzed by treating blood as Herschel-Bulkley fluid. Perturbation method is used to solve the resulting system of nonlinear partial differential equations with appropriate boundary conditions. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius and longitudinal impedance are obtained. The effects of different parameters on these flow quantities are discussed. It is found that the velocity and flow rate increase with the increase of the pressure gradient, body acceleration and pulsatile Reynolds number, whereas they decrease with the increase of the yield stress and depth of the stenosis. It is noted that the plug core radius and wall shear stress increase with the increase of the yield stress and depth of the stenosis, but they decrease with the increase of the body acceleration and pulsatile Reynolds number. It is also observed that the estimates of the increase in the longitudinal impedance rise with an increase of the stenosis depth and yield stress and an opposite trend is noticed with an increase of the body acceleration.

INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2020)

The pulsatile flow of blood through a tapered constricted narrow artery is investigated in this s... more 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.

Journal of Mechanical Science and Technology

International Journal of Engineering & Technology

The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in... more 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.

Journal of Physics: Conference Series

The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the... more The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the presence of magnetic field is analysed, modelling the suspension of all the erythrocytes in the inner phase region as Herschel-Bulkley fluid and the cell depleted plasma in the outer-phase region as Newtonian fluid. Explicit finite difference method is employed to obtain the numerical solution to various flow measurements from the modelled initial boundary value problem. It is found that when the magnetic field parameter increases, the velocity increases and wall shear stress and longitudinal impedance to flow increase. The estimates of the increase in the longitudinal impedance to flow for the two-phase H-B fluid model is higher than that of the single-phase H-B fluid model.

International Journal of Advances in Engineering Sciences and Applied Mathematics

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric sten... more This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.

International Journal of Non-Linear Mechanics

ABSTRACT