Modeling of Blood Flow in a Constricted Porous Vessel Under Magnetic Environment: An Analytical Approach

Sinha, A.; Shit, G. C.

doi:10.1007/s40819-014-0022-6

Cited by 4 publications

(9 citation statements)

References 28 publications

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“…In analytical work done by Srivastava [2], the role of porosity subjected to the MHD effects was studied by considering an inclined tapered artery with mild stenosis under the influence of an inclined magnetic field. The mathematical analysis carried out in their study discovered similar behaviours of blood when subjected to an external magnetic field with a porous medium effect as the one presented in the previous study highlighted in [1], [3], [5] and [7]. The axial velocity distributions were observed to have a respective enhancing and diminishing effect on the permeability of the porous vessel and magnetic field applied externally.…”

Section: Introductionsupporting

confidence: 60%

“…It has been reported in numerous studies that the development of stenotic artery certainly disturbs the nature of blood movement and contributes to serious detrimental effects on individual health. The pathological states of a diseased vessel as a porous structure should be taken seriously considering that stenosis is developed by the deposition of fatty substances and the proliferation of connective tissues on the endothelium [3][4][5][6][7]. Due to that, the geometry of stenosis has been modelled in previous works of literature by using various kinds of shapes to portray them close to its pathological condition.…”

Section: Introductionmentioning

confidence: 99%

“…Jain et al [3] examined analytically the influences of porosity constant and magnetic number on the Newtonian model of blood flow through an artery with a cosine shaped stenosis. Sinha et al [7] analytically explored the effects of a transverse magnetic field and porous medium on the Newtonian model of blood flow in terms of stream function, flow velocity as well as wall shear stress. A mathematical model of the Newtonian model of blood flow through a porous vessel with a pair of stenosis subjected to the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) principles was developed in [5].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Analysis of Blood Flow Behaviour in a Constricted Porous Bifurcated Artery under the Influence of Magnetic Field

Zain

Ismail²,

Johnston³

2023

CFDL

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A numerical investigation concerning the effect of arterial constriction on the flow behaviour of blood in a porous bifurcated artery under the influence of a transverse magnetic field has been carried out. The equations of motion governing the flow are derived in the Cartesian coordinate system by treating the fluid as an electrically conducting, Newtonian, incompressible and fully developed blood flow. The blood is considered to flow through a constricted bifurcated artery with overlapping stenosis located at the mother artery. This developed model is consistent with the principles of magnetohydrodynamics. A stabilized form of finite element method, known as the Galerkin least-squares method is employed in solving the governing equation with suitably prescribed boundary conditions. Then, the non-linear systems resulting from the developed model are linearized by an iterative technique called the Newton-Raphson method. The effects of various parameters particularly the severity of stenosis, magnetohydrodynamics constant and permeability parameter on blood flow characteristics are analysed graphically for the velocity profile and streamline pattern. The findings obtained show that the presence of a magnetic field caused a significant alteration in the blood flow behaviour. Slight changes occurred in the flow pattern with the porous medium consideration. The application of a magnetic field could be utilized in controlling the hemodynamic flow of blood by decelerating the flow velocity and reducing the vortex sizes with rising in Hartmann number. While the pathological state of arterial disease as a porous structure reveals that a more porous fluid medium could have slightly promoted the growth in vortex size.

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Section: Introductionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Analysis of Blood Flow Behaviour in a Constricted Porous Bifurcated Artery under the Influence of Magnetic Field

Zain

Ismail²,

Johnston³

2023

CFDL

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“…Overlapping shaped stenosis can be classified as multiple stenoses, which makes the study closer to the physiological situations of a diseased artery [9]. Since atherosclerosis is developed through the deposition of cholesterol, fatty substance, fibrin, calcium and cellular waste on the endothelium as well as through the proliferation of connective tissues inside the arterial wall, hence in a such pathological state the blood can be considered as flowing through a fictitious porous structure [3,[10][11][12]. Given that, the study of blood flow patterns in a porous stenosed vessel around the location that possesses a curvature, junction as well as bifurcation are fields of great interest to be explored in physiological problems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of Heat Transfer in Magnetohydrodynamic Blood Flow Through a Porous Bifurcated Artery with Overlapping Stenosis

Zain

Ismail²

2023

ARFMTS

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The influence of heat transfers on magnetohydrodynamic blood flow treated as a Newtonian rheological model in permeable bifurcated arteries with a magnetic field applied in a transverse direction has been presented in this study. The blood flow is considered steady, incompressible, electrically conducting and porous as it consists of fatty accumulation on blood cells. A mathematical model governing such flow phenomena is developed by the Navier-Stokes and energy equations. The governing equations with appropriate boundary conditions are solved numerically by using a stabilized form of the finite element method, called the Galerkin least-squares method. The implementation of this method managed to overcome two sources of undesirable pathologies suffered by the Classical Galerkin method in solving the incompressible flow. This involves the requirement to satisfy the Babuška-Brezzi stability condition and the inherent instability arising from the approximations of highly advective flows. As a result, stable and converged solutions are generated for the velocity, temperature, pressure, wall shear stress and heat transfer coefficient in the constricted bifurcated artery by employing an equal order (quadratic triangular element) of interpolation function for velocity, pressure and temperature subspaces. The developed algorithm is validated with reported findings from previous literature where a close agreement has been achieved. Effects of the porosity parameter and Hartmann number in the presence of heat on blood flow characteristics at several locations along the branch artery are computed and presented graphically. The finding obtained from this work may be beneficial for cryosurgery and hyperthermia treatment in analysing the temperature distributions inside the vessel.

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“…Many researchers 25 , 26 worked on blood flow problems in tubes by applying Adomian decomposition method (ADM). This method was developed by Adomian 27 .…”

Section: Introductionmentioning

confidence: 99%

Slip flow through a non-uniform channel under the influence of transverse magnetic field

Farooq

Mushtaq

Munir

et al. 2018

Sci Rep

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This study deals with the steady laminar slip flow of an incompressible Newtonian fluid in a non-uniform permeable channel under the influence of transverse magnetic field. The reabsorption through the wall is accounted for by considering flux as a function of downstream distance. The non-linear coupled partial differential equations of motion are first transformed into a single fourth order partial differential equation and then solved analytically using Adomain decomposition method. Effects of pertinent parameters on different flow properties are discussed by plotting graphs. Results reveal that magnetic field considerably influences the behavior of flow.

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Modeling of Blood Flow in a Constricted Porous Vessel Under Magnetic Environment: An Analytical Approach

Cited by 4 publications

References 28 publications

Numerical Analysis of Blood Flow Behaviour in a Constricted Porous Bifurcated Artery under the Influence of Magnetic Field

Numerical Analysis of Blood Flow Behaviour in a Constricted Porous Bifurcated Artery under the Influence of Magnetic Field

Dynamic Response of Heat Transfer in Magnetohydrodynamic Blood Flow Through a Porous Bifurcated Artery with Overlapping Stenosis

Slip flow through a non-uniform channel under the influence of transverse magnetic field

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