Fluid Model For Blood Flow Research Articles

Numerical and sensitivity study on the heat transfer due to bioconvection on unsteady radiative MHD blood flow over a permeable artery with chemical reaction effects

The primary goal of this research is to investigate the dynamics of nanoparticle-mediated blood flow in the presence of bioconvection effects caused by microorganisms. The boundary layer problem of unsteady magnetohydrodynamic blood flow in the porous medium of tissues in stretching motion is studied. The Casson fluid model of blood flow is mathematically represented by a system of partial differential equations (PDE). The resulting set of governing equations is numerically solved, and the physical interpretation is given for the outcomes that are presented as graphs and tables. The temperature and concentration distribution of blood, along with the organism density profile in the corresponding boundary layer, are plotted, and the effects of various physical parameters, including magnetic field, radiation, chemical reaction, and permeability of the porous medium, on the results are investigated. Additionally, physical effects on the heat and mass transfer coefficients of the flow are also discussed. It is observed that the rate of heat transfer and the temperature profile are improved by increasing the values of the thermophoresis and Brownian motion parameters. Furthermore, at the lowest value of the permeability parameter and the highest value of the Brownian motion factor, the maximum heat transfer rate is observed. The findings of the study bear the promise of significant application in targeted drug delivery, magnetic therapy, and therapeutic hyperthermia treatments.

Numerical solution of magnetohydrodynamics effects on a generalised power law fluid model of blood flow through a bifurcated artery with an overlapping shaped stenosis.

This paper presents a numerical analysis of blood flow in a diseased vessel within the presence of an external magnetic field. The blood flow was considered to be incompressible and fully developed, in that the non-Newtonian nature of the fluid was characterised as a generalised power law model for shear-thinning, Newtonian, and shear-thickening fluids. The impact of a transverse directed external magnetic field on blood flow through a stenosed bifurcated artery was investigated. The arterial geometry was considered as a bifurcated channel with overlapping shaped stenosis. The problem was treated mathematically using the Galerkin Least-Squares (GLS) method. The implementation of this numerical method managed to overcome the numerical instability faced by the classical Galerkin technique when adopted to a highly viscous flow. The benefit of GLS in circumventing the Ladyzhenskaya-Babuška-Brezzi (LBB) condition was utilized by evaluating both the velocity and pressure components at corner nodes of a unstructured triangular element. The non-linearity that emerged from the convective terms was then treated using the Newton-Raphson method, while the numerical integrals were computed using a Gaussian quadrature rule with six quadrature points. The findings obtained from this study were then compared with available results from the literature as well as Comsol multiphysics software to verify the accuracy and validity of the numerical algorithms. It was found that the application of magnetic field was able to overcome flow reversal by 39% for a shear-thinning fluid, 26% for a Newtonian fluid, and 27% for a shear-thickening fluid. The negative pressure and steep wall shear stress which occurs at the extremities of an overlapping stenosis throat were diminished by rise in magnetic intensity. This prevented thrombosis occurrence and produced a uniform calm flow.

A Stabilized Finite Element Formulation of Non-Newtonian Fluid Model of Blood Flow in A Bifurcated Channel with Overlapping Stenosis

A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.

Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery

An artery narrowing referred to as atherosclerosis or stenosis causes a reduction in the diameter of the artery. When blood flow through an artery consists of stenosis, the issue of solute dispersion is more challenging to solve. A mathematical model is developed to examine the unsteady solute dispersion in an overlapping stenosed artery portraying blood as Bingham fluid model. The governing of the momentum equation and the constitutive equation is solved analytically. The generalized dispersion model is imposed to solve the convective-diffusion equation and to describe the entire dispersion process. The dispersion function at steady-state decreases at the center of an artery as the stenosis height increase. A reverse behavior is shown at an unsteady-state. As the plug core radius, time and stenosis height increase, the dispersion function decreases at the center of an artery. There is a high amount of red blood cells at the center of the artery but no influences near the wall. Hence, this model is useful in transporting the drug or nutrients to the targeted stenosed region in the treatment of diseases and in understanding many physiological processes.

An implicit approach to the micropolar fluid model of blood flow under the effect of body acceleration

In the present study, the problem of simulating a non-Newtonian and two-dimensional blood flow in a flexible stenosed artery is examined by an implicit finite difference method. The streaming blood in the human artery is represented as a micropolar fluid. The governing non-Linear partial differential equations are modeled in cylindrical coordinates system and following a suitable radial coordinate transformation, they are solved numerically employing a Crank–Nicolson method with a suitable choice of initial and boundary conditions. An implicit approach is obtained for velocity distribution and the numerical solutions of flow rate and resistance impedance at the stenosis throat are founded by using velocity distribution. Effects of different types of tapered arteries, the stenosis and the amplitudes of body acceleration on the blood flow characteristics are presented graphically and discussed briefly. The motion of the arterial wall is paid due attention by comparing the blood flow characteristics through the elastic artery with the rigid ones. It is observed that the obtained results are in good agreement with previously conducted studies.

Effect of magnetic field and rotation on the micropolar fluid model of blood flow through stenotic arteries

The problem of blood flow through a horizontal non-symmetric artery with a mild stenosis has been investigated. Blood is modelled as a homogeneous and incompressible micropolar fluid. The effect of both rotation and magnetic field are studied analytically and computed numerically. To evaluate the influence of the stenosis shape, an appropriate geometry has been considered such that the shape of the stenosis can be changed simply just by varying a parameter (referred to as the shape parameter). The expressions for the flow characteristics such as velocity, the impedance (resistance to flow), the wall shear stress distribution and its magnitude at the stenosis throat have been derived and analysed for different values of shape parameter n, rotation parameter ω, the magnetic field parameter M, the coupling number N and the micropolar fluid parameter m.

Effect of magnetic field and rotation on the micropolar fluid model of blood flow through stenotic arteries

Effect of magnetic field and rotation on the micropolar fluid model of blood flow through stenotic arteries

A study on the effect of inclined magnetic field and Hall current on the micropolar fluid model of blood flow through stenotic arteries in a porous medium

A study on the effect of inclined magnetic field and Hall current on the micropolar fluid model of blood flow through stenotic arteries in a porous medium

A study on the effect of inclined magnetic field and Hall current on the micropolar fluid model of blood flow through stenotic arteries in a porous medium

The problem of blood flow through a horizontal non-symmetric artery with a mild stenosis in a porous medium has been investigated. The natures of blood in small arteries are analysed mathematically by considering it as a homogeneous and incompressible micropolar fluid. The effect of both rotation and inclined magnetic field are studied analytically and computed numerically. To evaluate the influence of the stenosis shape, an appropriate geometry has been considered such that the shape of the stenosis can be changed simply just by varying a parameter (referred to as the shape parameter). The expressions for the flow characteristics such as velocity, the impedance (resistance to flow), the wall shear stress distribution and its magnitude at the stenosis throat have been derived and analysed for different values of shape parameter n, rotation parameter Ω, the magnetic field parameter M, inclination angle of the magnetic field parameter (θ), permeability parameter (K1), the coupling number N and the micropolar fluid parameter m.

Theoretical Analysis of Shear Thinning Hyperbolic Tangent Fluid Model for Blood Flow in Curved Artery with Stenosis

Theoretical Analysis of Shear Thinning Hyperbolic Tangent Fluid Model for Blood Flow in Curved Artery with Stenosis

Biomathematical study of Sutterby fluid model for blood flow in stenosed arteries

In this paper, we have discussed the biomathematical analysis of Sutterby fluid model for blood flow in stenosed tapered arteries. The equations for the Sutterby fluid model are modeled in cylindrical geometry. The equations have been developed for the case of mild stenosis. Perturbation solutions are attained in terms of small Sutterby fluid parameter β for the velocity, impedance resistance and wall shear stress. Three types of arteries i.e. converging, diverging and non-tapered have been considered for the analysis and discussion. Graphical results have been presented for different parameters of interest. Streamlines have been plotted at the end of the paper.

Rheological properties of Reiner-Rivlin fluid model for blood flow through tapered artery with stenosis

Abstract In the present article, we have analyzed the Reiner-Rivlin fluid model for blood flow through a tapered artery with a stenosis. The constitutive equations for a Reiner-Rivlin fluid have been modeled in cylindrical coordinates. A perturbation series in dimensionless Reiner-Rivlin fluid parameter ( λ 1 ≪ 1 ) have been used to obtain explicit forms for the velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

The Polar Fluid Model for Blood Flow through a Tapered Artery with Overlapping Stenosis: Effects of Catheter and Velocity Slip.

The blood flow through an overlapping clogged tapered artery in the presence of catheter is discussed. Since cholesterol deposition is resulting in the stenosis formation, velocity slip at the arterial wall is considered. The equations governing the fluid flow have been solved analytically under the assumption of the mild stenosis. The analysis with respect to various parameters arising out of fluid and geometry considered, on physiological parameters such as impedance and wall shear stress at the maximum height of the stenosis as well as across the entire length of the stenosis has been reported. A table summarizing the locations of extreme heights and the corresponding annular radii is provided. It is observed that the wall shear stress is the same at both the locations corresponding to the maximum height of the stenosis in case of nontapered artery while it varies in case of tapered artery. It is also observed that slip velocity and diverging tapered artery facilitate the fluid flow. Shear stress at the wall is increasing as micropolar parameter is decreasing and the trend is reversed in case of coupling number. The results obtained are validated by comparing them with the experimental and theoretical results.

Carreau fluid model for blood flow through a tapered artery with a stenosis

In present article, we have studied the blood flow through tapered artery with stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Carreau fluid. Carreau fluid is a type of generalized Newtonian fluid. At low shear rate Carreau fluids behaves as a Newtonian fluid n=1 and at high shear rate as power law fluid. For n<1 Carreau fluid gives pseudoplastic(non-Newtonian), or shear-thinning fluids have a lower apparent viscosity at higher shear rates and for n>1 Carreau fluid behaves as Dilatant(non-Newtonian), or shear-thickening fluids increase in apparent viscosity at higher shear rates. All three cases are appropriate for blood flow in arteries because the assumption of Newtonian behavior of blood is acceptable for high shear rate flow, i.e. the case of flow through larger arteries. It is not, however, valid when the shear rate is low as is the flow in smaller arteries and in the downstream of the stenosis. It has been pointed out that in some diseased conditions, blood exhibits remarkable non-Newtonian properties. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shear stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Analytical solutions has been evaluated for velocity, resistance impedance, wall shear stress and shear stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

Influence of heat and chemical reactions on the Sisko fluid model for blood flow through a tapered artery with a mild stenosis

The present article studies the effects of heat and chemical reactions on the blood flow through tapered artery with a stenosis. The model incorporates Sisko fluid representation for the blood flow through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and the resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Analytical solutions have been evaluated for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Stream lines have been plotted at the end of the article.

The Casson fluid model for blood flow through an inclined tapered artery of an accelerated body in the presence of magnetic field

This paper deals with the analytical investigation of Casson model for axisymmetric pulsatile blood flow through an inclined stenosed artery of a periodically accelerated body under the influence of a magnetic field. Invoking suitable transformations, the flow governing partial differential equations are non-dimensionalised. For these non-dimensionalised equations, an exact solution representing the different flow characteristic has been derived by employing the perturbation method. Plug flow radius, plug flow velocity, flow rate and impedance analysis of the Casson fluid have been done graphically by varying the yield stress, inclination of artery, body acceleration and pressure gradient. Some important results are obtained pertaining to the medical interest.

Biomechanical Analysis of Eyring Prandtl Fluid Model for Blood Flow in Stenosed Arteries

Abstract In this article, we have examined biomechanical analysis of Eyring Prandtl fluid model for blood flow in stenosed arteries. Blood flow in arteries is an important phenomenon from biological and medical point of view. No one can survive without blood flow in tapered arteries. Blood flow is the continuous running of blood in the cardiovascular system. The human body is made up of several processes all carrying out various functions. We have the gastrointestinal system which aids the digestion and the absorption of food. We also have the respiratory system which is responsible for the absorption of O2 and elimination of CO2. The urinary system removes waste from the body. The cardiovascular system helps to distribute food, O2 and other products of metabolism. The reproductive system is responsible for perpetuating the species. The nervous and endocrine system is responsible for coordinating the integration and functions of other system. The equations govern the flow for considered model are presented in cylindrical coordinates. Perturbation solutions are developed in terms of small Eyring Prandtl fluid parameter β for the velocity, impedance resistance, wall shear stress and shearing stress at the stenosis throat. Three types of arteries i.e converging, diverging and non-tapered arteries have been considered for the analysis and discussion. Graphical results have been presented for different physical parameters of the flow problem. Streamlines have been plotted at the end of the article. We observed that due to increase in Eyring Prandtl fluid parameter α, β the stenosis shape n and maximum height of the stenosis δ the velocity profile increases.

Effects of heat and chemical reaction on Jeffrey fluid model with stenosis

In this article, we have studied a non-Newtonian fluid model for blood flow through a tapered artery with a stenosis by assuming blood as Jeffrey fluid. Heat and mass transfer phenomena have been taken into account by giving temperature 0 and concentration 0 to the upper wall of the arteries, while at the centre we have considered symmetry condition for both temperature and concentration. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature field and concentration, wall shear stress, shearing stress at the stenosis throat, and impedance of the artery are discussed. The results for Newtonian fluid are obtained as a special case from this model. Trapping phenomena have been discussed at the end of this article.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time λ1 and retardation time λ2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

JEFFREY FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

In this article, we have studied a non-Newtonian fluid model for blood flow through a tapered artery with a stenosis by assuming blood as Jeffrey fluid. The main purpose of our study was to follow the idea of Mekheimer and El Kot (2008), for Jeffrey fluid model, mean to study Jeffrey fluid model for blood flow through a tapered artery with a stenosis, Jeffrey fluid model is a non-Newtonian fluid model in which we consider convective derivative instead of time derivative. It is capable of describing the phenomena of relaxation and retardation time. The Jeffrey fluid has two parameters, the relaxation time λ1and retardation time [Formula: see text]. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, wall shear stress, shearing stress at the stenosis throat, and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.