SUSPENSION MODEL FOR BLOOD FLOW THROUGH ARTERIAL CATHETERIZATION

Mathematical inspection of heat transfer and unsteady viscous flow in a tunnel with trapezoidal shaped slender wall

An exploration is made to investigate numerically and theoretically the time dependent flow of blood along with heat transfer through abnormal artery having trapezoidal shaped plaque. The flow is taken to be Newtonian, laminar, unsteady and incompressible. A suitable geometrical model is constructed to simulate the trapezoidal stenosis affected artery. The governed 2-dimensional momentum and heat transfer equations are conventionalized by assuming mild trapezoidal stenosis. The renovate partial differential equations are further converted into ordinary differential equations by assist of transformations. The novelty of the work is to consider unsteady blood flow through trapezoidal shape stenosed artery. A technique of finite difference is used to discretize the updated dimensionless model numerically. Comprehensive graphical outcomes for a flow of blood are obtained. The effect of trapezoidal plaque on blood velocity, pressure and temperature are shown by surface graph inside the artery and also shown with the help of line graph.

A review on non-Newtonian fluid models for multi-layered blood rheology in constricted arteries

Haemodynamics is a branch of fluid mechanics which investigates the features of blood when it flows not only via blood vessels of smaller/larger diameter, but also under normal as well as abnormal flow states, such as in the presence of stenosis, aneurysm, and thrombosis. This review aims to discuss the rheological properties of blood, geometry of constrictions, dilations and the emergence of single-layered fluid to four-layered fluid models. To discuss further the influence of the aforesaid parameters on the physiologically important flow quantities, the mathematical formulation and solution methodology of the two-layered and four layered arterial blood flow problems studied by the authors (Afiqah and Sankar in ARPN J Eng Appl Sci 15:1129--1143, 2020, Comput Methods Programs Biomed 199:105907, 2021. 10.1016/j.cmpb.2020.105907) are recalled. It should be pointed out that the increasing resistive impedance to flow in three distinct states encompassing healthy, anaemic, and diabetic demonstrates that the greater the restriction in the artery, very few blood is carried to the pathetic organs, leading to subjects' death. It is also discovered that the pulsatile nature of blood movement produces a dynamic environment that poses a slew of intriguing and unstable fluid mechanical state. It is hoped that the intriguing results gathered from this literature survey and review conducted may help the medical practitioners to forecast blood behaviour mobility in stenotic arteries. Furthermore, the physiological information gathered from the available clinical data from the literature on patients diagnosed with diabetes and anaemia may be beneficial to doctors in deciding the therapeutic procedure for treating some particular cardiovascular disease.

Electro-osmotic flow of biological fluid in divergent channel: drug therapy in compressed capillaries

The multi-phase flow of non-Newtonian through a divergent channel is studied in this article. Jeffrey fluid is considered as the base liquid and tiny gold particles for the two-phase suspension. Application of external electric field parallel to complicated capillary with net surface charge density causes the bulk motion of the bi-phase fluid. In addition to, electro-osmotic flow with heat transfer, the simultaneous effects of viscous dissipation and nonlinear thermal radiation have also been incorporated. Finally, cumbersome mathematical manipulation yields a closed-form solution to the nonlinear differential equations. Parametric study reveals that more thermal energy is contributed in response to Brinkman number which significantly assists gold particles to more heat attain high temperature, as the remedy for compressed or swollen capillaries/arteries.

Interaction between blood and solid particles propagating through a capillary with slip effects

This article describes the interaction between solid particles and blood propagating through a capillary. A slip condition is considered on the walls of the capillary. The rheological features of the blood are discussed by considering as a two-phase Newtonian fluid model, i.e., the suspension of cells in plasma. A perturbation method is successfully applied to obtain the series solution of the governing coupled differential equations. The series solution for both fluid and particle phase are presented up to second order approximation. The expressions for the velocity and pressure distributions under slip effects are determined within a tube. Furthermore, the current results are beneficial to understand the rheological features of blood which will be helpful to interpret and analyze more complex blood flow models.

Examination of nanoparticles as a drug carrier on blood flow through catheterized composite stenosed artery with permeable walls

In this paper, we have discussed the influence of copper nanoparticles on a blood flow through composite stenosed artery with permeable walls. The nature of blood is discussed mathematically by considering it as viscous nanofluid. The study is carried out for a blood vessel under mild stenosis approximations and expressions of the temperature, velocity, resistance impedance to flow, wall shear stress and the pressure gradient is obtained by using corresponding boundary conditions. Results for the effects of permeability on blood flow through composite stenosis have been discussed graphically. The considered analysis also summarizes that the drug copper nanoparticles are efficient to reduce hemodynamics of stenosis and could be helpful to predict important uses for biomedical applications. Results indicate that nanoparticles are helpful as drug carriers to minimize the effects of resistance impedance to blood flow or coagulation factors due to stenosis.

Metallic nanoparticles analysis for the blood flow in tapered stenosed arteries: Application in nanomedicines

Blood flow model is recycled to study the influence of magnetic field and nanoparticles in tapered stenosed arteries. The metallic nanoparticles for the blood flow with water as base fluid are not explored so far. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing 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 for pure water and Copper water ( Cu -water).

Mathematical analysis of Phan-Thien–Tanner fluid model for blood in arteries

In the present paper, we have studied the blood flow through tapered artery with a stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Phan-Thien–Tanner fluid. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for 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.

Blood flow analysis in tapered stenosed arteries with pseudoplastic characteristics

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. Perturbation solutions have been evaluated for 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.

PARTICULATE SUSPENSION FLOW INDUCED BY SINUSOIDAL PERISTALTIC WAVES THROUGH ECCENTRIC CYLINDERS: THREAD ANNULAR

This paper describes a new model for obtaining analytical solutions of peristaltic flow through eccentric annuli. A mathematical model of peristaltic pumping of a fluid mixture (as blood model) in a circular eccentric cylinders is presented and it is motivated due to the fact that thread injection is a promising method for placing medical implants within the human body with minimum surgical trauma. For the eccentric annuli, the inner cylinder is rigid and moving with a constant velocity V, and the outer one is hollow flexible cylinder that has a sinusoidal wave traveling down its wall. The coupled differential equations for both the fluid and the particle phases have been solved by using two methods and the expressions for the velocity distribution of fluid and particle phase, flow rate, pressure drop, friction forces at the inner and outer cylinders have been derived. The results obtained are discussed in brief. The significance of the particle concentration and the eccentricity parameter as well as the nature of the basic flow has been well explained.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.