Flow of micropolar fluid through a tube with stenosis

Micropolar pulsatile blood flow conveying nanoparticles in a stenotic tapered artery: NON-Newtonian pharmacodynamic simulation

Two-dimensional rheological laminar hemodynamics through a diseased tapered artery with a mild stenosis present is simulated theoretically and computationally. The effect of different metallic nanoparticles homogeneously suspended in the blood is considered, motivated by drug delivery (pharmacology) applications. The Eringen micropolar model has been discussed for hemorheological characteristics in the whole arterial region. The conservation equations for mass, linear momentum, angular momentum (micro-rotation), and energy and nanoparticle species are normalized by employing suitable non-dimensional variables. The transformed equations are solved numerically subject to physically appropriate boundary conditions using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A good correlation is achieved between the FreeFEM++ computations and existing results. The effect of selected parameters (taper angle, Prandtl number, Womersley parameter, pulsatile constants, and volumetric concentration) on velocity, temperature, and micro-rotational (Eringen angular) velocity has been calculated for a stenosed arterial segment. Wall shear stress, volumetric flow rate, and hemodynamic impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing Prandtl number (Pr), the micro-rotational velocity decreases i.e., microelement (blood cell) spin is suppressed. Wall shear stress decreases with the increment in pulsatile parameters (B and e), whereas linear velocity increases with a decrement in these parameters. Furthermore, the velocity decreases in the tapered region with elevation in the Womersley parameter (α). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in hematology.

EFFECT OF INDUCED MAGNETIC FIELD ON BLOOD FLOW THROUGH A CONSTRICTED CHANNEL: AN ANALYTICAL APPROACH

A nonlinear micropolar fluid model is considered with a view to examine the effect of induced magnetic field on blood flow through a constricted channel. We assume that the flow is unidirectional and flowing through a narrow channel, where the Reynolds number is less than unity such as in microvessels. Under the low Reynolds number approximation, the analytical expressions for axial velocity, micro-rotation component, axial pressure gradient, axial induced magnetic field, resistance to flow and wall shear stress have been obtained. The flow characteristic phenomena have been analyzed by taking valid numerical values of the parameters, which are applicable to blood rheology. The present analytical solutions have been compared with the analytical solutions of Hartmann (Hartmann J. Hg-Dynamics-I: Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field, Mathematisk-Fysiske Meddeleser XV:6, 1937) and found excellent agreement. The study shows that with the increasing values of the magnetic field strength decreases the axial velocity at the central line of the channel, while the flow is accelerating in the vicinity of the channel wall. The induced magnetic field has an increasing effect on the micro-rotation component, which in turn produces increasing pressure gradient. The electrical response of the microcirculation increases with the increase in the Hartmann number and the stenosis height. Thus, the resultant flow predictions presented here may be useful for the potential applications in cardiovascular engineering.

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics considering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrotational velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.

PULSATILE FLOW AND HEAT TRANSFER OF A MAGNETO-MICROPOLAR FLUID THROUGH A STENOSED ARTERY UNDER THE INFLUENCE OF BODY ACCELERATION

With an aim to investigate the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis is under consideration in this article. The flow of blood is presented by an unsteady micropolar fluid, and the heat-transfer characteristics have been taken into account. The nonlinear equations that govern the flow are solved numerically using finite difference technique by employing a suitable coordinate transformation. The numerical results have been observed for axial and microrotation component of velocity, fluid acceleration, wall shear stress (WSS), flow resistance, temperature, and the volumetric flow rate. It thus turns out that the rate of heat transfer increases with the increase of Hartmann number H, while the WSS has a reducing effect on the Hartmann number H and an enhancing effect on the ratio of viscosity K as well as on the constriction height δ.