Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Nonlocal Shear Stress

The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations (Laplace and finite Hankel transforms). For the semianalytical solution, the inverse Laplace transform is found by means of Stehfest’s and Tzou’s algorithms. The numerical calculations were performed by using Mathcad software. The flow is significantly affected by Hartmann number, inclination angle, fractional parameter, permeability parameter, and pulsatile pressure gradient frequency, according to the findings. It is deduced that there exists a significant difference in the velocity of the flow at higher time when the magnitude of Reynolds number is small and large.

Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

Unsteady Flow and Heat Transfer of a Dusty Fluid through a Rectangular Channel

The present discussion deals with the study of an unsteady flow and heat transfer of a dusty fluid through a rectangular channel under the influence of pulsatile pressure gradient along with the effect of a uniform magnetic field. The analytical solutions of the problem are obtained using variable separable and Fourier transform techniques. The graphs are drawn for the velocity fields of both fluid and dust phases under the effect of Reynolds number. Further, changes in the Nusselt number are shown graphically, and, on the basis of these, the conclusions and discussions are given.

NUMERICAL SIMULATION OF UNSTEADY TWO-LAYERED PULSATILE BLOOD FLOW IN A STENOSED FLEXIBLE ARTERY: EFFECT OF PERIPHERAL LAYER VISCOSITY

The present paper deals with a theoretical investigation of blood flow in an arterial segment in the presence of stenosis. The streaming blood is treated to be composed of two different layers ‐ the central core and the plasma. The former is considered to be non‐Newtonian liquid characterised by the Power law model, while the latter is chosen to be Newtonian. The artery is simulated as an elastic (moving wall) cylindrical tube. The unsteady flow mechanism of the present study is subjected to a pulsatile pressure gradient arising from the normal functioning of the heart. The time‐variant geometry of the stenosis has been accounted for in order to improve resemblance to the real situation. The unsteady flow mechanism, subjected to pulsatile pressure gradient, has been solved using finite difference scheme by exploiting the physically realistic prescribed conditions. An extensive quantitative analysis has been performed through numerical computations of the flow velocity, the flux, the resistive impedances and the wall shear stresses, together with their dependence with the time, the input pressure gradient and the severity of the stenosis, presented graphically at the end of the paper in order to illustrate the applicability of the model under consideration. Special emphasis has been made to compare the existing results with the present ones and found to have a good agreement. Straipsnyje nagrinejamas kraujo srauto tekejimas esant stenozei. Nagrinejamas dvisluoks‐nis kraujo tekejimas. Arterija modeliuojama kaip vamzdis su elastinemis sienelemis. Kraujo srauto nestacionaruma sukelia širdies veikla. Skaitinis sprendinys randamas baigtiniu skirtumu metodu. Atlikta kokybine skaitiniu sprendiniu analize iliustruojanti greičiu, srautu, sieneles itampu priklausomybe laike. Skaitiniai rezultatai pakankamai gerai patvirtina eksperimentinius duomenis.

Effect of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates

In this paper the MHD of a Non-Newtonian unsteady flow of an incompressible fluid under the effect of couple stresses and a uniform external magnetic field is analysed by using the Eyring Powell model. In the first approximation the solution is obtained by using the Mathematica computational program with assuming a pulsatile pressure gradient in the direction of the motion. In the second order approximation a numerical solution of the non-linear partial differential equation is obtained by using a finite difference method. The effects of different parameters are discussed with the help of graphs in the two cases.

Dynamics of Cerebrospinal Fluid in the Subrachnoid Space Within Spinal Cavity

In this paper, a computational study was carried out to investigate the CSF dynamics in the spinal cavity. A theoretical and computational model was developed to simulate the pulsatile CSF flow and the deformation of the spinal cavity that results from transmission of the CSF pulse wave from the cranial cavity. Under a pulsatile pressure gradient, the velocity profile of the flow is blunt for large Womersley numbers, while for small Womersley numbers the velocity profile is parabolic. The phase relationship between the pressure and the velocity is also related to Womersley number. This is the first step to understand the pulsatile dynamics of the CSF in the spinal cavity and will help explain the cause of related diseases and improve the clinical treatment.