J. C. Misra

A NUMERICAL MODEL FOR THE MAGNETOHYDRODYNAMIC FLOW OF BLOOD IN A POROUS CHANNEL

Magnetohydrodynamic (MHD) principles may be used to study the flow of arterial blood under the action of an applied magnetic field. Such studies are of potential value in the treatment of cardiovascular disorders that may be associated with accelerated circulation. With an aim to providing a generalized model for studying the flow of blood in an electromagnetic field environment, a numerical model is developed here, by treating blood as a non-Newtonian fluid, the motion of which is taken to be governed by Walters B-fluid model. The channel flow characteristics of the fluid are studied here, when the channel is porous and is subjected to an external magnetic field. Using the similarity transformation and boundary layer approximations, the associated nonlinear partial differential equations of the problem are reduced to nonlinear ordinary differential equations. These are solved numerically by developing a finite difference scheme. The study provides useful estimates for the influence of Reynolds number Re, Hartmann number M, and viscoelastic parameter K1 on the flow characteristics. It bears the potential to explore some important information about the hemodynamical flow of blood in an artery when it is under the action of an external magnetic field.

THEORETICAL ANALYSIS OF BLOOD FLOW THROUGH AN ARTERIAL SEGMENT HAVING MULTIPLE STENOSES

The present paper is concerned with the study of a mathematical model for the flow of blood through a multi-stenosed artery. Blood is considered here to consist of a peripheral plasma layer which is free from red cells, and a core region which is represented by a Casson fluid. A suitable generalized geometry of multiple stenoses existing in the arterial segment under consideration is taken for the study. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in the study. The computational results are presented graphically.

THERMODYNAMIC AND MAGNETOHYDRODYNAMIC ANALYSIS OF BLOOD FLOW CONSIDERING ROTATION OF MICRO-PARTICLES OF BLOOD

Flow and heat transfer of blood under the action of an external magnetic field are analyzed in this paper. The flow is considered to take place in a channel that is bounded by stretchable walls. The surface velocity of the channel is assumed to vary linearly with axial distance. The microrotation of the micro-particles of blood is taken into account by treating blood as a micropolar fluid. The governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically by developing a suitable finite difference technique. Computational work has been carried out in order to have an estimate of the velocity, microrotation, and the temperature of the fluid for different values of various physical parameters of interest in the present study of blood flow dynamics. Different physiological aspects are discussed via graphical presentation of the computed results.

MULTIPHASE FLOW OF BLOOD THROUGH ARTERIES WITH A BRANCH CAPILLARY: A THEORETICAL STUDY

In this paper, we present a theoretical analysis of the problem of hematocrit reduction (due to plasma skimming) in a capillary that emerges from an artery making an angle α with the parent artery. The analysis bears the potential to explore a variety of information regarding some phenomenological aspects of this important physiological problem. The flow is considered to consist of three distinct phases, viz., the peripheral plasma layer, the cell-depleted middle layer, and the core region which usually has a high concentration of erythrocytes. This study deals with both steady and pulsatile flow of blood, which is treated as a non-Newtonian fluid of Herschel–Bulkley type. A computational procedure is developed for a quantitative measure of the velocity profile, the volumetric flow rate, and the hematocrit of blood in a specific situation. The procedure also gives us an opportunity to examine the nature of variation of these important hemodynamic factors; this observation holds true irrespective of whether the flow of blood is steady or pulsatile. The study reveals that the velocity of blood in the parent artery reduces when the fluid index/yield stress increases. It is further revealed that the volumetric flow rate of blood in the capillary also decreases with an increase in the value of the fluid index/yield stress of blood.

MATHEMATICAL MODELING OF BLOOD FLOW IN ARTERIES SUBJECT TO A VIBRATING ENVIRONMENT

A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when the flow takes place under the action of an external pressure gradient. The fluid flows between two porous plates lying parallel to each other. The fluid is considered to be injected on one plate with a constant velocity. The plates are considered to be oscillating with the same frequency in their own planes. However, the plate velocity of single-harmonic oscillation is not constant. The effects of various parameters representing couple stress, suction and magnitude of the oscillating pressure gradient on the velocity profile and wall shear stress are discussed. It is found that the presence of couple stress in the fluid enhances the velocity of the fluid in both axial and transverse directions, while a reverse phenomenon is observed for the wall shear stress.