Μελέτη κίνησης βιομαγνητικών ρευστών υπό την επίδραση μαγνητικού πεδίου

Abstract

The flow of biomagnetic fluids in the presence of an applied magnetic field is studied in the present thesis. As biomagnetic is defined a fluid that exists in a living creature (biofluid) and its flow is affected by the presence of a magnetic field. The most characteristic biofluid is the blood. The Newtonian viscous laminar incompressible blood flow is considered in the present thesis for the estimation of the parameters appearing in the problems under consideration. An introduction is made at the first chapter of the thesis concerning fundamental concepts of the magnetic fluids such as the magnetization and equilibrium flow. Experimental applications in the biomedicine are also given as well as the mathematical model describing the flow of biological fluids under the influence of an applied magnetic field. In order to investigate the effect of the magnetic field in the next three chapters basic flow problems of biomagnetic fluid (blood) are studied. In the second chapter the flow over a stretching sheet under the influence of an applied magnetic field is studied. The physical problem is described by a coupled system of non linear partial differential equations (pdes) with their appropriate boundary conditions. For the variation of the magnetization with the temperature and/or the magnetic field intensity two cases are considered (I and II). The arising system describing the physical problem is transformed into corresponding coupled systems of non linear ordinary differential equations (ods) after the introduction of proper non dimensional variables. For the numerical solution, finite differences are used for the case I, whereas a spectral method with Chebyshev polynomials is also used for the case II. It is apparent that the application of the magnetic field increases the skin friction and the pressure on the surface, whereas the heat transfer is reducing. A comparison is also made between the two numerical methods used in the case II. The efficiency and the accuracy of the spectral method over against the finite differences method are demonstrated. The superiority of the spectral method is apparent especially when high accuracy solution is desired. In the third chapter the fundamental problem of the biomagnetic fluid flow taking place in a rectangular duct under the influence of an applied magnetic field is studied. For the numerical solution of the problem, which is described by a coupled and non linear system of PDEs, with their appropriate boundary conditions, the stream function-vorticity formulation is adopted and the solution is obtained developing an efficient numerical technique based on the upwind finite differences joint with a line by line implicit method. Results concerning the velocity and temperature field, skin friction and rate of heat transfer indicate that the presence of magnetic field appreciable influence the flow field. The three dimensional, fully developed flow of a biomagnetic fluid in an impermeable rectangular duct under the influence of an applied magnetic field is numerically studied in the fourth chapter. The system of the partial differential equations, resulting after the introduction of appropriate non-dimensional variables, is solved applying an efficient numerical technique based on a pressure-linked pseudotransient method on a collocated grid. Results concerning the existence and the uniqueness of the solution are also given. The obtained results, for different values for the parameters entering into the problem under consideration, show that the flow is appreciably influenced by the presence of the magnetic field in the sense of reduction of the axial velocity and the formation of two vortices at the transverse plane. These first results indicate that the magnetic field significantly influences the blood flow and encourage further study in more complex geometries, oscillatory flow or including the non-Newtonian behaviour of blood in order to demonstrate applications in biomechanics and biomedicine.