Biofluid flow in a channel under the action of a uniform localized magnetic field

Abstract

In this work the fundamental problem of the biomagnetic (blood) fluid flow in a channel under the influence of a steady localized magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and blood is considered as a homogeneous Newtonian fluid. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by the development of an efficient numerical technique based on finite differences. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the magnetic field influences considerably the flow field. It is also obtained that the electrical conductivity of blood should be taken into account at the area of the uniform magnetic field. List of symbolsH magnetic field strength (A m À1 ) B magnetic field induction ðB ¼ l o HÞ (Tesla) T temperature (K) T u temperature of upper plate T l temperature of lower plate L length of plates (m) h distance between plates (m) ðx; yÞ components of the cartesian system ðu; vÞ velocity components p pressure q fluid density (kg m À3 ) r electrical conductivity (S m À1 ) l dynamic viscosity (kg m À1 s À1 ) l o magnetic permeability of vacuum (H m À1 ) c p specific heat at constant pressure (J kg À1 K À1 ) k thermal conductivity (J m À1 s À1 K À1 )

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

“…The computational data has been compared to the numerical data taken from Tzirakis et al [1] where the fluid has been considered as Newtonian. For this simple preliminary analysis, differently from [1] where a computational mesh consists of 2000 quadrilateral elements was used, a grid of approximately 14000 elements has been found [9] to be more effective in the present study providing high-accuracy and agreement with the results of Tzirakis et al [1]. A uniform inlet velocity profile has been considered relying on [1] as well as the magnetic field strength has been taken as B 0 = 25 √ 7 T esla.…”

“…However, the two-dimensional Hartmann flow as a first preliminary case is considered for the validation of the implemented UDFs in the ANSYS-FLUENT environment, because the flow physics is relatively simple and the size of the computational domain is small. The fully developed outlet velocity profile of the Hartmann flow compared to the computational data of Tzirakis et al [1] is shown in Figure 1. It can be seen in Figure 1 that the outlet velocity profile of a fully developed Hartmann flow is different from the fully developed velocity distribution of an incompressible laminar flow without the presence of a magnetic field as it is expected.…”

“…A number of theoretical and numerical studies were carried out in the literature to investigate the blood flow behaviour under the action of a magnetic field with particular interest to flows in rectangular ducts and stenosed tubes [1,2,3]. Tzirtzilakis et al [4] proposed a numerical approach to study a blood flow in a three-dimensional rectangular duct where an 8 T esla magnetic field was generated by an electrically conducing wire on the lower wall of the duct.…”

“…Another numerical study was carried out by Tzirtzilakis and Loukopoulos [1] to investigate the behaviour of blood flows in a two-dimensional small planar channel under the action of a uniform external magnetic field of 8 T esla generated from two finite disks. The blood was considered as a Newtonian fluid with constant electrical conductivity.…”

“…For incompressible flows coupled with MHD and FHD models, the Lorentz force and a Joule heating term appear due to the MHD effects and the magnetization and magnetocaloric terms appear due to the FHD effects in the non-linear momentum and temperature equations, respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD for incompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangular channel. Their model excluded the non-linear viscous behaviour of blood flows considering blood as a Newtonian biofluid.…”