Of concern in this paper is an investigation of the entrance length behind singularities in cardiovascular hemodynamics under magnetic environment. In order to get better interpretation of scan MRI images, the characteristics of blood flow and electromagnetic field within the circulatory system have to be furthermore investigated. A 3D numerical model has been developed as an example of blood flowing through a straight circular tube. The governing coupled nonlinear differential equations of magnetohydrodynamic (MHD) fluid flow are reduced to a nondimensional form, which are then characterized by four dimensionless parameters. With an aim to validate our numerical approach, the computational results are compared with those of the analytical solution available in the developed region far from the singularity. The hydraulic impedance by unit length within the developed flow region increases with the magnetic field. The time average entrance length with a greater precision on the unsteady case decreases with increasing magnetic field strength. The overall voltage characteristics do not depend on the developed flow field within the entry region. 1. Introduction The steady and unsteady entrance flow region is important for biofluid dynamics, particularly the flow of blood in arteries with or without presence of magnetic field. It is important to understand and quantify the flow characteristics of blood in the entrance region such as near the origin of arterial branches, arterial constrictions, and aortic arch. It is also important for experimental models to create the appropriate inlet boundary conditions and for computational models to choose the length of the computational domain or mesh generation which requires the distance to be fully developed. Several investigators [1–4] have described the steady entrance flow and unsteady/oscillatory entrance flow [5, 6] in a circular tube. In spite of that, a huge number of studies on fully developed flow in a straight circular vessels are available in the scientific literatures. The analytical solution for steady flow first is described by Hagen-Poiseuille and unsteady flow by Womersley [7, 8]. But no attempt is available to determine both the steady and unsteady entrance length using three-dimensional modelling of computational fluid dynamics approach in the presence of magnetic environment. Although He and Ku [9] have determined the unsteady entrance flow region in a straight tube by using spectral element simulation of the fully unsteady two-dimensional Navier-Stokes equations in the absence of magnetic field.
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