Numerical solution of mass transfer to micropolar fluid flow past a stenosed artery

Abstract

A study about blood flow behaviour numerically and mathematically becomes invaluable tool in interpreting and analyzing the circulatory system. In this study, a mathematical model of fluid flow and mass transfer past through a stenoses artery is developed. The blood behaves as non-Newtonian fluid. The blood flow is considered to be unsteady, nonlinear, axisymmetric, two-dimensional and fully developed which is described by micropolar fluid. Meanwhile, the arterial wall is considered to be rigid. The geometry of stenosis is given by cosine-shaped plotted using MATLAB programme based on existing coding. The governing equations of the problem consist of continuity equation, momentum equation and convection-diffusion equation that govern mass transport to flow are formulated in cylindrical coordinate system. Then, all of the governing equations are written in dimensionless form by using dimensionless quantities in order to avoid difficulties. A radial coordinate transformation of the governing equation together with the set of initial and boundary are also needed in order to avoid interpolation error during discretization. A numerical technique has been performed in this study. Finite difference method in staggered grid known as Marker and Cell (MAC) method aid by existing MATLAB programme has been selected to solve all the governing equations involced. Successive over relaxive (SOR) method is also proposed in handling the poisson equation for pressure. Finally, two stability restriction which optimized the time step size at each calculation play an important role to limit the numerical computational. As a result, the value of wall shear stress and separation zone for micropolar fluid are lower than Newtonian fluid due to the presence of rotational viscosity. The values of wall shear stress and velocity were highest at around of critical stenotic region. While, the mass concentration were decrease and converge to zero at the arterial wall as the both wall shear stress and axial velocity decrease.