Numerical Simulation of Magnetohydrodynamic Blood Flow through Stenosed Arteries Using the R-functions Method

A novel technique based on the method of R-functions (RFM) for investigation of the influence of the magnetic field on the blood flow dynamics in stenosed arteries is developed. This approach is based on solving the MHD free convection problem in complex-shaped closed cavities. The RFM combines the means of analytical geometry and variational techniques of mathematical physics, such as the least squares method, the Galerkin method, et al. In the study, the streamfunction-vorticity formulations of the Navier-Stokes equations in rectangular and cylindrical coordinates are used. The semi-analytical expressions in the form of expansions in certain functional bases are obtained for the streamfunction. Unlike other conventional techniques, these expressions satisfy boundary conditions exactly and approximate the physical fields inside the channel with accuracy depending on the number of terms of the expansion. The effects of the Rayleigh number and the Hartmann number on the blood flow inside the axisymmetric stenosed channel are investigated. The results demonstrate good accordance with numerical simulation of the MHD arterial blood flow in constricted channels, performed with the use of the finite element method (FEM).