Mathematical models for some realistic problems in stenosed artery analytical study

Abstract

newline The doctoral research work is devoted to develop the solution of steady axi-symmetric Navier-Stokes conservation equations incorporating Reiner Rivlin stress and strain rate relation. Semi-analytical Perturbation and exact solutions are obtained to determine flow field for axially symmetric stenosed artery. The computed resultsfrom both the methods are compared.It is observed that the mean squared difference of axial velocity obtained from both the techniques increases with the increase in cross viscosity. Thus, solutions obtained from Perturbation method is relatively close to exact solution at lower values of cross viscosity. Further, results of Reiner Rivlin are compared with the results of Newtonian, Power Law and Casson fluid. The comparison of results isutilised to establish the suitability of non-Newtonian Reiner Rivlin constitutive relation to determine the flow field of blood in stenosed artery. Further, the effect of overlapping stenosis is compared with symmetric stenosis of different shape parameters. It is observed that the flow filed in case of overlapping stenosis is significantly different from symmetric stenosis. Thus, observing the deviation of flow field it is possible to diagnose the acuteness of stenosis.