Mathematical Modelling of Pulsatile Blood Flow in Straight Rigid Artery System

The study of flow characteristics of blood in circulatory system is extremely useful in designing diagnostic tools for the treatment of cardiovascular diseases. In the study, analytical and numerical works are presented to demonstrate the behavior of the blood flow in a straight rigid artery system in creeping flow regime. Here, blood is considered as a working fluid system and it can also be treated as a viscoelastic fluid material. The rheological behavior of the blood flow is defined in terms of Casson fluid model. In the context of hydrodynamic study of pulsatile blood flow in the straight rigid artery system, analytical solutions are performed using zeroth-order Bessel function approach and validated with the obtained numerical results based on the finite difference method (FDM). In the context of FDM, FTCS scheme in terms of explicit method is used to solve the non-dimensional essential governing equations numerically. A good agreement between the analytical and numerical method based on FDM is observed as: ±\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm$$\end{document} 10% for specific value of Womersley number α=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\alpha =3\right)$$\end{document} and ±\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm$$\end{document} 7% for operating Reynolds number (Re = 5), respectively. In order to visualize the dimensional velocity and pressure distribution within the straight rigid artery system, finite element method is performed using COMSOL Multiphysics software. The obtained numerical study shows that the pressure distribution decreases as a function of axial position of straight rigid artery system and radial velocity significantly changes as a function of transverse position and gradually reaches fully developed flow.