A theoretical model for pulsatile blood flow with applications to cerebrovascular diseases

A solution for fully developed pulsatile flow of a couple stress fluid through a circular, rigid tube of infinite length has been obtained in the form of a Bessel-Fourier series. The velocity profiles and flow rates for different values of flow parameters have been shown graphically. It has been observed that velocity and flow rate are almost in phase with pressure gradient for low values of pulsatile Reynolds number alpha (alpha 2 = 0.1). For higher values of alpha(= 2) a phase difference of approximately 30 degrees between the velocity profile and pressure gradient has been observed. The obtained results are in good agreement with other theoretical and experimental results. The present analysis is valid for both values of alpha , i.e., alpha greater than or equal to 1 and alpha less than 1, whereas the existing analysis for pulsatile flow of couple stress fluid is valid for only alpha less than 1. The first, second, and third approximate solutions have been obtained and it is found that the convergence of the solutions is quite fast and the series could be terminated after the second term. This theoretical work could be useful in the measurement of blood flow rates, its apparent viscosity, and peripheral resistance of the circulatory system which, at present, are thought to be some of the main causes of many cerebrovascular diseases and stroke problems.U