Pulsatile flow of a couple stress fluid through circular tubes with applications to blood flow

Abstract

A method has been developed for the study of the pulsatile flow of a couple stress fluid (blood) through circular tubes. The first, second and third approximate solution for flow velocity, wall shear, flow rate and relative viscosity have been obtained in closed form in terms of couple stress parameter $\overline{\mathit{\alpha }}$ and $\overline{\mathit{\eta }}$ , pulsatile Reynolds number α, phase ϕ and time factor nt. The velocity and flow rate variations with different parameter have been shown graphically which indicate that they are almost in phase with the pressure gradient. Further, a method has been suggested to determine experimentally the value of pulsatile Reynolds number α for blood. The effects of the parameters $\overline{\mathit{\alpha }}$ , $\overline{\mathit{\eta }}$ , α, ϕ and nt on relative viscosity have been discussed. It is found that the theoretical results, obtained by the present analysis, are in good agreement with the experimental and other theoretical results on blood flow.