Two layered poiseuille flow model for blood flow through arteries of small diameter and arterioles

Abstract

In the present paper, a two layered Poiseuille flow problem has been formulated and its analytic solution has been obtained. It is shown that the classical Poiseuille flow and Poiseuille flow with couple stress are special cases of the present problem. Velocity profiles for various values of couple stress parameters $\overline{\mathit{\alpha }}$ and $\overline{\mathit{\eta }}$ have been obtained. It is found that, for small values of $\overline{\mathit{\alpha }}$ , these velocity profiles are blunted and are qualitatively in good agreement with experimental results for blood flow. It is also observed that a decrease in tube diameter leads to an increase in the bluntness of the velocity profiles.