A critical study of Poiseuille flow of couple stress fluid with applications to blood flow

Abstract

In this paper, the Poiseuille flow of couple stress fluid has been critically examined. It is shown that the method used for comparing the theoretical and experimental results is erroneous and the values of the couple stress parameters obtained for blood flow are incorrect. The existing method for determining the couple stress parameters has been improved. The computational work in the improved method is considerably less. It is observed that both the couple stress parameters are functions of concentration c and an empirical relation between concentration, $\overline{\mathit{\alpha }}$ and $\overline{\mathit{\eta }}$ has been obtained. It is of interest to note that the shear viscosity μ and non-dimensional axial velocity are functions of concentration. This is in contrast with the existing result, i.e., μ is independent of c and non-dimensional axial velocity is insensitive of c( $\overline{\mathit{\alpha }}$ ). Finally, some uses of determining the values of $\overline{\mathit{\alpha }}$ and $\overline{\mathit{\eta }}$ have been suggested.