Examination of non-Newtonian flow through stenosed arteries using an analytical model

The steady, laminar, incompressible, axisymmetric stenotic blood flow is investigated with a non-polynomial solution assumption. The wall geometry of the stenosis is constructed as a fixed cosine curve. The rheology of blood is modeled as a generalized power-law fluid. The variations of the coefficients constructing both axial and radial velocity profiles through the stenotic tube are calculated with the examination of the analytical relations in closed form. The streamlines, separation and reattachment points, velocity profiles, and pressure variations are also obtained for the Newtonian cases in order to check the validation of the analytical approach. We observed that the results obtained are in good agreement with the ones that are widely available in the literature. Comparisons were made with non-Newtonian studies, which are rare for low Reynolds numbers in the literature, and with the numerical analyses performed in this study. As an important result of the analytical approach, it was concluded that the location of the separation and reattachment points and the existence of the separation-reattachment region are directly related to one of the coefficients in the non-polynomial solution assumption. Added to this, the ratio of the Reynolds number to the power-law exponent has a remarkable meaning in the characterization of the flow streamlines. Also, we introduce a rather simple formula of Reynolds number for blood-like power-law fluids.

Automated summary

The steady, laminar, incompressible, axisymmetric stenotic blood flow is investigated using a non-polynomial solution assumption. The wall geometry of the stenosis is modeled as a fixed cosine curve, and the blood rheology is modeled as a generalized power-law fluid. The variations of the coefficients for the velocity profiles are calculated analytically, and the obtained results are validated against Newtonian cases and previous literature. The study concludes that the separation and reattachment points and the existence of the separation-reattachment region are directly related to one of the coefficients in the non-polynomial solution assumption. The Reynolds number to power-law exponent ratio is significant in characterizing the flow streamlines, and a simplified formula for Reynolds number is introduced for blood-like power-law fluids.