Hello Pawan,

have you tried to use Poiseuille flow in a pipe with an oscillating pressure gradient? As I do not know whether you are looking to use formula for incompressible fluid or other, you might start with this reference Article The Pulsating Viscous Flow Superposed on the Steady Laminar ...

What kind of pulsatile flows you're looking for? sinusoidal?

Thank you Filip Konecny sir for your response. Sir, I have not tried using Poiseuille flow in a pipe with an oscillating pressure gradient.

I want to use it specifically for simulating blood flow in a healthy and stenosed artery, taking it as an incompressible fluid. Since the blood flow is pulsatile in nature, my intention is to find a pressure drop in an arterial segment. Initially, I want to take a straight pipe to do the analysis.

Jiarong Hong sir, I am looking for a pulsatile flow having velocity profile as a function of cosine and sine functions.

For simplicity, I can take a sinusoidal flow profile.

My intention is to find a pressure drop across a stenosis in an arterial segment.

Please give me your suggestion regarding this.

There are standard test book solution for this. for example, Gary leal, advanced transport phenomena, chp. 3.

Hello Pawan,

I have attached recent paper about using mathematical modulation using the Ostwald–de Waele power fluid.

This paper also discusses in depth the mathematical relationship and the performance of a real non-Newtonian fluid.

You can find discussions/formulae to the laminar, incompressible, two-dimensional, pulsatile flow between two parallel plates of a power-law fluid, which is governed by the continuity and momentum equations. You can also find discussion about flow enhancement, wall-shear stress distribution, dispersion coefficient, and discharge. The Ostwald–de Waele power fluid might represents good modulation medium for your research to start with, before your further engagement with more complex fluids with needs to model e.g., the minimum and a maximum effective viscosity, which depends on the physical chemistry at the molecular level.

Thank you Mr. Jiarong Hong and Mr. Filip Konecny for your wonderful answers. The literature suggested by both of you was very helpful in developing my unserstanding of the mathematics and physics of the pulsatile flow through a pipe.