A Study on the Effect of Various Fluid, Flow and Mechanical Parameters on the Flow of Newtonian Fluid in an Expanding and Contracting Pipe

Abstract

In this paper, a study has been carried out to understand the effect of the fluid, flow and the mechanical parameters on a pulsatile flow of a Newtonian fluid in an expanding and contracting pipe. The fluid parameters considered are the viscosity and the density, flow parameters are the amplitude of the pressure gradient and the frequency of oscillations, and the mechanical parameter considered is the radius of the pipe. A mathematical model is constructed in the cylindrical polar coordinate system with the fluid flow assumed to be axisymmetric. Further, the fluid is taken to be incompressible, and the radius of the pipe to vary with time. Navier–Stokes equations are used to describe this fluid flow problem. The resulting nonlinear coupled system of equations together with an appropriate boundary and initial conditions is solved using the homotopy perturbation method. The model is then applied to the human circulatory system, and the effect of the three sets of parameters on wall shear stress and volumetric flux is studied. Data for the model parameters are taken from literature on human blood, and human circulatory system and graphs have been plotted to understand their effect on the flow.