A Numerical Analysis of Viscoelastic Flow Between Porous Moving Walls

Abstract

A viscoelastic fluid flow between porous moving walls is studied. This study is motivated by flow of biological fluids through veins and arteries with moving walls. Most studies in fluid flow rarely include moving walls. A special analysis of viscoelastic fluid flow between moving walls is considered, the problem was previously considered for Newtonian fluids which resulted in a simple fourth order differential equation. The present study resulted in the fifth-order modified Proudman-Johnson equation. A unique partial differential equation is developed which is then solved numerically by the Simple Iteration Method (SIM). The numerical method is newly developed based on the fixed point theorem.The method agrees with other numerical solutions in the literature. The important results reported are that the effect of varying viscoelastic and the drag-force parameters result in decreasing velocity profiles for both high and low Reynolds numbers. Wall dilation and injection/suction effects affect velocity profiles giving more understanding of the flow of biological fluids in both Newtonian and non-Newtonian fluids.