Numerical Investigation: Unsteady Flow of an Incompressible Elastico-Viscous Fluid in a Tube of Spherical Cross Section on a Porous Boundary

Abstract

Exact solution of an unsteady flow of elastico-viscous fluid through a porous media in a tube of spherical cross section under constant pressure gradient has been obtained in this paper. Initially, the flow is generated by a constant pressure gradient. After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in a tube of spherical cross section by taking into account of the porosity factor of the bounding surface is investigated. The problem is solved in two-stages: the first stage is a steady motion in tube under the influence of a constant pressure gradient, the second stage concern with an unsteady motion. The problem is solved employing separation of variables technique. The results are expressed in terms of a non-dimensional porosity parameter, elastico-viscosity parameter, which depends on the Non-Newtonian coefficient. The flow parameters are found to be identical with that of Newtonian case as elastic-viscosity parameter and porosity tends to infinity. Numerical results were simulated in MATLAB software to analyze the effect of Elastico-viscous parameter, porosity parameter on the velocity profile. Boundary conditions were satisfied. It is seen that the effect of elastico-viscosity parameter, porosity parameter of the bounding surface has significant effect on the velocity parameter.