Numerical Results of Viscoelastic Fluid Flow in a Pipe filled with and without porous media via model of Darcy-Brinkman associated with Constitutive Oldroyd–B Model.

Abstract

This paper presents numerical methods to solve differential equations arising from mathematical model in viscoelastic fluid flow through a circular pipe full with porous media through by using Darcy–Brinkman model includes of the conservation of momentum and conservation of mass conveyance attached with the constitutive Oldroyd–B model. The research is communicated by means of numerical results of the problems of given differential equations associated by means of initial conditions and boundary conditions, happening in the knowledge of viscoelastic flow in pipes through porous media and without porous media. Main work of this paper is signified in three mutually partial differential equations. The results are comparison to the known finite element method. Numerical calculations of the governing differential equations are accomplished accepting solver ND–Solve purpose in Mathematica.