An Analysis of Stresses and Applications of Viscoelastic Fluid Flow in a circular Pipe through Porous media via with Oldroyd–B Constitutive Model

Abstract

In the field of computational fluid dynamics, finding the analytical solutions of partial differential equations governing complex problems presents a challenge to the researchers. Our basic aim is to find the symmetries of Lei- group theory of viscoelastic fluid flows to obtain the results to the PDE’s system including the continuity equation, momentum equations and constitutive equations related with viscoelastic stresses, under suitable initial and boundary conditions.This paper presents the passing hydrodynamics actions of the viscoelastic fluid flow in pipes through porous media related with Darcy-Brinkman model. The research is lectured by means of analytical results and also numerical results of the problems of given differential equations associated by means of initial and boundary conditions, happening in the knowledge of viscoelastic flow in pipes through porous media. The solutions of problem of this paper are obtained adopting the Lie group of transformation theoretic approach and analytical solution is obtained under the symmetries for the equations through Lie group technique