Study for Darcy-Brinkman model connected Oldroyd–B Constitutive Model related with Solutions of Velocity of Viscoelastic Fluid Flow in a circular Pipe filled with Porous Media

The basic purpose of this research paper is to investigate the solution of velocity of viscoelastic fluid flow with Porous media in a circular pipe to use the Lei- group technique to the system of PDE’s comprising the continuity, momentum and constitutive; equations, under appropriate initial and boundary conditions. The associated problem is organized by using the Darcy-Brinkman model connected with Oldroyd–B constitutive model. The investigation is arranged through analytical solutions of the PDE’s system connected with initial and boundary value problem. The analytical solution is established under the symmetries for the system through Lie group method.