Analytical and numerical solutions of fluid flow filled with and without porous media in circular pipes

This paper is connected with obtaining solutions of partial differential equations related with the Newtonian and non-Newtonian fluids flow through pipes filled with porous media by means of one-parameter transformation groups which leave the equation invariant.Solutions of a boundary-value problem for a partial differential equation occurring in the research of the flow of Newtonian and non-Newtonian fluids through a porous medium have been confidential. The solution of this problem is found by means of the Lie-group analysis approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduces to an ordinary differential equation with the appropriate boundary conditions. Two families of invariant results are acquired. Also to verify the method and compare the results obtained in the present work against other analytical and numerical solutions available in open literature.