This paper presents a finite element Galerkin method for simulating the flow of a viscous, incompressible fluid through a porous medium established between two coaxial cylinders. The governing equations are solved numerically, and the temperature and velocity profiles of the flow are obtained. The results show that the Galerkin finite element method improves the accuracy of the temperature and velocity profiles, compared to other numerical methods. The study has implications for the areas of fluid mechanics and applied mathematics. The results can be used to design and optimize devices that use porous media to control the flow of fluids. The study also provides insights into the applied physics of fluid flow through porous medium.